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Journal articles on the topic 'Compressible and incompressible fluids'

Author: Grafiati

Published: 5 June 2025

Last updated: 8 July 2025

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1

Godin, Oleg A. "Finite-amplitude acoustic-gravity waves: exact solutions." Journal of Fluid Mechanics 767 (February 12, 2015): 52–64. http://dx.doi.org/10.1017/jfm.2015.40.

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AbstractWe consider strongly nonlinear waves in fluids in a uniform gravity field, and demonstrate that an incompressible wave motion, in which pressure remains constant in each fluid parcel, is supported by compressible fluids with free and rigid boundaries. We present exact analytic solutions of nonlinear hydrodynamics equations which describe the incompressible wave motion. The solutions provide an extension of the Gerstner wave in an incompressible fluid with a free boundary to waves in compressible three-dimensionally inhomogeneous moving fluids such as oceans and planetary atmospheres.

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2

BENDAHMANE, MOSTAFA, ZIAD KHALIL, and MAZEN SAAD. "CONVERGENCE OF A FINITE VOLUME SCHEME FOR GAS–WATER FLOW IN A MULTI-DIMENSIONAL POROUS MEDIUM." Mathematical Models and Methods in Applied Sciences 24, no. 01 (2013): 145–85. http://dx.doi.org/10.1142/s0218202513500498.

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This paper deals with construction and convergence analysis of a finite volume scheme for compressible/incompressible (gas–water) flows in porous media. The convergence properties of finite volume schemes or finite element scheme are only known for incompressible fluids. We present a new result of convergence in a two or three dimensional porous medium and under the only consideration that the density of gas depends on global pressure. In comparison with incompressible fluid, compressible fluids requires more powerful techniques; especially the discrete energy estimates are not standard.

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3

Zhu, Zeqi, Hongxia Li, Jianjun Fu, and Qian Sheng. "Approximation of a Class of Incompressible Third Grade Fluids Equations." Discrete Dynamics in Nature and Society 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/627584.

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This paper discusses the approximation of weak solutions for a class of incompressible third grade fluids equations. We first introduce a family of perturbed slightly compressible third grade fluids equations (depending on a positive parameterϵ) which approximate the incompressible equations asϵ→0+. Then we prove the existence and uniqueness of weak solutions for the slightly compressible equations and establish that the solutions of the slightly compressible equations converge to the solutions of the incompressible equations.

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4

Shen, Jie, Xiaofeng Yang, and Qi Wang. "Mass and Volume Conservation in Phase Field Models for Binary Fluids." Communications in Computational Physics 13, no. 4 (2013): 1045–65. http://dx.doi.org/10.4208/cicp.300711.160212a.

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AbstractThe commonly used incompressible phase field models for non-reactive, binary fluids, in which the Cahn-Hilliard equation is used for the transport of phase variables (volume fractions), conserve the total volume of each phase as well as the material volume, but do not conserve the mass of the fluid mixture when densities of two components are different. In this paper, we formulate the phase field theory for mixtures of two incompressible fluids, consistent with the quasi-compressible theory [28], to ensure conservation of mass and momentum for the fluid mixture in addition to conservation of volume for each fluid phase. In this formulation, the mass-average velocity is no longer divergence-free (solenoidal) when densities of two components in the mixture are not equal, making it a compressible model subject to an internal con-straint. In one formulation of the compressible models with internal constraints (model 2), energy dissipation can be clearly established. An efficient numerical method is then devised to enforce this compressible internal constraint. Numerical simulations in confined geometries for both compressible and the incompressible models are carried out using spatially high order spectral methods to contrast the model predictions. Numerical comparisons show that (a) predictions by the two models agree qualitatively in the situation where the interfacial mixing layer is thin; and (b) predictions differ significantly in binary fluid mixtures undergoing mixing with a large mixing zone. The numerical study delineates the limitation of the commonly used incompressible phase field model using volume fractions and thereby cautions its predictive value in simulating well-mixed binary fluids.

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5

Nasu, Shoichi, and Mutsuto Kawahara. "An Analysis of Compressible Viscous Flows Around a Body Using Finite Element Method." Advanced Materials Research 403-408 (November 2011): 461–65. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.461.

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The objective of this paper is an analysis of a body in a compressible viscous flow using the finite element method. Generally, when the fluid flow is analyzed, an incompressible viscous flow is often applied. However fluids have compressibility in actual phenomena. Therefore, the compressibility should be concerned in Computational Fluid Dynamics [CFD]. In this study, two kind of equation is applied to basic equations. One is compressible Navier-stokes equation, the other is incompressible Navier-stokes equation considering density variation. These analysis results of both equations are compared.

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6

Colombo, Rinaldo M., and Graziano Guerra. "BV Solutions to 1D isentropic Euler equations in the zero mach number limit." Journal of Hyperbolic Differential Equations 13, no. 04 (2016): 685–718. http://dx.doi.org/10.1142/s0219891616500181.

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Two compressible immiscible fluids in 1D and in the isentropic approximation are considered. The first fluid is surrounded and in contact with the second one. As the Mach number of the first fluid vanishes, we prove the rigorous convergence for the fully nonlinear compressible to incompressible limit of the coupled dynamics of the two fluids. A key role is played by a suitably refined wave front tracking algorithm, which yields precise [Formula: see text], [Formula: see text] and weak* convergence estimates, either uniform or explicitly dependent on the Mach number.

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7

PRUŠA, VÍT, and K. R. RAJAGOPAL. "ON MODELS FOR VISCOELASTIC MATERIALS THAT ARE MECHANICALLY INCOMPRESSIBLE AND THERMALLY COMPRESSIBLE OR EXPANSIBLE AND THEIR OBERBECK–BOUSSINESQ TYPE APPROXIMATIONS." Mathematical Models and Methods in Applied Sciences 23, no. 10 (2013): 1761–94. http://dx.doi.org/10.1142/s0218202513500516.

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Viscoelastic fluid like materials that are mechanically incompressible but are compressible or expansible with respect to thermal stimuli are of interest in various applications ranging from geophysics and polymer processing to glass manufacturing. Here we develop a thermodynamical framework for the modeling of such materials. First we illustrate the basic ideas in the simpler case of a viscous fluid, and after that we use the notion of natural configuration and the concept of the maximization of the entropy production, and we develop a model for a Maxwell type viscoelastic fluid that is mechanically incompressible and thermally expansible or compressible. An important approximation in fluid mechanics that is frequently used in modeling buoyancy driven flows is the Oberbeck–Boussinesq approximation. Originally, the approximation was used for studying the flows of viscous fluids in thin layers subject to a small temperature gradient. However, the approximation has been used almost without any justification even for flows of non-Newtonian fluids induced by strong temperature gradients in thick layers. Having a full system of the governing equations for a Maxwell type viscoelastic mechanically incompressible and thermally expansible or compressible fluid, we investigate the validity of the Oberbeck–Boussinesq type approximation for flows of this type of fluids. It turns out that the Oberbeck–Boussinesq type approximation is in general not a good approximation, in particular if one considers "high Rayleigh number" flows. This indicates that the Oberbeck–Boussinesq type approximation should not be used routinely for all buoyancy driven flows, and its validity should be thoroughly examined before it is used as a mathematical model.

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8

Caggio, Matteo. "Inviscid incompressible limit for compressible micro-polar fluids." Nonlinear Analysis 216 (March 2022): 112695. http://dx.doi.org/10.1016/j.na.2021.112695.

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9

Secchi, Paolo. "On the incompressible limit of inviscid compressible fluids." ANNALI DELL UNIVERSITA DI FERRARA 46, no. 1 (2000): 21–33. http://dx.doi.org/10.1007/bf02837288.

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10

Breit, Dominic, Eduard Feireisl, and Martina Hofmanová. "Incompressible Limit for Compressible Fluids with Stochastic Forcing." Archive for Rational Mechanics and Analysis 222, no. 2 (2016): 895–926. http://dx.doi.org/10.1007/s00205-016-1014-y.

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11

Pérez-Ràfols, F., P. Wall, and A. Almqvist. "On compressible and piezo-viscous flow in thin porous media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2209 (2018): 20170601. http://dx.doi.org/10.1098/rspa.2017.0601.

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In this paper, we study flow through thin porous media as in, e.g. seals or fractures. It is often useful to know the permeability of such systems. In the context of incompressible and iso-viscous fluids, the permeability is the constant of proportionality relating the total flow through the media to the pressure drop. In this work, we show that it is also relevant to define a constant permeability when compressible and/or piezo-viscous fluids are considered. More precisely, we show that the corresponding nonlinear equation describing the flow of any compressible and piezo-viscous fluid can be transformed into a single linear equation. Indeed, this linear equation is the same as the one describing the flow of an incompressible and iso-viscous fluid. By this transformation, the total flow can be expressed as the product of the permeability and a nonlinear function of pressure, which represents a generalized pressure drop.

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12

Panda, Santosh Kumar. "An Orifice Flow Analysis on the Basis of Density and Viscosity Effects of Fluids." WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER 18 (December 31, 2023): 140–46. http://dx.doi.org/10.37394/232012.2023.18.12.

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The orifice flow measurement produces errors due to highly turbulent and backflow in downstream which have to be overcome. Determine the Δp, and coefficient of discharge (Cd) for flow through the orifice CFD analysis. The input parameters vary with the variance of Reynolds number (Re), fluids with the deviation of density and viscosity, area ratio (σ). The range of Re (20000- 100000), σ (0.2- 0.6), density (ρr), and viscosity (µr) ratio vary as per the fluids considered. The various incompressible and compressible fluids are considered for the study of flow through the orifice based on the difference in density and viscosity properties. The fluids considered for studies are Air, Ammonia (NH3), Carbon dioxide (CO2), Hydrogen (H2), and Sulphur dioxide (SO2) as compressible fluid category, and water (H2O), liquid ammonia (LNH3), liquid hydrogen (LH2), liquid oxygen (LO2), liquid R12 (Dichlorodifluoromethane) as incompressible fluid category. Correlations are also proposed from the above numerical database to determine Cd as a function of Re, σ, ρr, and µr for the orifice. The correlation provides a significant contribution to the viscous fluid flow measurement with the flow through the orifice.

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13

Satiawati, Listiana, Harin Widiyatni, and Yusraida Khairani Dalimunthe. "PERHITUNGAN TEKANAN DARI ALIRAN RADIAL FLUIDA INKOMPRESSIBLE PADA RESERVOIR." PETRO: Jurnal Ilmiah Teknik Perminyakan 12, no. 4 (2023): 221–32. http://dx.doi.org/10.25105/petro.v12i4.17949.

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This research is a continuation of several previous studies that have been published, in general studying fluid flow in reservoirs. There are 2 fluid flows in reservoirs, namely linear and radial, while there are 3 types of fluids, namely incompressible, slightly compressible and compressible. In this study, the pressure and pressure drop of incompressible fluids at a certain distance from the well to the reservoir are calculated. The equation used to calculate fluid pressure is derived from the Darcy Equation. To obtain accurate data, the calculations are carried out repeatedly with 1 ft intervals, namely to get an overview of changes in pressure. The initial calculations were done manually but because the calculations were quite difficult and repetitive, the Fortran software was used to calculate them. Numerical calculations were carried out with some rock permeability data. The calculated results obtained pressure characteristics from a certain radius to the well with several values of rock permeability and these results are expressed by a graph between pressure and radius.

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14

Disconzi, Marcelo M., and David G. Ebin. "Motion of slightly compressible fluids in a bounded domain, II." Communications in Contemporary Mathematics 19, no. 04 (2016): 1650054. http://dx.doi.org/10.1142/s0219199716500541.

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We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is near the analogous solution for an incompressible fluid provided the initial conditions for the two problems are close. In particular, the divergence of the initial velocity of the compressible flow at time zero is assumed to be small. Furthermore, we find that solutions to the compressible motion problem in Lagrangian coordinates depend differentiably on their initial data, an unexpected result for this type of nonlinear equations.

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15

Tailleux, Rémi. "Thermodynamics/Dynamics Coupling in Weakly Compressible Turbulent Stratified Fluids." ISRN Thermodynamics 2012 (March 8, 2012): 1–15. http://dx.doi.org/10.5402/2012/609701.

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In traditional and geophysical fluid dynamics, it is common to describe stratified turbulent fluid flows with low Mach number and small relative density variations by means of the incompressible Boussinesq approximation. Although such an approximation is often interpreted as decoupling the thermodynamics from the dynamics, this paper reviews recent results and derive new ones that show that the reality is actually more subtle and complex when diabatic effects and a nonlinear equation of state are retained. Such an analysis reveals indeed: (1) that the compressible work of expansion/contraction remains of comparable importance as the mechanical energy conversions in contrast to what is usually assumed; (2) in a Boussinesq fluid, compressible effects occur in the guise of changes in gravitational potential energy due to density changes. This makes it possible to construct a fully consistent description of the thermodynamics of incompressible fluids for an arbitrary nonlinear equation of state; (3) rigorous methods based on using the available potential energy and potential enthalpy budgets can be used to quantify the work of expansion/contraction in steady and transient flows, which reveals that is predominantly controlled by molecular diffusive effects, and act as a significant sink of kinetic energy.

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Zhang, Chao, and Igor Menshov. "Eulerian modelling of compressible three-fluid flows with surface tension." Russian Journal of Numerical Analysis and Mathematical Modelling 34, no. 4 (2019): 225–40. http://dx.doi.org/10.1515/rnam-2019-0019.

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Abstract The paper addresses a numerical approach for calculating three-fluid hydrodynamics on Eulerian grids with taking into account surface tension and viscous effects. The medium considered consists of three different compressible fluids separated with interfaces. The fluids are assumed to be immiscible. The three-fluid flow is described by the reduced equilibrium model derived from the non-equilibrium three-phase model by performing an asymptotic analysis in the limit of zero relaxation time. To simulate surface tension effects, we extend the continuum surface force (CSF) model of two-fluid incompressible flow to the case of compressible three-fluid flow. A thermodynamically consistent surface energy of the compressible three-fluid flow is obtained by means of splitting the surface tension between distinct fluids into pairs of specific phase related surface tensions. Some aspects of the numerical method for solving the system of governing equations of the considered three-fluid model are discussed. Numerical results presented demonstrate the accuracy and robustness of the proposed model in simulating dynamics of interfaces and surface tension effects.

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17

Secchi, P. "On the Singular Incompressible Limit of Inviscid Compressible Fluids." Journal of Mathematical Fluid Mechanics 2, no. 2 (2000): 107–25. http://dx.doi.org/10.1007/pl00000948.

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18

Bianchini, Roberta, and Roberto Natalini. "Well-posedness of a model of nonhomogeneous compressible–incompressible fluids." Journal of Hyperbolic Differential Equations 14, no. 03 (2017): 487–516. http://dx.doi.org/10.1142/s0219891617500163.

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We propose a model of a density-dependent compressible–incompressible fluid, which is intended as a simplified version of models based on mixture theory as, for instance, those arising in the study of biofilms, tumor growth and vasculogenesis. Though our model is, in some sense, close to the density-dependent incompressible Euler equations, it presents some differences that require a different approach from an analytical point of view. In this paper, we establish a result of local existence and uniqueness of solutions in Sobolev spaces to our model, using the Leray projector. Besides, we show the convergence of both a continuous version of the Chorin–Temam projection method, viewed as a singular perturbation approximation, and the artificial compressibility method.

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19

Guillopé, Colette, Ali Mneimné, and Raafat Talhouk. "Asymptotic behaviour, with respect to the isothermal compressibility coefficient, for steady flows of weakly compressible viscoelastic fluids." Asymptotic Analysis 35, no. 2 (2003): 127–50. https://doi.org/10.3233/asy-2003-571.

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In this paper, we study the behaviour, in terms of compressibility, of steady flows of weakly compressible viscoelastic fluids having a differential constitutive law. The models considered here are Jeffreys' and Maxwell's. In both cases, we establish the existence of an asymptotic expansion in the neighbourhood of the steady incompressible fluid flow, with respect to the vanishing isothermal compressibility coefficient.

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Vidal, Jérémie, and David Cébron. "Acoustic and inertial modes in planetary-like rotating ellipsoids." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2239 (2020): 20200131. http://dx.doi.org/10.1098/rspa.2020.0131.

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The bounded oscillations of rotating fluid-filled ellipsoids can provide physical insight into the flow dynamics of deformed planetary interiors. The inertial modes, sustained by the Coriolis force, are ubiquitous in rapidly rotating fluids and Vantieghem (2014, Proc. R. Soc. A , 470 , 20140093. doi:10.1098/rspa.2014.0093 ) pioneered a method to compute them in incompressible fluid ellipsoids. Yet, taking density (and pressure) variations into account is required for accurate planetary applications, which has hitherto been largely overlooked in ellipsoidal models. To go beyond the incompressible theory, we present a Galerkin method in rigid coreless ellipsoids, based on a global polynomial description. We apply the method to investigate the normal modes of fully compressible, rotating and diffusionless fluids. We consider an idealized model, which fairly reproduces the density variations in the Earth’s liquid core and Jupiter-like gaseous planets. We successfully benchmark the results against standard finite-element computations. Notably, we find that the quasi-geostrophic inertial modes can be significantly modified by compressibility, even in moderately compressible interiors. Finally, we discuss the use of the normal modes to build reduced dynamical models of planetary flows.

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Zhang, Zhong Xing, Peng Zhe Qiao, Tao Li, and Tao Xiang. "An Efficient SPH Approach for Nearly Incompressible Fluid Simulation." Applied Mechanics and Materials 543-547 (March 2014): 1667–70. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1667.

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In this paper, we present an efficient approach based on Smoothed Particle Hydrodynamics (SPH) to simulate nearly incompressible fluids. The proposed method is an extension of the traditional SPH method designed for compressible fluids. We first introduce a new scheme for pressure evaluation to satisfy the incompressibility constraints. Then novel calculation methods for pressure force and viscosity force are discussed. Finally, the results demonstrate that our method is more capable of realistically simulating fluids with near-incompressibility than previous method.

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22

Araque-Martinez, Aura N., and Larry W. Lake. "The Effect of Compressibility and Outer Boundaries on Incipient Viscous Fingering." SPE Reservoir Evaluation & Engineering 24, no. 03 (2021): 619–38. http://dx.doi.org/10.2118/201310-pa.

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Summary The knowledge of the effects of instability and heterogeneity on displacements, primarily enhanced oil recovery, and carbon dioxide storage are well known, although they remain difficult to predict. The usual recourse to modeling these effects is through numerical simulation. Simulation remains the gold standard for prediction; however, its results lack generality, being case-specific. There are also several analytic models for displacements that are usually more informative than simulation results. However, these methods apply to steady-state, incompressible flow. Carbon dioxide injection for storage uses compressible fluids and, in the absence of producers, will not approach steady-state flow (Wu et al. 2017). Consequently, it is unlikely that storage will be in reservoirs of open boundaries (steady-state flow). Flow of compressible fluid necessitates the use of closed or partially sealed boundaries, a factor that is consistent with compressible flow. This work deals with the conditions that cause the onset of incipient viscous fingering or Saffman-Taylor (ST) instability. The actual growth and propagation of fingers, a subject of much recent literature, is not discussed here. The original ST formalism of M &gt; 1 for gravity-free flow is highly restrictive: it is for linear flow of nonmixing incompressible fluids in steady-state flow. In this work, we relax the incompressible flow restriction and thereby broaden the ST criterion to media that have sealing and/or partially sealing outer boundaries. We use the nonlinear partial differential equation for linear flow and developed analytic solutions for a tracer flow analog and also for a two-fluid compressible flow. The analysis is restricted to stabilized flow and to constant compressibility fluids, but we are not restricted to small compressibility fluids. There is no transition (mixing) zone between displacing and displaced fluids; the displacement is piston-like. The absence of a transition zone means that the results apply to both miscible and immiscible displacements, absent dispersion, or local capillary pressure. The assumption of a sharp interface is to focus on the combined effect of mobility ratio and compressibility. We use the product of the fluid compressibility and pressure drop (cfΔP) to differentiate the compressibility groups (Dake 1978; Dranchuk and Quon 1967), where ΔP is defined as the pressure drop within the specific fluid region. The results will be based on proposed analytical solutions compared to numerical simulation. The proposed formulation is less restrictive than the original ST formalism of M &gt; 1 and allows evaluation of viscous fingering initiation or ST stability criterion in the presence of different boundary conditions (open vs. closed boundaries) with compressible fluids under the stated assumptions, which is the scope of this work. The key contribution here is the effect of external boundaries, which consequently makes necessary the use of compressible fluids. Absent compressibility, the necessary condition for the growth of a viscous finger is simply the mobility ratio, M &gt; 1. It is the objective of this work to study how the ST criterion is affected by the presence of sealing and partially sealing outer boundaries with the consequent inclusion of compressible flows as in carbon dioxide storage and enhanced oil recovery by gas injection. The results show that adding compressibility always makes displacements more unstable for stabilized background flow, even for a favorable mobility ratio (M &lt; 1) at extremely large compressibility (e.g., cf &gt; 5×10−3 1/psi). For a sealed external boundary (no production or leakage), displacements will become more stable as a front approaches an external boundary for all mobility ratios (M) investigated.

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Yabe, T. "A universal cubic interpolation solver for compressible and incompressible fluids." Shock Waves 1, no. 3 (1991): 187–95. http://dx.doi.org/10.1007/bf01413793.

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Liu, Ping, Sakdirat Kaewunruen, and Bai-jian Tang. "Dynamic Pressure Analysis of Hemispherical Shell Vibrating in Unbounded Compressible Fluid." Applied Sciences 8, no. 10 (2018): 1938. http://dx.doi.org/10.3390/app8101938.

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This paper is the first to highlight the vibrations of a hemispherical shell structure interacting with both compressible and incompressible fluids. To precisely calculate the pressure of the shell vibrating in the air, a novel analytical approach has been established that has existed in very few publications to date. An analytical formulation that calculates pressure was developed by integrating both the ‘small-density method’ and the ‘Bessel function method’. It was considered that the hemispherical shell vibrates as a simple harmonic function, and the fluid is non-viscous. For comparison, the incompressible fluid model has been analyzed. Surprisingly, it is the first to report that the pressure of the shell surface is proportional to the vibration acceleration, and the velocity amplitude decreased at the rate of 1 r 2 when the fluid was incompressible. Otherwise, the surface pressure of the hemispherical shell was proportional to the vibration velocity, and the velocity amplitude decreased with the rate of 1 r when the fluid was compressible. The compressibility of fluid played an important role in the dynamic pressure of the shell structure. Furthermore, the scale factor derived by the theoretical approach was the product of the density and the sound velocity of the fluid ( ρ o c ) exactly. In this study, the analytical solutions were verified by the calibrated numerical simulations, and the analytical formulation were rigorously tested by extensive parametric studies. These new findings can be used to guide the optimal design of the spherical shell structure subjected to wind load, seismic load, etc.

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Oggian, T., D. Drikakis, D. L. Youngs, and R. J. R. Williams. "Computing multi-mode shock-induced compressible turbulent mixing at late times." Journal of Fluid Mechanics 779 (August 19, 2015): 411–31. http://dx.doi.org/10.1017/jfm.2015.392.

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Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late-time behaviour of a single-shocked Richtmyer–Meshkov instability (RMI) and the associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that the RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field, the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible–incompressible solver that removes the low-Mach-number limitations of the compressible solvers, thus allowing numerical simulations of late-time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

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Dastgeer, S., and G. P. Zank. "Turbulence in nearly incompressible fluids: density spectrum, flows, correlations and implication to the interstellar medium." Nonlinear Processes in Geophysics 12, no. 1 (2005): 139–48. http://dx.doi.org/10.5194/npg-12-139-2005.

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Abstract. Interstellar scintillation and angular radio wave broadening measurements show that interstellar and solar wind (electron) density fluctuations exhibit a Kolmogorov-like k-5/3 power spectrum extending over many decades in wavenumber space. The ubiquity of the Kolmogorov-like interstellar medium (ISM) density spectrum led to an explanation based on coupling incompressible magnetohydrodynamic (MHD) fluctuations to density fluctuations through a "pseudosound" relation within the context of "nearly incompressible" (NI) hydrodynamics (HD) and MHD models. The NI theory provides a fundamentally different explanation for the observed ISM density spectrum in that the density fluctuations can be a consequence of passive scalar convection due to background incompressible fluctuations. The theory further predicts generation of long-scale structures and various correlations between the density, temperature and the (magneto) acoustic as well as convective pressure fluctuations in the compressible ISM fluids in different thermal regimes that are determined purely by the thermal fluctuation level. In this paper, we present the results of our two dimensional nonlinear fluid simulations, exploring various nonlinear aspects that lead to inertial range ISM turbulence within the context of a NI hydrodymanics model. In qualitative agreement with the NI predictions and the in-situ observations, we find that i) the density fluctuations exhibit a Kolmogorov-like spectrum via a passive convection in the field of the background incompressible fluctuations, ii) the compressible ISM fluctuations form long scale flows and structures, and iii) the density and the temperature fluctuations are anti-correlated.

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27

Tenenev, V. A., T. Raeder, and A. A. Chernova. "Incorporation of Fluid Compressibility into the Calculation of the Stationary Mode of Operation of a Hydraulic Device at High Fluid Pressures." Nelineinaya Dinamika 17, no. 2 (2021): 195–209. http://dx.doi.org/10.20537/nd210205.

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This paper is concerned with assessing the correctness of applying various mathematical models for the calculation of the hydroshock phenomena in technical devices for modes close to critical parameters of the fluid. We study the applicability limits of the equation of state for an incompressible fluid (the assumption of constancy of the medium density) to the simulation of processes of the safety valve operation for high values of pressures in the valve. We present a scheme for adapting the numerical method of S. K. Godunov for calculation of flows of incompressible fluids. A generalization of the method for the Mie – Grüneisen equation of state is made using an algorithm of local approximation. A detailed validation and verification of the developed numerical method is provided, and relevant schemes and algorithms are given. Modeling of the hydroshock phenomenon under the valve actuation within the incompressible fluid model is carried out by the openFoam software. The comparison of the results for the weakly compressible

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Guillopé, Colette, Zaynab Salloum, and Raafat Talhouk. "Regular flows of weakly compressible viscoelastic fluids and the incompressible limit." Discrete & Continuous Dynamical Systems - B 14, no. 3 (2010): 1001–28. http://dx.doi.org/10.3934/dcdsb.2010.14.1001.

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29

Bowman, S. "A note on Hamiltonian structures for compressible, stratified and incompressible fluids." Letters in Mathematical Physics 13, no. 2 (1987): 147–51. http://dx.doi.org/10.1007/bf00955204.

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Mohammed, Fatima A. "Development of algorithm for Newtonian compressible fluid flow based on finite element method." BASRA JOURNAL OF SCIENCE 39, no. 3 (2021): 339–54. http://dx.doi.org/10.29072/basjs.2021302.

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In this article, we present the numerical investigation for compressible Newtonian flow in two dimensional axisymmetric channel. Galerkin finite element method is applied to accommodate compressible and incompressible flows. A continuity equation and time-dependent conservation of momentum equations are used to describe the motion of the fluid, which are maintained in the cylindrical coordinate system (axisymmetric). To meet the method analysis, Poiseuille flow along a circular channel under an isothermal state is used as a simple test problem. This test is conducted by taking a circular section of the pipe. Comparision between compressible and incompressible results in terms of convergence has been conducted for axial velocity and pressure. Findings reveal that, convergence-rates of velocity and pressure is faster an incompressible case compared to compressible. In addition, the level of velocity convergence is higher than pressure for both compressible and incompressible. Moreover, the low level of Mach number demonstrates that piecewise-constant density interpolation is equitable to linear density interpolation

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Kubo, Takayuki, and Yoshihiro Shibata. "On the Evolution of Compressible and Incompressible Viscous Fluids with a Sharp Interface." Mathematics 9, no. 6 (2021): 621. http://dx.doi.org/10.3390/math9060621.

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In this paper, we consider some two phase problems of compressible and incompressible viscous fluids’ flow without surface tension under the assumption that the initial domain is a uniform Wq2−1/q domain in RN (N≥2). We prove the local in the time unique existence theorem for our problem in the Lp in time and Lq in space framework with 2<p<∞ and N<q<∞ under our assumption. In our proof, we first transform an unknown time-dependent domain into the initial domain by using the Lagrangian transformation. Secondly, we solve the problem by the contraction mapping theorem with the maximal Lp-Lq regularity of the generalized Stokes operator for the compressible and incompressible viscous fluids’ flow with the free boundary condition. The key step of our proof is to prove the existence of an R-bounded solution operator to resolve the corresponding linearized problem. The Weis operator-valued Fourier multiplier theorem with R-boundedness implies the generation of a continuous analytic semigroup and the maximal Lp-Lq regularity theorem.

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Li, Weipeng, Yitong Fan, Davide Modesti, and Cheng Cheng. "Decomposition of the mean skin-friction drag in compressible turbulent channel flows." Journal of Fluid Mechanics 875 (July 18, 2019): 101–23. http://dx.doi.org/10.1017/jfm.2019.499.

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The mean skin-friction drag in a wall-bounded turbulent flow can be decomposed into different physics-informed contributions based on the mean and statistical turbulence quantities across the wall layer. Following Renard & Deck’s study (J. Fluid Mech., vol. 790, 2016, pp. 339–367) on the skin-friction drag decomposition of incompressible wall-bounded turbulence, we extend their method to a compressible form and use it to investigate the effect of density and viscosity variations on skin-friction drag generation, using direct numerical simulation data of compressible turbulent channel flows. We use this novel decomposition to study the skin-friction contributions associated with the molecular viscous dissipation and the turbulent kinetic energy production and we investigate their dependence on Reynolds and Mach number. We show that, upon application of the compressibility transformation of Trettel & Larsson (Phys. Fluids, vol. 28, 2016, 026102), the skin-friction drag contributions can be only partially transformed into the equivalent incompressible ones, as additional terms appear representing deviations from the incompressible counterpart. Nevertheless, these additional contributions are found to be negligible at sufficiently large equivalent Reynolds number and low Mach number. Moreover, we derive an exact relationship between the wall heat flux coefficient and the skin-friction drag coefficient, which allows us to relate the wall heat flux to the skin-friction generation process.

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PANTUSO, DANIEL, and KLAUS-JÜRGEN BATHE. "A FOUR-NODE QUADRILATERAL MIXED-INTERPOLATED ELEMENT FOR SOLIDS AND FLUIDS." Mathematical Models and Methods in Applied Sciences 05, no. 08 (1995): 1113–28. http://dx.doi.org/10.1142/s0218202595000589.

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A four-node quadrilateral element is presented which shows promise for general compressible and incompressible two-dimensional analysis of solids and fluids. The element is based on a mixed interpolation of displacements (velocities), pressure and strains (velocity strains). We show that the element satisfies a numerical inf-sup test, and give results of some analysis problems that demonstrate the capabilities of the element.

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34

Khesin, Boris, Gerard Misiołek, and Klas Modin. "Geometric hydrodynamics and infinite-dimensional Newton’s equations." Bulletin of the American Mathematical Society 58, no. 3 (2021): 377–442. http://dx.doi.org/10.1090/bull/1728.

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We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton’s equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include equations of compressible and incompressible fluid dynamics, magnetohydrodynamics, shallow water systems and equations of relativistic fluids. We illustrate this with a survey of selected examples, as well as with new results, using the tools of infinite-dimensional information geometry, optimal transport, the Madelung transform, and the formalism of symplectic and Poisson reduction.

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35

Huang, Jiaxi, Ning Jiang, Yi-Long Luo, and Lifeng Zhao. "Small data global regularity and scattering for 3D Ericksen–Leslie compressible hyperbolic liquid crystal model." Journal of Hyperbolic Differential Equations 19, no. 04 (2022): 717–73. http://dx.doi.org/10.1142/s0219891622500199.

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We study the Ericksen–Leslie hyperbolic system for compressible liquid crystal model in three spatial dimensions. Global regularity and scattering for small and smooth initial data near equilibrium are proved for the case that the system is a nonlinear coupling of compressible Navier–Stokes equations with wave map to [Formula: see text]. The main strategy relies on an interplay between the control of high order energies and decay estimates, which is based on the idea inspired by the method of space-time resonances. Unlike the incompressible model, the different behaviors of the decay properties of the density and velocity field for compressible fluids at different frequencies play a key role, which is a particular feature of compressible model.

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36

Formentin, Sara Mizar, Juan Carlos Alcérreca Huerta, and Barbara Zanuttigh. "MODELLING WAVE-STRUCTURE INTERACTION WITH A NEW COMPRESSIBLE TWO-PHASE FLOW SOLVER." Coastal Engineering Proceedings, no. 37 (September 1, 2023): 29. http://dx.doi.org/10.9753/icce.v37.papers.29.

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This contribution presents and investigates the effects of the air entrainment and air compressibility on the shape and magnitude of the wave impacts occurring at crown walls on top of sea defenses. To this purpose, a new solver, developed in the OpenFoam environment to represent the wave interactions with impermeable and porous coastal structures, accounting for the fluid compressibility, is checked against recent laboratory tests of wave overtopping and wave impacts. By comparing the first results of this new code to the ones obtained with the native solver dealing with incompressible fluids exclusively, significant advances in the representation of the pressure signals and peaks at the walls seem to be achieved.

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Barna, Imre Ferenc, Gabriella Bognar, and Krisztian Hriczo. "SELF-SIMILAR ANALYTIC SOLUTION OF THE TWO-DIMENSIONAL NAVIER-STOKES EQUATION WITH A NON-NEWTONIAN TYPE OF VISCOSITY." Mathematical Modelling and Analysis 21, no. 1 (2016): 83–94. http://dx.doi.org/10.3846/13926292.2016.1136901.

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We investigate Navier-Stokes (NS) and the continuity equations in Cartesian coordinates and Eulerian description for the two dimensional incompressible nonNewtonian fluids. Due to the non-Newtonian viscosity we consider the Ladyzenskaya model with a non-linear velocity dependent stress tensor. The key idea is the multidimensional generalization of the well-known self-similar Ansatz, which has already been used for non-compressible and compressible viscous flow studies. Geometrical interpretations of the trial function are also discussed. Our recent results are compared to the former Newtonian ones.

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A., Saba, I. Yusuf S., O. Olaoye D., and O. Jatto A. "Application of Diffusion Magnetic Resonance Imaging Equation to Compressible and Incompressible Fluid Particles in a Spherical Region." International Journal of Mathematical Sciences and Optimization: Theory and Applications 10, no. 3 (2024): 10–30. https://doi.org/10.5281/zenodo.13152986.

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In the previous work, the response of viscous and non-viscous fluids to magnetic resonancewas examined. In this research work, Diffusion magnetic resonance imaging, MRI, is used tostudy, analyse and compare the response of particles of compressible and incompressible fluidsin a spherical region. The fluids considered are hydrogen gas and paraffin oil. The general flowequation was evolved from the fundamental Bloch equations. The general flow equation wassolved using the method of separation of variables and applied to spherical region leading toLegendre equation of the first and second kinds. From the results obtained, it can be concludedthat the value of Magnetization for hydrogen gas ranges from 9.28819444503×10^13 to 9.35×10^14.However, appreciable change can be noticed when magnetization is 9.2881944500003 × 10^13.For paraffin oil, the value of Magnetization ranges from 2.749305556000075×10^14 to 2.75×10^14with appreciable change noticed at magnetization value of 2.7493055560000094 × 10^14. Theanalytical solution of Diffusion MRI equation adopted in this research work has shown thedifference in compressible (hydrogen gas) and incompressible (paraffin oil) fluids in a sphericalregion through the magnetization values that were generated. This is laying credence to theeffectiveness and non-invasive properties of MRI.

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39

Benakrach, H., M. Taha-Janan, and M. Z. Es-Sadek. "Simulation of compressible and incompressible flows in the presence of shocks." MATEC Web of Conferences 286 (2019): 07018. http://dx.doi.org/10.1051/matecconf/201928607018.

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The purpose of the present work is to use a finite volume method for solving Euler equations in the presence of shocks and discontinuities, with a generalized equation of state. This last choice allows to treat both compressible and incompressible fluids. The first results of the work are presented. They consist in simulating two-dimensional single-specie flows in the presence of shocks. The results obtained are compared with the analytical results considered as benchmarks in the domain.

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40

Solonnikov, V. A. "$L_2$-theory for two viscous fluids of different types: Compressible and incompressible." St. Petersburg Mathematical Journal 32, no. 1 (2021): 91–137. http://dx.doi.org/10.1090/spmj/1640.

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41

Samuel, G. Robello, and Stefan Miska. "Performance of Positive Displacement Motor (PDM) Operating On Air." Journal of Energy Resources Technology 125, no. 2 (2003): 119–25. http://dx.doi.org/10.1115/1.1575776.

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Recent increase in application of horizontal wells and in particular underbalanced drilling, has triggered the necessity of a powerful pneumatic downhole motor. To enhance the technology and make the system effective, a mathematical model is required to identify the opportunities for the modification of power section design. It is well known that the performance of positive displacement motor operating on compressible fluid drops down drastically as compared to the operation under incompressible fluids. The frequent motor replacement during the operation incrementally increases the operating cost despite deriving potential benefits from underbalanced drilling.

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42

Lions, P. L., and N. Masmoudi. "Incompressible limit for a viscous compressible fluid." Journal de Mathématiques Pures et Appliquées 77, no. 6 (1998): 585–627. http://dx.doi.org/10.1016/s0021-7824(98)80139-6.

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43

Thakur, Pankaj, Nishi Gupta, and Satya Bir Singh. "Creep strain rates analysis in cylinder under temperature gradient materials by using Seth’s theory." Engineering Computations 34, no. 3 (2017): 1020–30. http://dx.doi.org/10.1108/ec-05-2016-0159.

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Purpose The purpose of this paper is to present study of creep strain rates in a circular cylinder under temperature gradient materials by using Seth’s transition theory. Design/methodology/approach Seth’s transition theory is applied to the problem of creep stresses and strain rates in a cylinder under temperature gradient materials by finite deformation. Neither the yield criterion nor the associated flow rule is assumed here. The results obtained here are applicable to compressible materials. If the additional condition of incompressibility is imposed, then the expression for stresses corresponds to those arising from Tresca yield condition. Findings Thermal effect increases the values of axial stress at the external surface of a circular cylinder for incompressible material as compared to compressible materials. With the introduction of thermal effects, the maximum value of strain rates occurs at the external surface for incompressible material as compared to the compressible materials. Originality/value The model proposed in this paper is used commonly either as pressure vessels intended for storage industrial gases or media transportation of high pressurized fluids and the design of turbine rotors.

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44

Zank, G. P., and W. H. Matthaeus. "The equations of reduced magnetohydrodynamics." Journal of Plasma Physics 48, no. 1 (1992): 85–100. http://dx.doi.org/10.1017/s002237780001638x.

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The equations of high- and low-beta reduced magnetohydrodynamics (RMHD) are considered anew in order to elucidate the relationship between compressible MHD and RMHD and also to distinguish RMHD from recently developed models of nearly incompressible MHD. Our results, summarized in two theorems, provide the conditions under which RMHD represents a valid reduction of compressible MHD. The equations for low-beta RMHD and high-beta RMHD are shown to be identical. Furthermore, as a direct consequence of our analysis, the conditions under which both two-dimensional incompressible MHD (in terms of the spatial co-ordinates as well as the fluid variables) and 2½ dimensional incompressible MHD (i.e. only two-dimensional in the spatial co-ordinates) represent a valid reduction of three-dimensional compressible MHD are also formulated. It is found that the elimination of all high-frequency and long-wavelength modes from the magneto-fluid reduces the fully compressible MHD equations to either two-dimensional incompressible MHD in the plasma beta (β) limit β ≪ 1, or 2½-dimensional incompressible MHD for β ≈ 1. Our approach clarifies several inconsistencies to be found in previous investigations in that the reduction is exact. Our results and analysis are expected to be of interest for plasma fusion and space and solar physics.

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45

FEIREISL, EDUARD. "FLOWS OF VISCOUS COMPRESSIBLE FLUIDS UNDER STRONG STRATIFICATION: INCOMPRESSIBLE LIMITS FOR LONG-RANGE POTENTIAL FORCES." Mathematical Models and Methods in Applied Sciences 21, no. 01 (2011): 7–27. http://dx.doi.org/10.1142/s0218202511004964.

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We study the singular limit of the compressible Navier–Stokes system in the whole space ℝ3, where the Mach number and Froude number are proportional to a small parameter ε → 0. The central issue is the local decay of the acoustic energy proved by means of the RAGE theorem. The result is quite general and the proposed approach can be applied to a large variety of problems that concern propagation of acoustic waves in compressible fluids. In particular, the method can be used for showing stability of various numerical schemes based on the so-called hybrid methods.

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GUILLOPÉ, COLETTE, ZAYNAB SALLOUM, and RAAFAT TALHOUK. "EXISTENCE RESULTS FOR FLOWS OF SLIGHTLY COMPRESSIBLE VISCOELASTIC FLUIDS IN A BOUNDED DOMAIN WITH CORNERS." Analysis and Applications 10, no. 04 (2012): 381–411. http://dx.doi.org/10.1142/s0219530512500194.

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Steady flows of slightly compressible viscoelastic fluids of Oldroyd's type with zero boundary conditions are considered on a bounded two-dimensional domain with an isolated corner point. We prove the existence and the uniqueness of the solution for small data in weighted Sobolev spaces [Formula: see text], where the index ξ characterizes the power growth of the solution near the angular point. The proof follows from an analysis of a linearized problem through the fixed point theory. We use a method of decomposition for such linearized equations: the velocity field u is split into a non-homogeneous incompressible part v and a compressible part ∇φ.

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Hv, Gangamani. "Acoustic Tunnelling of Internal Gravity waves in the stratified fluids." JOURNAL OF ADVANCES IN PHYSICS 15 (February 16, 2019): 6121–37. http://dx.doi.org/10.24297/jap.v15i0.8051.

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This paper focuses on the study of acoustic propagation of internal gravity waves which generates small scale variations through propagation and hence can obtain transmission co-efficients using N2 buoyancy frequency variation of a compressible stratified fluid for a small regions. We have also analysed the results using the asymptotic expansions for large compressible limits. The reduction of the transmission in the N2-barrier region for the density layers sandwiched along with acoustic waves is obtained through graphs for different density barrier regions. The dispersion characteristics shows the contours of the transmission in the wave number plane. The curves for ! < N0 are hyperbolic, representing internal gravity waves as these become the dispersionwaves for an incompressible fluid and the curve with ! > N0 are ellipsoids which represent the acoustic gravity or infrasonic waves for the cut off frequency

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Rajagopal, K. R., G. Saccomandi, and L. Vergori. "On the approximation of isochoric motions of fluids under different flow conditions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2180 (2015): 20150159. http://dx.doi.org/10.1098/rspa.2015.0159.

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There has been considerable interest, ever since the development of the approximation by Oberbeck and Boussinesq concerning fluids that are mechanically incompressible but thermally compressible, in giving a rigorous justification for the same. For such fluids, it would be natural to assume that the determinant of the deformation gradient (which is a measure of the volume change of the body) depends on the temperature. However, such an assumption has the attendant drawbacks of the specific heat of the fluid at constant volume being zero and the speed of sound in the fluid being complex. In this paper, we consider a generalization of the Oberbeck–Boussinesq approximation, wherein the volume change depends both on the temperature and on the pressure that the fluid is subject to. We show that within the context of this generalization, the specific heat at constant volume can be defined meaningfully, and it is not zero.

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AlTammar, Murtadha J., Deepen Gala, Mukul M. Sharma, and James McAndrew. "Laboratory visualization of fracture initiation and propagation using compressible and incompressible fracturing fluids." Journal of Natural Gas Science and Engineering 55 (July 2018): 542–60. http://dx.doi.org/10.1016/j.jngse.2018.05.010.

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Davydov, A. A., B. N. Chetverushkin, and E. V. Shil’nikov. "Simulating flows of incompressible and weakly compressible fluids on multicore hybrid computer systems." Computational Mathematics and Mathematical Physics 50, no. 12 (2010): 2157–65. http://dx.doi.org/10.1134/s096554251012016x.

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