Relevant bibliographies by topics / Fluid mechanics – Mathematics

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Fluid mechanics – Mathematics'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Fluid mechanics – Mathematics"

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Holt, Maurice, Graham F. Carey, and J. Tinsley Oden. "Finite Elements: Fluid Mechanics." Mathematics of Computation 52, no. 185 (1989): 249. http://dx.doi.org/10.2307/2008669.

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Barnes, H. A. "Fluid Mechanics." Journal of Non-Newtonian Fluid Mechanics 37, no. 2-3 (1990): 387. http://dx.doi.org/10.1016/0377-0257(90)90014-3.

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Cartwright, Julyan H. E., and Oreste Piro. "The fluid mechanics of poohsticks." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2179 (2020): 20190522. http://dx.doi.org/10.1098/rsta.2019.0522.

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The year 2019 marked the bicentenary of George Gabriel Stokes, who in 1851 described the drag—Stokes drag—on a body moving immersed in a fluid, and 2020 is the centenary of Christopher Robin Milne, for whom the game of poohsticks was invented; his father A. A. Milne’s The House at Pooh Corner , in which it was first described in print, appeared in 1928. So this is an apt moment to review the state of the art of the fluid mechanics of a solid body in a complex fluid flow, and one floating at the interface between two fluids in motion. Poohsticks pertains to the latter category, when the two fluids are water and air. This article is part of the theme issue ‘Stokes at 200 (part 2)’.
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Manikta Puspitasari, M. Dewi, Kuni Nadliroh, and Muhammad Najibulloh Muzaki. "Students’ Epistemic Game according to SOLO Taxonomy in Completing Fluid Mechanics Problem." Jurnal Pembelajaran Fisika 8, no. 2 (2019): 167–75. http://dx.doi.org/10.23960/jpf.v8.n2.202005.

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The purpose of this study is to describe the students’ epistemic game of high physics-capable. This study is qualitative. The participants are students taking fluid mechanics courses. The collect data of this study use fluid mechanics test, physics understanding test, and interview. The understanding test determines the students’ understanding level, while the determining students’ epistemic game by SOLO taxonomy uses the fluid mechanic's test. The students complete the first test by using mapping mathematics to meaning at a relational level and transliteration to mathematics at a multi structural level. Pictorial analysis in level extended abstract and transliteration to mathematics in level relational are used by the students in completing the problem of the second test. Meanwhile, this study result showed that mapping mathematics to the meaning and recursive plug and chug at a relational level is used by the students for completing the third test. Furthermore, the students completing the fourth test used transliteration to mathematics and recursive plug and chug at a relational level The students’ epistemic game by SOLO taxonomy of this study can be used to develop physics learning. Keywords: epistemic game, SOLO taxonomy, fluid mechanics
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Et. al., Santosh Jakapure,. "Regular Pertibution Solutions In Fluid Mechanics." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 2 (2021): 1578–84. http://dx.doi.org/10.17762/turcomat.v12i2.1436.

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Disregarding the fast advances in both scalar and equal computational devices, the huge number and expansiveness of factors associated with both plan and opposite issues utilize refined and even generally straightforward (parabolized or limit layer) liquid stream models unreasonable. With this limitation, it very well might be presumed that a significant group of strategies for numerical/computational advancement are decreased or surmised models. In this examination a joined perturbation/mathematical displaying approach is created which will give a thoroughly inferred chain of importance of arrangements. These arrangements are described by changing degrees of unpredictability versus logical devotion.
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ZAGANESCU, Nicolae-Florin, Rodica ZAGANESCU, and Constantin-Marcian GHEORGHE. "Academician CAIUS IACOB – a Brilliant Mathematician Fascinated by Mechanics." INCAS BULLETIN 12, no. 1 (2020): 243–48. http://dx.doi.org/10.13111/2066-8201.2020.12.1.23.

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The paper presents some interesting aspects related to the biography and works of Romanian mathematician Caius Iacob (1912–1992). He was famous for his works in the fields of mathematical analysis, fluid mechanics, classical hydrodynamics and compressible-flow theory. At the age of 19, he graduated from the Mathematics Faculty in Bucharest, and then he went to Paris to continue his studies at the Faculty of Sciences, where he worked on a PhD thesis under the advice of famous French mathematician Henri Villat. On 24 June 1935, Caius Iacob successfully presented to the Sorbonne committee his PhD thesis about “Determination of conjugated harmonic functions with some limit conditions, and their applications in hydrodynamics”. Returning to Romania, Caius Iacob had a long and successful career teaching mathematics and mechanics at the universities of Timişoara, Cluj and Bucharest. His most important work is considered the “Mathematical introduction to the mechanics of fluids”. This book, providing original ways to work with classical hydrodynamics and compressible-flow theory, was published in Romanian in 1952 and in French in 1959. In 1955, he was elected a Corresponding Member of the Romanian Academy, becoming a titular Member in 1963. He was also President of the Mathematics Section of the Romanian Academy from 1980 until the end of his life, in 1992. In 1991, he initiated the foundation of the “Romanian Academy Institute of Applied Mathematics”. In 2001 the institute merged with the “Centre for Mathematical Statistics”, which had been created in 1964 by mathematician Gheorghe Mihoc, thus creating the “Gheorghe Mihoc – Caius Iacob Institute of Mathematical Statistics and Applied Mathematics” of the Romanian Academy.
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Feistauer, M. "Analysis in Compressible Fluid Mechanics." ZAMM 78, no. 9 (1998): 579–96. http://dx.doi.org/10.1002/(sici)1521-4001(199809)78:9<579::aid-zamm579>3.0.co;2-c.

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Craik, Alex D. D. "Thomas Young on fluid mechanics." Journal of Engineering Mathematics 67, no. 1-2 (2009): 95–113. http://dx.doi.org/10.1007/s10665-009-9298-7.

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Bazilevs, Yuri, Kenji Takizawa, and Tayfun E. Tezduyar. "Special issue on computational fluid mechanics and fluid–structure interaction." Computational Mechanics 48, no. 3 (2011): 245. http://dx.doi.org/10.1007/s00466-011-0621-6.

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Smith, D. J., A. A. Smith, and J. R. Blake. "Mathematical embryology: the fluid mechanics of nodal cilia." Journal of Engineering Mathematics 70, no. 1-3 (2010): 255–79. http://dx.doi.org/10.1007/s10665-010-9383-y.

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Dissertations / Theses on the topic "Fluid mechanics – Mathematics"

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Smith, Andrew. "The fluid mechanics of embryonic nodal cilia." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4626/.

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Symmetry breaking of the left-right body axis is a crucial step in development for many vertebrate species. In many this is initiated with a directional cilia-driven fluid flow in the organising structure. This work focuses on the mouse and the zebrafish organising structures, the node and Kupffer's vesicle, wherein cilia perform a tilted rotation producing an asymmetric flow. Using singularities of Stokes flow, slender body theory and the boundary integral equation, a computational model of flow in the mouse node for a range of cilia configurations simulating developmental stages is developed and run on the University of Birmingham's cluster, BlueBEAR. The results show the emergence of a directional flow as the cilia tilt increases. To model the Kupffer's vesicle the regularised boundary integral equation is used with a mesh representation of the entire domain to investigate potential cilia mechanisms that produce the observed flow as there is not a consensus. The results show that a combination of the experimental observations could be a sufficient mechanism. This model is expanded using observations of cilia with two rotation frequencies which are incorporated by allowing such cilia to ‘wobble’. This wobble accentuates the asymmetric flow in wildtype embryos and diminishes it in mutant embryos. All of these results agree well with experiment suggesting that vertebrates develop a combination of rotation mechanisms in their organising structures before an appropriate symmetry breaking flow is established.
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Dashti, Masoumeh. "Some problems in the mathematical theory of fluid mechanics." Thesis, University of Warwick, 2008. http://wrap.warwick.ac.uk/3665/.

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This thesis addresses three problems related to the mathematical theory of fluid mechanics. Firstly, we consider the three-dimensional incompressible Navier-Stokes equations with an initial condition that has H1-Sobolev regularity. We show that there is an a posteriori condition that, if satisfied by the numerical solutions of the equations, guarantees the existence of a strong solution and therefore the validity of the numerical computations. This is an extension of a similar result proved by Chernyshenko, Constantin, Robinson & Titi (2007) to less regular solutions not considered by them. In the second part, we give a simple proof of uniqueness of fluid particle trajectories corresponding to the solution of the d-dimensional Navier Stokes equations, d = 2, 3, with an initial condition that has H(d/2)−1-Sobolev regularity. This result has been proved by Chemin & Lerner (1995) using the Littlewood-Payley theory for the flow in the whole space Rd. We provide a significantly simpler proof, based on the decay of Sobolev norms ( of order more than (d/2)−1 ) of the velocity field after the initial time, that is also valid for the more physically relevant case of bounded domains. The last problem we study is the motion of a fluid-rigid disk system in the whole plane at the zero limit of the rigid body radius. We consider one rigid disk moving with the fluid flow and show that when the radius of the disk goes to zero, the solution of this system converges, in an appropriate sense, to the solution of the Navier-Stokes equations describing the motion of only fluid in the whole plane. We then prove that the trajectory of the centre of the disk, at the zero limit of its radius, coincides with a fluid particle trajectory. We also show an equivalent result for the limiting motion of a spherical tracer in R3, over a small enough time interval.
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Breward, C. J. W. "The mathematics of foam." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300849.

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The aim of this thesis is to derive and solve mathematical models for the flow of liquid in a foam. A primary concern is to investigate how so-called `Marangoni stresses' (i.e. surface tension gradients), generated for example by the presence of a surfactant, act to stabilise a foam. We aim to provide the key microscopic components for future foam modelling. We begin by describing in detail the influence of surface tension gradients on a general liquid flow, and various physical mechanisms which can give rise to such gradients. We apply the models thus devised to an experimental configuration designed to investigate Marangoni effects. Next we turn our attention to the flow in the thin liquid films (`lamellae') which make up a foam. Our methodology is to simplify the field equations (e.g. the Navier-Stokes equations for the liquid) and free surface conditions using systematic asymptotic methods. The models so derived explain the `stiffening' effect of surfactants at free surfaces, which extends considerably the lifetime of a foam. Finally, we look at the macroscopic behaviour of foam using an ad-hoc averaging of the thin film models.
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Cosper, Lane. "Existence of a Unique Solution to a System of Equations Modeling Compressible Fluid Flow with Capillary Stress Effects." Thesis, Texas A&M University - Corpus Christi, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10790012.

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<p> The purpose of this thesis is to prove the existence of a unique solution to a system of partial differential equations which models the flow of a compressible barotropic fluid under periodic boundary conditions. The equations come from modifying the compressible Navier-Stokes equations. The proof utilizes the method of successive approximations. We will define an iteration scheme based on solving a linearized version of the equations. Then convergence of the sequence of approximate solutions to a unique solution of the nonlinear system will be proven. The main new result of this thesis is that the density data is at a given point in the spatial domain over a time interval instead of an initial density over the entire spatial domain. Further applications of the mathematical model are fluid flow problems where the data such as concentration of a solute or temperature of the fluid is known at a given point. Future research could use boundary conditions which are not periodic.</p><p>
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Rahantamialisoa, Faniry Nadia Zazaravaka. "Complex fluid dynamical computations via the Finite Volume Method." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29860.

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Numerical simulations of the complex flows of viscoelastic fluids are investigated. The viscoelastic fluids are modelled, primarily, via the Johnson-Segalman constitutive model. Our Numerical approach is based on finite volume method, based on the Johnson-Segalman constitutive model and implemented on the OpenFOAM® platform. The Johnson-Segalman model also easily reduces to the Oldroyd-B model under certain conditions of the material parameters. Since computations using the Oldroyd-B model have been extensively documented in the literature, we take advantage of the mathematical modelling connection between the Johnson-Segalman and Oldroyd-B models to validate the accuracy of our Johnson-Segalman solver via reduction to the Oldroyd-B model. Numerical validation of our results is conducted via the most commonly used benchmark problems. The final aim of our work is to assess the viability and efficiency of our numerical solver via an investigation into the complex fluid dynamical processes associated with shear banding.
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Fay, Gemma Louise. "Mathematical modelling of turbidity currents." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:62bb9382-1c50-47f3-8f59-66924cc31760.

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Turbidity currents are one of the primary means of transport of sediment in the ocean. They are fast-moving, destructive fluid flows which are able to entrain sediment from the seabed and accelerate downslope in a process known as `ignition'. In this thesis, we investigate one particular model for turbidity currents; the `Parker model' of Parker, Pantin and Fukushima (1986), which models the current as a continuous sediment stream and consists of four equations for the depth, velocity, sediment concentration and turbulent kinetic energy of the flow. We propose two reduced forms of the model; a one-equation velocity model and a two-equation shallow-water model. Both these models give an insight into the dynamics of a turbidity current propagating downstream and we find the slope profile to be particularly influential. Regions of supercritical and subcritical flow are identified and the model is solved through a combination of asymptotic approximations and numerical solutions. We next consider the dynamics of the four-equation model, which provides a particular focus on Parker's turbulent kinetic energy equation. This equation is found to fail catastrophically and predict complex-valued solutions when the sediment-induced stratification of the current becomes large. We propose a new `transition' model for turbulent kinetic energy which features a switch from an erosional, turbulent regime to a depositional, stably stratified regime. Finally, the transition model is solved for a series of case studies and a numerical parameter study is conducted in an attempt to answer the question `when does a turbidity current become extinct?'.
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Garratt, T. J. "The numerical detection of Hopf bifurcations in large systems arising in fluid mechanics." Thesis, University of Bath, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.292839.

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Chutsagulprom, Nawinda. "Thin film flows in curved tubes." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:35071002-e487-4cd3-b85f-3aca6dcb0c93.

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The main motivation of this thesis comes from a desire to understand the behaviours of blood flow in the vicinity of atheroma. The initiation and development of atherosclerosis in arteries are normally observed in the areas of low or oscillating wall shear stress, such as on the outer wall of a bifurcation and the inside of the bends. We start by building on the background to the areas related to our models. We focus on the models of fluid flow travelling through a curved tube of uniform curvature because most arteries are tapered and curved. The flow of an incompressible Newtonian fluid in a curved tube is modelled. The derivation of the corresponding equations of the motion is presented. The equations are then solved for a steady and oscillatory driving axial pressure gradient. In each case, the flow is governed by different dimensionless parameters. The problem is solved for a variety of parameter regimes by using asymptotic technique as well as numerical method. Some aspects of thin-film flows are studied. The well-known thin film equation is derived using lubrication theory. The stability of a thin film in a straight tube and the effects of a surfactant droplet on a liquid film are presented. The moving contact line problem, one of the controversial topics in fluid dynamics, is also discussed. The leading-order equations governing thin-film flow over a stationary curved substrate is derived. Various approaches and the application of flow on particular substrates are shown. Finally, we model two-layer viscous fluids using lubrication approximation. By assuming the thickness of a lower liquid layer is much thinner than that of the upper liquid layer, the equation governing the liquid-liquid interface is derived. The steady-state and trasient solutions of the evolution equation is computed both analytically and computationally.
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Shipley, Rebecca Julia. "Multiscale modelling of fluid and drug transport in vascular tumours." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:8f663f70-8d23-49ad-8348-1763359d8f62.

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Understanding the perfusion of blood and drugs in tumours is fundamental to foreseeing the efficacy of treatment regimes and predicting tumour growth. In particular, the dependence of these processes on the tumour vascular structure is poorly established. The objective of this thesis is to derive effective equations describing blood, and drug perfusion in vascular tumours, and specifically to determine the dependence of these on the tumour vascular structure. This dependence occurs through the interaction between two different length scales - that which characterizes the structure of the vascular network, and that which characterizes the tumour as a whole. Our method throughout is to use homogenization as a tool to evaluate this interaction. In Chapter 1 we introduce the problem. In Chapter 2 we develop a theoretical model to describe fluid flow in solid tumours through both the vasculature and the interstitium, at a number of length scales. Ultimately we homogenize over a network of capillaries to form a coupled porous medium model in terms of a vascular density. Whereas in Chapter 2 it is necessary to specify the vascular structure to derive the effective equations, in Chapter 3 we employ asymptotic homogenization through multiple scales to derive the coupled equations for an arbitrary periodic vascular network. In Chapter 4, we extend this analysis to account for advective and diffusive transport of anticancer drugs delivered intravenously; we consider a range of reaction properties in the interstitium and boundary conditions on the vascular wall. The models derived in Chapters 2–4 could be applied to any drug type and treatment regime; to demonstrate their potential, we simulate the delivery of vinblastine in dorsal skinfold chambers in Chapter 5 and make quantitative predictions regarding the optimal treatment regime. In the final Chapter we summarize the main results and indicate directions for further work.
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Al-Wali, Azzam Ahmad. "Explicit alternating direction methods for problems in fluid dynamics." Thesis, Loughborough University, 1994. https://dspace.lboro.ac.uk/2134/6840.

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Recently an iterative method was formulated employing a new splitting strategy for the solution of tridiagonal systems of difference equations. The method was successful in solving the systems of equations arising from one dimensional initial boundary value problems, and a theoretical analysis for proving the convergence of the method for systems whose constituent matrices are positive definite was presented by Evans and Sahimi [22]. The method was known as the Alternating Group Explicit (AGE) method and is referred to as AGE-1D. The explicit nature of the method meant that its implementation on parallel machines can be very promising. The method was also extended to solve systems arising from two and three dimensional initial-boundary value problems, but the AGE-2D and AGE-3D algorithms proved to be too demanding in computational cost which largely reduces the advantages of its parallel nature. In this thesis, further theoretical analyses and experimental studies are pursued to establish the convergence and suitability of the AGE-1D method to a wider class of systems arising from univariate and multivariate differential equations with symmetric and non symmetric difference operators. Also the possibility of a Chebyshev acceleration of the AGE-1D algorithm is considered. For two and three dimensional problems it is proposed to couple the use of the AGE-1D algorithm with an ADI scheme or an ADI iterative method in what is called the Explicit Alternating Direction (EAD) method. It is then shown through experimental results that the EAD method retains the parallel features of the AGE method and moreover leads to savings of up to 83 % in the computational cost for solving some of the model problems. The thesis also includes applications of the AGE-1D algorithm and the EAD method to solve some problems of fluid dynamics such as the linearized Shallow Water equations, and the Navier Stokes' equations for the flow in an idealized one dimensional Planetary Boundary Layer. The thesis terminates with conclusions and suggestions for further work together with a comprehensive bibliography and an appendix containing some selected programs.
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Books on the topic "Fluid mechanics – Mathematics"

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Katz, Joseph. Introductory fluid mechanics. Cambridge University Press, 2010.

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Rodrigo Diez, José Luis, 1977-, ed. Mathematical aspects of fluid mechanics. Cambridge University Press, 2012.

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N, Seetharamu K., ed. Engineering fluid mechanics. Alpha Science International, 2005.

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Frontiers in Experimental Fluid Mechanics. Springer Berlin Heidelberg, 1989.

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Monin, A. S. Statistical fluid mechanics: Mechanics of turbulence. Dover Publications, 2007.

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Spurk, Joseph H. Fluid Mechanics: Problems and Solutions. Springer Berlin Heidelberg, 1997.

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M, Rahman. Mechanics of real fluids. WIT Press, 2011.

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1958-, Katz Ira M., and Schaffer James P, eds. Introduction to fluid mechanics. Oxford University Press, 2005.

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Muralidhar, K. Advanced engineering fluid mechanics. Narosa, 1996.

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Gautam, Biswas, ed. Advanced engineering fluid mechanics. 2nd ed. Alpha Science International, 2005.

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Book chapters on the topic "Fluid mechanics – Mathematics"

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Neu, John. "Ideal fluid mechanics." In Graduate Studies in Mathematics. American Mathematical Society, 2009. http://dx.doi.org/10.1090/gsm/109/06.

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Padula, Mariarosaria. "Topics in Fluid Mechanics." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21137-9_1.

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P.L., Sachdev*, and Srinivasa Rao Ch. "Asymptotics in Fluid Mechanics." In Springer Monographs in Mathematics. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87809-6_5.

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Cutland, Nigel J. "2. Stochastic Fluid Mechanics." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-540-44531-9_2.

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Kawahara, Mutsuto. "Continuum Mechanics of Fluid Flows." In Mathematics for Industry. Springer Japan, 2016. http://dx.doi.org/10.1007/978-4-431-55450-9_7.

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Raman, Venkat. "Particulate Flows (Fluid Mechanics)." In Encyclopedia of Applied and Computational Mathematics. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_509.

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Constantin, Peter. "Singular Limits in Fluid Mechanics." In Current and Future Directions in Applied Mathematics. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2012-1_14.

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Van Dyke, M. "Slow Variations in Fluid Mechanics." In Applied Mathematics in Aerospace Science and Engineering. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4757-9259-1_1.

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Van Dyke, M. "Computer-Extended Series in Fluid Mechanics." In Applied Mathematics in Aerospace Science and Engineering. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4757-9259-1_2.

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Busuioc, Adriana Valentina, and T. S. Ratiu. "A Fluid Problem with Navier-Slip Boundary Conditions." In Advances in Mechanics and Mathematics. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-90-481-9577-0_14.

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Conference papers on the topic "Fluid mechanics – Mathematics"

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Bogdanov, Alexander, Alexander Degtyarev, and Vasily Khramushin. "Direct computational experiments in fluid mechanics using three-dimensional tensor mathematics." In 2017 Computer Science and Information Technologies (CSIT). IEEE, 2017. http://dx.doi.org/10.1109/csitechnol.2017.8312158.

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Boutéca, M., and J. P. Sarda. "Fluid Flow in Porous Media and Related Rock Mechanics Problems." In ECMOR II - 2nd European Conference on the Mathematics of Oil Recovery. European Association of Geoscientists & Engineers, 1990. http://dx.doi.org/10.3997/2214-4609.201411116.

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Degtyarev, Alexander, Vasily Khramushin, and Julia Shichkina. "Tensor methodology and computational geometry in direct computational experiments in fluid mechanics." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992291.

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Gajjar, Jitesh S. B. "Preface of the "Symposium on recent advances in theoretical fluid dynamics, hydrodynamic stability theory, and biological fluid mechanics"." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825470.

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Dong, A., S. Ahmed, and G. de Marsily. "Development of Geostatistical Methods Dealing with the Boundary Conditions Problem Encountered in Fluid Mechanics of Porous Media." In ECMOR II - 2nd European Conference on the Mathematics of Oil Recovery. European Association of Geoscientists & Engineers, 1990. http://dx.doi.org/10.3997/2214-4609.201411096.

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Kurylko, O. B. "Modelling of mixing scenario of a viscous fluid inside a rectangular cavity under a complex velocity distribution." In MATHEMATICS, PHYSICS, MECHANICS, ASTRONOMY, COMPUTER SCIENCE AND CYBERNETICS: ISSUES OF PRODUCTIVE INTERACTION. Baltija Publishing, 2021. http://dx.doi.org/10.30525/978-9934-26-115-2-4.

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Rossmann, Jenn S., Clive L. Dym, and Lori C. Bassman. "An Integrated Introduction to Engineering Mechanics: A Continuum Approach." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-69131.

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The essence of continuum mechanics, the internal response of materials to external loading, is often obscured by the complex mathematics of its formulation. Rather than introducing solid and fluid behavior as two distinct fields and waiting for an advanced course to demonstrate the mathematical connections between them, we have developed an integrated introduction to both fields. We will discuss the eight-year history of this course at Harvey Mudd and Lafayette Colleges, and the course materials we have developed. This one semester course covers material typically spread over several courses, including statics, strength of materials, and introductory fluid mechanics. We posit a spectrum of material behavior that has Hookean solids at one extreme, and Newtonian fluids at the other, with many interesting combinations (e.g. biomaterials, viscoelastic materials) in between. By building progressively from one-dimensional to higher dimension formulations, we are able to make continuum concepts such as the Cartesian stress tensor accessible to early undergraduate students. From this gradual development of ideas, with many illustrative case studies interspersed, students develop both physical intuition for how engineering materials behave, and the mathematical techniques needed to describe this behavior. We will discuss the rewards and challenges of introducing continuum mechanics early in the curriculum.
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Tyrylgin, A., M. Vasilyeva, Q. Zhang, D. Spiridonov, and V. Alekseev. "Mathematical modeling of the fluid flow and geo-mechanics in the fractured porous media using generalized multiscale finite element method." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 10th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’18. Author(s), 2018. http://dx.doi.org/10.1063/1.5064938.

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Schetz, Joseph A. "A Distributed and Distance Learning Course “Fluid Flows in Nature”." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-37220.

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Abstract:
This course was originally designed and conventionally taught to build upon and broaden a basic, traditional engineering knowledge of fluid flows into new and stimulating areas concerning a wide variety of natural occurrences and phenomena that involve fluid motions in important ways. Topics covered include: continuity and consequences in nature, drag of sessile systems and motile animals; gliding and soaring; flying and swimming; internal flows in organisms; low Reynolds number flows; fluid-fluid interfaces and stratified flows; unsteady flows in nature; atmospheric flows and wind engineering; and environmental fluid mechanics. The course is intended for upper-level students in engineering and science and presumes a background in the fundamentals of fluid flows at the level of a first engineering course in fluid mechanics. It proved popular with students majoring in mechanical, civil, aerospace and ocean engineering with occasional students from mathematics and sciences for a typical enrollment of 80–100 students. An unexpected, but welcome and powerful, benefit occurs in the form of reinforcing and deepening student understanding of traditional topics in engineering fluid mechanics by contrast with the often very different situations encountered in nature. An OnLine version of the course was introduced for the Spring Semester of 2006. Enrollment promptly and steadily increased to the point where 230 students registered in the Spring Semester of 2010. It is felt that a course of this type where conventional instructional materials do not exist is particularly suited to the OnLine format.
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Korotkii, A. I., and I. A. Tsepelev. "Reconstruction of the fluid viscosity of unsteady-state flows of the incompressible fluid by velocity measurements on the free flow surface." In PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0035500.

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Reports on the topic "Fluid mechanics – Mathematics"

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Majda, Andrew J. Mathematical Analysis of Strong Fluid Mechanical Effects in Reactive & Nonreactive Flows. Defense Technical Information Center, 1995. http://dx.doi.org/10.21236/ada300175.

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Majda, Andrew J. Mathematical Analysis of Strong Fluid Mechanical Effects at High Mach Number in Reactive and Nonreactive Flow. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada253617.

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