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Journal articles on the topic 'Stokes' method'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Vermeulen, N., C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont. "Stokes-Anti-Stokes Iterative Resonator Method for Modeling Raman Lasers." IEEE Journal of Quantum Electronics 42, no. 11 (2006): 1144–56. http://dx.doi.org/10.1109/jqe.2006.883469.

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2

Zhang, Shu Hua, Xiao Jing Yuan, and Qian Yin. "Discontinuous Galerkin (DG) Finite Element Method for the Improved Stokes Equations." Advanced Materials Research 250-253 (May 2011): 291–97. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.291.

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In this paper, firstly, discontinuous Galerkin method for improved Stokes equation is proposed. We derive a discontinuous Galerkin (DG) finite element formulation for the improved Stokes equations. Special case of the generalized solution equation for linear and stationary improved Stokes equations retrogresses into generalized solution equation for classical Stokes equation. It is proved that the classical solution and the generalized solution is consistent for the improved Stokes equations, existence and uniqueness of generalized solution for the improved Stokes equations are also proved.

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3

DE OLIVEIRA, P. M. C. "RELAXATION METHOD FOR NAVIER–STOKES EQUATION." International Journal of Modern Physics C 23, no. 04 (2012): 1250021. http://dx.doi.org/10.1142/s0129183112500210.

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The motivation for this work was a simple experiment [P. M. C. de Oliveira, S. Moss de Oliveira, F. A. Pereira and J. C. Sartorelli, preprint (2010), arXiv:1005.4086], where a little polystyrene ball is released falling in air. The interesting observation is a speed breaking. After an initial nearly linear time-dependence, the ball speed reaches a maximum value. After this, the speed finally decreases until its final, limit value. The provided explanation is related to the so-called von Kármán street of vortices successively formed behind the falling ball. After completely formed, the whole st

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4

Abboud, Toufic, Michel Salaun, and Stéphanie Salmon. "Integral method for the Stokes problem." Comptes Rendus Mathematique 334, no. 1 (2002): 71–76. http://dx.doi.org/10.1016/s1631-073x(02)02222-7.

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5

Choe, Hi Jun, and Jeong Ho Chu. "A spectral method for Stokes equations." Applied Mathematics and Computation 104, no. 2-3 (1999): 131–51. http://dx.doi.org/10.1016/s0096-3003(98)10062-0.

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6

Abramov, V. I., and B. B. Tagunov. "Method for calibration of stokes radiopolarimeter." Measurement Techniques 34, no. 1 (1991): 83–87. http://dx.doi.org/10.1007/bf00978301.

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7

Park, Chunjae. "P1-nonconforming divergence-free finite element method on square meshes for Stokes equations." Journal of Numerical Mathematics 28, no. 4 (2020): 247–61. http://dx.doi.org/10.1515/jnma-2019-0056.

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AbstractRecently, the P1-nonconforming finite element space over square meshes has been proved stable to solve Stokes equations with the piecewise constant space for velocity and pressure, respectively. In this paper, we will introduce its locally divergence-free subspace to solve the elliptic problem for the velocity only decoupled from the Stokes equation. The concerning system of linear equations is much smaller compared to the Stokes equations. Furthermore, it is split into two smaller ones. After solving the velocity first, the pressure in the Stokes problem can be obtained by an explicit

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8

Nafa, Kamel. "Analysis of Subgrid Stabilization Method for Stokes-Darcy Problems." Advances in Numerical Analysis 2016 (September 22, 2016): 1–9. http://dx.doi.org/10.1155/2016/7389102.

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A number of techniques, used as remedy to the instability of the Galerkin finite element formulation for Stokes like problems, are found in the literature. In this work we consider a coupled Stokes-Darcy problem, where in one part of the domain the fluid motion is described by Stokes equations and for the other part the fluid is in a porous medium and described by Darcy law and the conservation of mass. Such systems can be discretized by heterogeneous mixed finite elements in the two parts. A better method, from a computational point of view, consists in using a unified approach on both subdom

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9

Sene, Ndolane. "Integral Balance Methods for Stokes’ First Equation Described by the Left Generalized Fractional Derivative." Physics 1, no. 1 (2019): 154–66. http://dx.doi.org/10.3390/physics1010015.

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In this paper, the integral balance methods of the Stokes’ first equation have been presented. The approximate solution of the fractional Stokes’ first equation using the heat balance integral method has been proposed. The approximate solution of the fractional Stokes’ first equation using the double integral methods has been proposed. The generalized fractional time derivative operator has been used. The graphical representations of the cubic profile and the quadratic profile for the Stokes’ first problem have been provided. The impacts of the orders of the generalized fractional derivative i

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10

He, Yinnian. "Finite Element Iterative Methods for the 3D Steady Navier--Stokes Equations." Entropy 23, no. 12 (2021): 1659. http://dx.doi.org/10.3390/e23121659.

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In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair Xh×Mh. The method consists of transmitting the finite element solution (uh,ph) of the 3D steady Navier–Stokes equations into the finite element solution pairs (uhn,phn) based on the finite element space pair Xh×Mh of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair Xh×Mh satisfies the discrete inf-sup condition in a 3D domain Ω. Here, we present the weak formulations of the

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11

Droniou, Jérôme, and Robert Eymard. "Study of the mixed finite volume method for Stokes and Navier-Stokes equations." Numerical Methods for Partial Differential Equations 25, no. 1 (2009): 137–71. http://dx.doi.org/10.1002/num.20333.

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12

Nguyen, Cong T., Ruslan D. Khlynov, Victoria A. Ryzhova, et al. "Calibration Methods of a Portable Polarizing System for Monitoring Optically Inhomogeneous Media." Computation 10, no. 8 (2022): 131. http://dx.doi.org/10.3390/computation10080131.

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Theoretical aspects of methods for calibrating Stokes polarimeters are considered. The prospects and opportunities for implementing the presented methods for calibrating portable polarization systems used in biology and medicine are determined. Based on a comparative analysis, a method for calibrating a portable Stokes polarimeter for medical applications is proposed. The chosen method provides the smallest error in measuring the parameters of the Stokes vector for calculating the parameters of optical anisotropy and researching the polarization properties of biological tissues. A series of ex

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13

Mužík, Juraj. "The use of dual reciprocity method for 2D laminar viscous flow." MATEC Web of Conferences 310 (2020): 00044. http://dx.doi.org/10.1051/matecconf/202031000044.

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The paper presents the use of the dual reciprocity multidomain singular boundary method (SBMDR) for the solution of the laminar viscous flow problem described by Navier-Stokes equations. A homogeneous part of the solution is solved using a singular boundary method with the 2D Stokes fundamental solution - Stokeslet. The dual reciprocity approach has been chosen because it is ideal for the treatment of the nonhomogeneous and nonlinear terms of Navier-Stokes equations. The presented SBMDR approach to the solution of the 2D flow problem is demonstrated on a standard benchmark problem - lid-driven

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14

Tuncer, Ismail H. "Two-Dimensional Unsteady Navier-Stokes Solution Method." AIAA Journal 35, no. 3 (1997): 471–76. http://dx.doi.org/10.2514/2.153.

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15

Epstein, B., A. Jacobs, and A. Nachshon. "Aerodynamically Accurate Three-Dimensional Navier-Stokes Method." AIAA Journal 35, no. 6 (1997): 1089–90. http://dx.doi.org/10.2514/2.202.

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16

KIM, Hyoung-Jin, and Kazuhiro NAKAHASHI. "Unstructured Adjoint Method for Navier-Stokes Equations." JSME International Journal Series B 48, no. 2 (2005): 202–7. http://dx.doi.org/10.1299/jsmeb.48.202.

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17

He, Xinyu. "A probabilistic method for Navier-Stokes vortices." Journal of Applied Probability 38, no. 4 (2001): 1059–66. http://dx.doi.org/10.1239/jap/1011994192.

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Consider a Navier-Stokes incompressible turbulent fluid in R2. Let x(t) denote the position coordinate of a moving vortex with initial circulation Γ0 > 0 in the fluid, subject to a force F. Define x(t) as a stochastic process with continuous sample paths described by a stochastic differential equation. Assuming a suitable notion of weak rotationality, it is shown that the stochastic equation is equivalent to a linear partial differential equation for the complex function ψ, i∂ψ/∂t = [-Γ0Δ + F] ψ, where |ψ|2 = ρ(x,t), ρ being the probability density function of finding the vortex centre in p

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18

Boulbry, Bruno, Jessica C. Ramella-Roman, and Thomas A. Germer. "Improved method for calibrating a Stokes polarimeter." Applied Optics 46, no. 35 (2007): 8533. http://dx.doi.org/10.1364/ao.46.008533.

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19

Szalmás, L. "Entropic lattice Boltzmann method beyond Navier–Stokes." Physica A: Statistical Mechanics and its Applications 380 (July 2007): 36–42. http://dx.doi.org/10.1016/j.physa.2007.03.002.

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20

He, Xinyu. "A probabilistic method for Navier-Stokes vortices." Journal of Applied Probability 38, no. 04 (2001): 1059–66. http://dx.doi.org/10.1017/s0021900200019239.

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Consider a Navier-Stokes incompressible turbulent fluid in R 2. Let x(t) denote the position coordinate of a moving vortex with initial circulation Γ0 &gt; 0 in the fluid, subject to a force F. Define x(t) as a stochastic process with continuous sample paths described by a stochastic differential equation. Assuming a suitable notion of weak rotationality, it is shown that the stochastic equation is equivalent to a linear partial differential equation for the complex function ψ, i∂ψ/∂t = [-Γ0Δ + F] ψ, where |ψ|2 = ρ(x,t), ρ being the probability density function of finding the vortex centre

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21

Roberts, Nathan V., Tan Bui-Thanh, and Leszek Demkowicz. "The DPG method for the Stokes problem." Computers & Mathematics with Applications 67, no. 4 (2014): 966–95. http://dx.doi.org/10.1016/j.camwa.2013.12.015.

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22

Epstein, B., A. Jacobs, and A. Nachshon. "Aerodynamically accurate three-dimensional Navier-Stokes method." AIAA Journal 35 (January 1997): 1089–90. http://dx.doi.org/10.2514/3.13633.

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23

Lechleiter, Armin, and Tobias Rienmüller. "Factorization method for the inverse Stokes problem." Inverse Problems & Imaging 7, no. 4 (2013): 1271–93. http://dx.doi.org/10.3934/ipi.2013.7.1271.

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24

Lifits, S. A., S. Yu Reutskiy, G. Pontrelli, and B. Tirozzi. "Quasi Trefftz Spectral Method for Stokes Problem." Mathematical Models and Methods in Applied Sciences 07, no. 08 (1997): 1187–212. http://dx.doi.org/10.1142/s021820259700058x.

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A new numerical Quasi Trefftz Spectral Method (QTSM) which was earlier suggested for solving boundary value and initial value problems with elliptic operators is applied to linear stationary hydrodynamic problems. The primitive variables [Formula: see text] are used. The method has been found to work well for different problems, including free boundary ones. The problem of the Stefan type in the domain with moving boundary is also considered. The possibilities of further developments of QTSM are discussed.

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25

Carroll, T. A., M. Kopf, and K. G. Strassmeier. "A fast method for Stokes profile synthesis." Astronomy & Astrophysics 488, no. 2 (2008): 781–93. http://dx.doi.org/10.1051/0004-6361:200809981.

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26

Haak, Bernhard H., and Peer Chr Kunstmann. "On Kato’s Method for Navier–Stokes Equations." Journal of Mathematical Fluid Mechanics 11, no. 4 (2008): 492–535. http://dx.doi.org/10.1007/s00021-008-0270-5.

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27

Li, Yuan, and Rong An. "Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions." Abstract and Applied Analysis 2013 (2013): 1–17. http://dx.doi.org/10.1155/2013/125139.

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This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh sizeHin combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh sizeh. The error estimate obtained in this paper shows that ifH,h, andεcan be chosen appropriately, then these two-level iteration penalty methods are

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28

Ju, Lili, and Zhu Wang. "Exponential Time Differencing Gauge Method for Incompressible Viscous Flows." Communications in Computational Physics 22, no. 2 (2017): 517–41. http://dx.doi.org/10.4208/cicp.oa-2016-0234.

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AbstractIn this paper, we study an exponential time differencing method for solving the gauge system of incompressible viscous flows governed by Stokes or Navier-Stokes equations. The momentum equation is decoupled from the kinematic equation at a discrete level and is then solved by exponential time stepping multistep schemes in our approach. We analyze the stability of the proposed method and rigorously prove that the first order exponential time differencing scheme is unconditionally stable for the Stokes problem. We also present a compact representation of the algorithm for problems on rec

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29

Wang, Aiwen, Xin Zhao, Peihua Qin, and Dongxiu Xie. "An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations." Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/520818.

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We investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e.,Q1−P0andP1−P0). Firstly, in contrast to other stabilized methods, they are parameter free, no calculation of higher-order derivatives and edge-based data structures, implemented at the element level with minimal cost. In addition, the Oseen two-level stabilized method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh sizeH, a large general Stokes equa

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30

Huang, Pengzhan, Yinnian He, and Xinlong Feng. "Numerical Investigations on Several Stabilized Finite Element Methods for the Stokes Eigenvalue Problem." Mathematical Problems in Engineering 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/745908.

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Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.

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31

Goswami, Deepjyoti, and Pedro D. Damázio. "A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data." Numerical Mathematics: Theory, Methods and Applications 8, no. 4 (2015): 549–81. http://dx.doi.org/10.4208/nmtma.2015.m1414.

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AbstractWe analyze here, a two-grid finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse grid of size H and solving a Stokes problem on a fine grid of size h, h « H. This method gives optimal convergence for velocity in H1-norm and for pressure in L2-norm. The analysis mainly focuses on the loss of regularity of the solution at t = 0 of the Navier-Stokes equations.

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32

Lin, San-Yih, Yan-Shin Chin, and Tsuen-Muh Wu. "A Modified Penalty Method for Stokes Equations and Its Applications to Navier–Stokes Equations." SIAM Journal on Scientific Computing 16, no. 1 (1995): 1–19. http://dx.doi.org/10.1137/0916001.

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33

Kimura, Masato, Kazunori Matsui, Adrian Muntean, and Hirofumi Notsu. "Analysis of a projection method for the Stokes problem using an $$\varepsilon $$-Stokes approach." Japan Journal of Industrial and Applied Mathematics 36, no. 3 (2019): 959–85. http://dx.doi.org/10.1007/s13160-019-00373-3.

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34

Matthies, G., P. Skrzypacz, and L. Tobiska. "Superconvergence of a 3D finite element method for stationary Stokes and Navier-Stokes problems." Numerical Methods for Partial Differential Equations 21, no. 4 (2005): 701–25. http://dx.doi.org/10.1002/num.20058.

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35

SUN, YUZHI, and Z. J. WANG. "NUMERICAL EXPERIMENTS OF THE SPECTRAL VOLUME METHOD FOR VISCOUS FLOWS." Modern Physics Letters B 19, no. 28n29 (2005): 1439–42. http://dx.doi.org/10.1142/s0217984905009602.

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In this paper, the spectral volume (SV) method is experimented for the Navier-Stokes equations by treating the viscous terms with a mixed formulation named the local Discontinuous Galerkin approach. The formulation of the SV method for the two-dimensional compressible Navier-Stokes equations is described. The solver is used to solve several viscous flow problems to show its potential.

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36

Du, Guangzhi, and Liyun Zuo. "A parallel partition of unity method for the nonstationary Navier-Stokes equations." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 8 (2017): 1675–86. http://dx.doi.org/10.1108/hff-06-2016-0214.

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Purpose The purpose of this paper is to propose a parallel partition of unity method (PPUM) to solve the nonstationary Navier-Stokes equations. Design/methodology/approach This paper opted for the nonstationary Navier-Stokes equations by using the finite element method and the partition of unity method. Findings This paper provides one efficient parallel algorithm which reaches the same accuracy as the standard Galerkin method but saves a lot of computational time. Originality/value In this paper, a PPUM is proposed for nonstationary Navier-Stokes. At each time step, the authors only need to s

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37

Gualtieri, Marco, Songhao Li, and Brent Pym. "The Stokes groupoids." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 739 (2018): 81–119. http://dx.doi.org/10.1515/crelle-2015-0057.

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Abstract We construct and describe a family of groupoids over complex curves which serve as the universal domains of definition for solutions to linear ordinary differential equations with singularities. As a consequence, we obtain a direct, functorial method for resumming formal solutions to such equations.

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38

Zhang, Tong, and Shunwei Xu. "Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations." Advances in Applied Mathematics and Mechanics 5, no. 1 (2013): 19–35. http://dx.doi.org/10.4208/aamm.11-m11178.

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AbstractIn this work, two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered. These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair. Moreover, the two-level stabilized finite volume methods involve solving one small Navier-Stokes problem on a coarse mesh with mesh size H, a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size or a large general Stokes equations for the Newton two-level stabilized finite volume me

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39

Weng, Zhifeng, and Yaoxiong Cai. "An Efficient Algorithm with Stabilized Finite Element Method for the Stokes Eigenvalue Problem." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/6362505.

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This paper provides a two-space stabilized mixed finite element scheme for the Stokes eigenvalue problem based on local Gauss integration. The two-space strategy contains solving one Stokes eigenvalue problem using theP1-P1finite element pair and then solving an additional Stokes problem using theP2-P2finite element pair. The postprocessing technique which increases the order of mixed finite element space by using the same mesh can accelerate the convergence rate of the eigenpair approximations. Moreover, our method can save a large amount of computational time and the corresponding convergenc

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40

Elsayed, E. M., Rasool Shah, and Kamsing Nonlaopon. "The Analysis of the Fractional-Order Navier-Stokes Equations by a Novel Approach." Journal of Function Spaces 2022 (April 5, 2022): 1–18. http://dx.doi.org/10.1155/2022/8979447.

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This article introduces modified semianalytical methods, namely, the Shehu decomposition method and q-homotopy analysis transform method, a combination of decomposition method, the q-homotopy analysis method, and the Shehu transform method to provide an approximate method analytical solution to fractional-order Navier-Stokes equations. Navier-Stokes equations are widely applied as models for spatial effects in biology, ecology, and applied sciences. A good agreement between the exact and obtained solutions shows the accuracy and efficiency of the present techniques. These results reveal that t

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41

Zani, Veronica, Roberto Pilot, Danilo Pedron, and Raffaella Signorini. "Near-Infrared Multiwavelength Raman Anti-Stokes/Stokes Thermometry of Titanium Dioxide." Chemosensors 12, no. 9 (2024): 191. http://dx.doi.org/10.3390/chemosensors12090191.

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The use of multiple wavelengths to excite Titanium Dioxide Raman scattering in the near-infrared was investigated for optical nanothermometry. Indeed, Raman spectroscopy can be a very interesting technique for this purpose, as it offers non-disruptive contactless measurements with a high spatial resolution, down to a few µm. A method based on the ratio between the anti-Stokes and Stokes peaks of Anatase Titanium Dioxide was proposed and tested at three different wavelengths, 785, 800 and 980 nm, falling into the first biological transparency window (BTW-I). Using a temperature-controller stage

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42

Chakraborty, Arnab, and HV Warrior. "Study of turbulent flow past a square cylinder using partially-averaged Navier–Stokes method in OpenFOAM." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 14 (2020): 2821–32. http://dx.doi.org/10.1177/0954406220910176.

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The present paper reports numerical simulation of turbulent flow over a square cylinder using a novel scale resolving computational fluid dynamics technique named Partially-Averaged Navier–Stokes (PANS), which bridges Reynolds-Averaged Navier–Stokes (RANS) with Direct Numerical Simulation (DNS) in a seamless manner. All stream-wise and wall normal mean velocity components, turbulent stresses behavior have been computed along the flow (streamwise) as well as in transverse (wall normal) direction. The measurement locations are chosen based on the previous studies so that results could be compare

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43

Yoshikawa, Yuki, and Shinsuke Shigeto. "A Simple Calibration Method of Anti-Stokes–Stokes Raman Intensity Ratios Using the Water Spectrum for Intracellular Temperature Measurements." Applied Spectroscopy 74, no. 10 (2020): 1295–96. http://dx.doi.org/10.1177/0003702820933908.

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Presented here is a facile and practical method for calibrating anti-Stokes–Stokes intensity ratios in low-frequency Raman spectra that is devised specifically for temperature measurements inside cells. The proposed method uses as an intensity standard the low-frequency Raman spectrum of liquid water, a major molecular component of cells, whose temperature is independently measured with a thermocouple. Rather than calibrating pixel intensities themselves, we obtain a correction factor at each Raman shift in the 20–200 cm−1 region by dividing the anti-Stokes–Stokes intensity ratio calculated th

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44

Qu, Wenzhen, and Wen Chen. "Solution of Two-Dimensional Stokes Flow Problems Using Improved Singular Boundary Method." Advances in Applied Mathematics and Mechanics 7, no. 1 (2015): 13–30. http://dx.doi.org/10.4208/aamm.2013.m359.

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AbstractIn this paper, an improved singular boundary method (SBM), viewed as one kind of modified method of fundamental solution (MFS), is firstly applied for the numerical analysis of two-dimensional (2D) Stokes flow problems. The key issue of the SBM is the determination of the origin intensity factor used to remove the singularity of the fundamental solution and its derivatives. The new contribution of this study is that the origin intensity factors for the velocity, traction and pressure are derived, and based on that, the SBM formulations for 2D Stokes flow problems are presented. Several

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45

Gordovskyy, M., S. Shelyag, P. K. Browning, and V. G. Lozitsky. "Using the Stokes V widths of Fe I lines for diagnostics of the intrinsic solar photospheric magnetic field." Astronomy & Astrophysics 633 (January 2020): A136. http://dx.doi.org/10.1051/0004-6361/201937027.

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Aims. The goal of this study is to explore a novel method for the solar photospheric magnetic field diagnostics using Stokes V widths of different magnetosensitive Fe I spectral lines. Methods. We calculate Stokes I and V profiles of several Fe I lines based on a one-dimensional photospheric model VAL C using the NICOLE radiative transfer code. These profiles are used to produce calibration curves linking the intrinsic magnetic field values with the widths of blue peaks of Stokes V profiles. The obtained calibration curves are then tested using the Stokes profiles calculated for more realistic

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46

Zhu, Xingwen, and Lixiang Zhang. "Smoothing Analysis of Distributive Red-Black Jacobi Relaxation for Solving 2D Stokes Flow by Multigrid Method." Mathematical Problems in Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/572198.

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Smoothing analysis process of distributive red-black Jacobi relaxation in multigrid method for solving 2D Stokes flow is mainly investigated on the nonstaggered grid by using local Fourier analysis (LFA). For multigrid relaxation, the nonstaggered discretizing scheme of Stokes flow is generally stabilized by adding an artificial pressure term. Therefore, an important problem is how to determine the zone of parameter in adding artificial pressure term in order to make stabilization of the algorithm for multigrid relaxation. To end that, a distributive red-black Jacobi relaxation technique for t

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47

KRELL, STELLA. "FINITE VOLUME METHOD FOR GENERAL MULTIFLUID FLOWS GOVERNED BY THE INTERFACE STOKES PROBLEM." Mathematical Models and Methods in Applied Sciences 22, no. 05 (2012): 1150025. http://dx.doi.org/10.1142/s0218202511500254.

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We study the approximation of solutions to the steady Stokes problem with a discontinuous viscosity coefficient (interface Stokes problem) in the 2D "Discrete Duality Finite Volume" (DDFV) framework. In order to take into account the discontinuities of the viscosity and to prevent consistency defect in the scheme, we propose to modify the definition of the numerical fluxes on the edges of the mesh where the discontinuity occurs. We first show how to design our modified scheme, called m-DDFV, and we analyze its well-posedness and its convergence properties. Finally, we provide numerical results

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48

Tan, Zhijun, K. M. Lim, and B. C. Khoo. "An Implementation of MAC Grid-Based IIM-Stokes Solver for Incompressible Two-Phase Flows." Communications in Computational Physics 10, no. 5 (2011): 1333–62. http://dx.doi.org/10.4208/cicp.161009.220211a.

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AbstractIn this paper, a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with interfaces. The velocity components along the interface are introduced as two augmented variables and the resulting augmented equation is then solved by the GMRES method. The augmented variables and /or the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines and are then applied to the fluid through the jump conditions.

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49

Liu, An, Yuan Li, and Rong An. "Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions." Advances in Applied Mathematics and Mechanics 8, no. 6 (2016): 932–52. http://dx.doi.org/10.4208/aamm.2014.m595.

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AbstractIn this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the H1 norm and the pressure in the L2 norm are derived. Finally, the nume

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50

Solomon, Khmelnik. "The Emergence Mechanism and Calculation Method of Turbulent Flows." Papers of Independent Authors, ISSN 2225-6717, 2013 22 (February 26, 2013): 14–27. https://doi.org/10.5281/zenodo.3980773.

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An explanation is offered of the mechanism of turbulent flows emergence, based of the Maxwell-like gravitation equations, updated  after some known experiments. It is shown that the moving molecules of flowing liquid interact  like electrical charges. The forces of such interaction can be calculated and included to the Navier-Stokes equations as mass forces. Navier-Stocks equations complemented by these forces     become equations of hydrodynamics for turbulent flow. For the calculations of turbulent flows the known methods of Navier-Stokes equations solution may

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