NUMERICAL IMPLEMENTATION OF THE TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATION |
CHOI, YONGHO
(DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
JEONG, DARAE (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) LEE, SEUNGGYU (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) KIM, JUNSEOK (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) |
1 | A.S. Almgren, J.B. Bell, and W.G. Szymczak, A numerical method for the incompressible Navier-Stokes equations based on an approximate projection, SIAM J. Sci. Comput., 17(2) (1996), 358-369. DOI |
2 | V. Barbu, Partial Differential Equations and Boundary Value Problems, Kluwer, Dordrecht, 1998. |
3 | J.B. Bell, P. Colella, and H.M. Glaz, A second-order projection method for the incompressible Navier-Stokes equations, J. Comput. Phys., 85(2) (1989), 257-283. DOI ScienceOn |
4 | A.J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comput., 22 (1968), 745-762. DOI ScienceOn |
5 | A.J. Chorin, J.E. Marsden, and J.E. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer, New York, 1990. |
6 | M.O. Deville, P.F. Fischer, and E.H. Mund, High-order Methods for Incompressible Fluid Flow, 9 Cambridge University Press, 2002. |
7 | J.A. Escobar-Vargas, P.J. Diamessis, and C.F. Van Loan, The numerical solution of the pressure Poisson equation for the incompressible Navier-Stokes equations using a quadrilateral spectral multidomain penalty method, J. Comp. Phys.(submitted) (2011). |
8 | S.R. Fulton, P.E. Ciesielski, and W.H. Schubert, Multigrid methods for elliptic problems: A review, Mon. Weather Rev., 114(5) (1986), 943-959. DOI |
9 | M. Griebel, T. Dornseifer, and T. Neunhoeffer, Numerical Simulation in Fluid Dynamics: a Practical Introduction, SIAM, Philadelphia, 1997. |
10 | J.L. Guermond, P. Minev, and J. Shen, An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg., 195(44) (2006), 6011-6045. DOI ScienceOn |
11 | J.L. Guermond and J. Shen, Quelques resultats nouveaux sur les methodes de projection, C. R. Acad. Sci. Paris, 333(12) (2001), 1111-1116. DOI ScienceOn |
12 | J.L. Guermond and J. Shen, Velocity-correction projection methods for incompressible flows, SIAM J. Numer. Anal., 41(1) (2003), 112-134. DOI ScienceOn |
13 | T. Guillet and R. Teyssier, A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries, J. Comput. Phys., 230(12) (2011), 4756-4771. DOI ScienceOn |
14 | M.M. Gupta and J. Zhang, High accuracy multigrid solution of the 3D convection-diffusion equation, Appl. Math. Comput., 113(2) (2000), 249-274. DOI ScienceOn |
15 | K. Gustafson and K. Halasi, Cavity flow dynamics at higher Reynolds number and higher aspect ratio, J. Comput. Phys., 70(2) (1987), 271-283. DOI ScienceOn |
16 | F.H. Harlow and J.E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8(12) (1965), 2182-2189. DOI |
17 | G.E. Karniadakis, M. Israeli, and S.A. Orszag, High-order splitting methods for the incompressible Navier-Stokes equations, J. Comput. Phys., 97(2) (1991), 414-443. DOI ScienceOn |
18 | J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59(2) (1985), 308-323. DOI ScienceOn |
19 | L. Landau and E.M. Lifshitz, Fluid mechanics, Course of Theoretical Physics 6 (2nd revised ed.), Pergamon Press (1987), 552. |
20 | G. Markham and M.V. Proctor, Modifications to the two-dimensional incompressible fluid flow code ZUNI to provide enhanced performance, CEGB Report TPRD/L/0063/M82, 1983. |
21 | S.A. Orszag, M. Israeli, and M. Deville, Boundary conditions for incompressible flows, J. Sci. Comput., 1(1) (1986), 75-111. DOI |
22 | R. Peyret and T.D. Taylor, Computational Methods for Fluid Flow, Springer-Verlag, New York, 1985. |
23 | P.J. Roache, Computational Fluid Dynamics, Hermosa publishers, Albuquerque, 1972. |
24 | R. Temam, Sur l'approximation de la solution des equations de Navier-Stokes par la methode des pas fractionnaires (II), Arch. Rational Mech. Anal., 33(5) (1969), 377-385. DOI |
25 | L.J.P. Timmermans, P.D. Minev, and F.N. Van De Vosse, An approximate projection scheme for incompressible flow using spectral elements, Int. J. Numer. Meth. Fluids, 22(7) (1996), 673-688. DOI |
26 | U. Trottenberg, C.W. Oosterlee, and A. Schuller, Multigrid, Academic press, London, 2000. |
27 | J.J.I.M. Van Kan, A second-order accurate pressure-correction scheme for viscous incompressible flow, SIAM J. Sci. Comput., 7(3) (1986), 870-891. DOI |
28 | J.E. Welch, F.H. Harlow, J.P. Shannon, and B.J. Daly, The MAC (Marker-and-Cell) Method - A computing technique for solving viscous, incompressible, transient fluid-flow problems involving free surfaces, Los Alamos Scientific Laboratory Report LA-3425, University of California, Los Alamos, 1966. |
29 | Q. Zhang, A fourth-order approximate projection method for the incompressible Navier-Stokes equations on locally-refined periodic domains, Appl. Numer. Math., 77 (2014), 16-30. DOI ScienceOn |