Moving mesh finite element methods for the incompressible Navier-Stokes equations

SIAM Journal on Scientific Computing

Volumn 26, Issue 3, 2005, Pages 1036-1056

  Di, Yana ^a   Li, Ruo ^a   Tang, Tao ^b   Zhang, Pingwen ^a  

^a PEKING UNIVERSITY   (China)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

Divergence free preserving interpolation; Incompressible flow; Moving mesh method; Navier Stokes equations

Indexed keywords

ALGORITHMS; COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; INTERPOLATION; MAPPING; REYNOLDS NUMBER; SHEAR FLOW;

DIVERGENCE FREE PRESERVING INTERPOLATION; MESH MOVING ALGORITHMS; MOVING MESH METHOD; SHEAR LAYERS;

NAVIER STOKES EQUATIONS;

EID: 19744364449     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/030600643     Document Type: Article

References (36)

1. J. BELL, P. COLELLA, AND H. GLAZ, A second-order projection method for the incompressible Navier-Stokes equations, J. Comput. Phys., 85 (1989), pp. 257-283.
2. J. U. BRACKBILL AND J. S. SALTZMAN, Adaptive zoning for singular problems in two dimensions, J. Comput. Phys., 46 (1982), pp. 342-368.
3. D. L. BROWN AND M. L. MINION, Performance of under-resolved two-dimensional incompressible flow simulations, J. Comput. Phys., 122 (1995), pp. 165-183.
4. A. BRUGER, B. GUSTAFSSON, P. LOTSTEDT, AND J. NILSSON, High Order Accurate Solution of the Incompressible Navier-Stokes Equations, J. Comput. Phys., to appear, 2004.
5. W. M. CAO, W. Z. HUANG, AND R. D. RUSSELL, An r-adaptive finite element method based upon moving mesh PDEs, J. Comput. Phys., 149 (1999), pp. 221-244.
6. H. D. CENICEROS AND T. Y. HOU, An efficient dynamically adaptive mesh for potentially singular solutions, J. Comput. Phys., 172 (2001), pp. 609-639.
7. A. J. CHORIN, Numerical solution of the Navier-Stokes equations, Math. Comp., 22 (1968), pp. 745-762.
8. A. S. DVINSKY, Adaptive grid generation from harmonic maps on Riemannian manifolds, J. Comput. Phys., 95 (1991), pp. 450-476.
9. W. E AND C.-W. SHU, A numerical resolution study of high order essentially nonoscillatory schemes applied to incompressible flows, J. Comput. Phys., 110 (1994), pp. 39-46.
10. W. E AND C.-W. SHU, Small-scale structures in Boussinesq convection, Phys. Fluids, 6 (1994), pp. 49-58.
11. W. E AND J.-G. LIU, Essentially compact schemes for unsteady viscous incompressible flows, J. Comput. Phys., 126 (1996), pp. 122-138.
12. H. C. ELMAN, Preconditioning for the steady-state Navier-Stokes equations with low viscosity, SIAM J. Sci. Comput., 20 (1999), pp. 1299-1316.
13. V. GIRAULT AND P.-A. RAVIART, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Springer-Verlag, Berlin, 1986.
14. M. GUNZBURGER, Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice and Algorithms, Academic Press, Boston, 1989.
15. R. HAMILTON, Harmonic Maps of Manifolds with Boundary, Lecture Notes in Math. 471, Springer-Verlag, New York, 1975.
16. C. W. HIRT, A. A. AMSDEN, AND J. L. COOK, An arbitrary Lagrangian-Eulerian computing method for all flow speeds, J. Comput. Phys., 14 (1974), pp. 227-253.
17. W. HUANG AND W. SUN, Variational mesh adaptation. II. Error estimates and monitor functions, J. Comput. Phys., 184 (2003), pp. 619-648.
18. T. J. R. HUGHES, W. K. LIU, AND T. K. ZIMMERMANN, Lagrangian-Eulerian finite element formulation for incompressible viscous flows, Comput. Methods Appl. Mech. Engrg., 29 (1981), pp. 329-349.
19. D. KAY, D. LOGHIN, AND A. WATHEN, A preconditioner for the steady-state Navier-Stokes equations, SIAM J. Sci. Comput., 24 (2002), pp. 237-256.
20. R. J. LEVEQUE, High-resolution conservative algorithms for advection in incompressible flow, SIAM J. Numer. Anal., 33 (1996), pp. 627-665.
21. M. LI, T. TANG, AND B. FORNBERG, A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations, Internat. J. Numer. Methods Fluids, 20 (1995), pp. 1137-1151.
22. R. LI, T. TANG, AND P. W. ZHANG, Moving mesh methods in multiple dimensions based on harmonic maps, J. Comput. Phys., 170 (2001), pp. 562-588.
23. R. LI, T. TANG, AND P. W. ZHANG, A moving mesh finite element algorithm for singular problems in two and three space dimensions, J. Comput. Phys., 177 (2002), pp. 365-393.
24. J.-G. LIU AND C.-W. SHU, A high-order discontinuous Galerkin method for 2D incompressible flows, J. Comput. Phys., 160 (2000), pp. 577-596.
25. J. LOPEZ AND J. SHEN, An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries. I. Axisymmetric cases, J. Comput. Phys., 139 (1998), pp. 308-326.
26. R. KUPFERMAN AND E. TADMOR, A fast, high resolution, second-order central scheme for incompressible flows, Proc. Natl. Acad. Sci. U.S.A., 94 (1997), pp. 4848-4852.
27. H. NESSYAHU AND E. TADMOR, Nonoscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87 (1990), pp. 408-463.
28. J.-F. REMACLE, J. E. FLAHERTY, AND M. S. SHEPHARD, An adaptive discontinuous Galerkin technique with an orthogonal basis applied to compressible flow problems, SIAM Rev., 45 (2003), pp. 53-72.
29. Y. SAAD, Iterative Methods for Sparse Linear Systems, PWS Publishing, Boston, 1996.
30. R. SCHOEN AND S. T. YAU, On univalent harmonic maps between surfaces, Invent. Math., 44 (1978), pp. 265-278.
31. Z.-J. TAN, Z.-R. ZHANG, Y.-Q. HUANG, AND T. TANG, Moving mesh methods with locally varying time steps, J. Comput. Phys., 200 (2004), pp. 347-367.
32. H. Z. TANG AND T. TANG, Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal., 41 (2003), pp. 487-515.
33. H. Z. TANG, T. TANG, AND P. W. ZHANG, An adaptive mesh redistribution method for nonlinear Hamilton-Jacobi equations in two- and three-dimensions, J. Comput. Phys., 188 (2003), pp. 543-572.
34. T. E. TEZDUYAR, M. BEHR, AND J. LIOU, A new strategy for finite element computations involving moving boundaries and interfaces - the deforming-spatial-domain/space-time procedure. I. The concept and the preliminary tests, Comput. Methods Appl. Mech. Engrg., 94 (1992), pp. 339-351.
35. H. A. VAN DER VORST, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 631-644.
36. A. WINSLOW, Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh, J. Comput. Phys., 1 (1967), pp. 149-172.