A staggered grid-based explicit jump immersed interface method for two-dimensional Stokes flows

International Journal for Numerical Methods in Fluids

Volumn 57, Issue 10, 2008, Pages 1527-1543

  Rutka, Vita ^a  

^a UNIVERSITY OF KONSTANZ   (Germany)

Author keywords

Discontinuous solutions; Finite differences; Interface problem; Staggered grid; Stokes equations

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; FAST FOURIER TRANSFORMS; FINITE DIFFERENCE METHOD; FOURIER TRANSFORMS; INITIAL VALUE PROBLEMS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL ANALYSIS; POISSON EQUATION; TWO DIMENSIONAL;

COMPUTATIONAL DOMAIN; CONJUGATE GRADIENT; DISCONTINUOUS SOLUTIONS; FINITE DIFFERENCES; FINITE DIFFERENCING; FIRST ORDERS; FOURIER; IMMERSED INTERFACE METHOD; INTERFACE PROBLEM; POISSON SOLVERS; PRESSURE EQUATIONS; PRESSURE VARIABLES; RECTANGULAR DOMAINS; SECOND-ORDER CONVERGENCE; STAGGERED GRID; STAGGERED GRIDS; STOKES EQUATIONS; STOKES FLOWS; SUB-PROBLEMS;

CONJUGATE GRADIENT METHOD;

EID: 48749085072     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1694     Document Type: Article

References (28)

1. Galdi GP. An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Volume I: Linearised Steady Problems (2nd edn). Springer: Berlin, 1998.
2. Temam R. Navier-Stokes Equations: Theory and Numerical Analysis. North-Holland: Amsterdam, 1977.
3. Junk M, Illner R. A new derivation of Jeffery's equation. Journal of Mathematical Fluid Mechanics 2006; 8:1-34.
4. Triebsch LK. A discrete boundary integral approach to 3D cell problems with complex geometry. Master's Thesis, University of Kaiserslautern, August 2001.
5. Wiegmann A. Computation of the permeability of porous materials from their microstructure by FFF-Stokes. Technical Report 129, Fraunhofer ITWM, Kaiserslautern, 2007.
6. LeVeque RJ, Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM Journal on Numerical Analysis 1994; 31:1019-1044.
7. LeVeque RJ, Li Z. Immersed interface methods for Stokes flow with elastic boundaries or surface tension. SIAM Journal on Scientific Computing 1997; 18(3):709-735.
8. Li Z, Lubkin SR. Numerical analysis of interfacial two-dimensional Stokes flow with discontinuous viscosity and variable surface tension. International Journal for Numerical Methods in Fluids 2001; 37:525-540.
9. Li Z, Ito K, Lai M-C. An augmented approach for Stokes equations with a discontinuous viscosity and singular forces. Technical Report CRSC-TR04-23, North Carolina State University, 2004.
10. Li Z, Wan X, Ito K, Lubkin S. An augmented pressure boundary condition for a Stokes flow with a non-slip boundary condition. Communications in Computational Physics 2006; 1:874-885.
11. Wiegmann A. The explicit-jump immersed interface method and interface problems for differential equations. Ph.D. Thesis, University of Washington, 1998.
12. Wiegmann A, Bube KP. The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions. SIAM Journal on Numerical Analysis 2000; 37(3):827-862.
13. Fletcher CAJ. Computational Techniques for Fluid Dynamics, Volume II, Specific Techniques for Different Flow Categories. Springer: Berlin, 1988.
14. Strikwerda JC. Finite difference methods for the Stokes and Navier-Stokes equations. SIAM Journal on Scientific and Statistical Computing 1984; 5:56-68.
15. Shin D, Strikwerda JC. Inf-Sup conditions for finite difference approximations of the Stokes equations. Journal of Australian Mathematical Society Series B 1997; 39:121-134.
16. Shin D, Strikwerda JC. Fast solvers for finite difference approximations for the Stokes and Navier-Stokes equations. Journal of Australian Mathematical Society, Series B 1996; 38:274-290.
17. Wiegmann A. Fast Poisson, fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds. Technical Report LBNL-43565, Lawrence Berkeley National Laboratory, Berkeley, CA, June 1999.
18. Iliash Y, Rossi T, Toivanen J. Two iterative methods for solving the Stokes problem. Technical Report 2, Laboratory of Scientific Computing, Department of Mathematics, University of Jyvaskyla, 1993.
19. Sethian JA, Wiegmann A. Structural boundary design via level set and explicit jump immersed interface methods. Journal of Computational Physics 2000; 163(2):489-528.
20. Rutka V. Immersed interface methods for elliptic boundary value problems. Ph.D. Thesis, TU Kaiserslautern, 2005.
21. Li Z. The immersed interface method - a numerical approach for partial differential equations with interfaces. Ph.D. Thesis, University of Washington, 1994.
22. Iliev O, Tiwari S. A generalized (meshfree) finite difference discretization for elliptic interface problems. In Lecture Notes in Computer Sciences, vol. 2542/2003, Dimov I, Lirkov I, Margenov S, Zlatev Z (eds). Springer: Berlin, 2003; 488-497.
23. Kelley CT. Iterative Methods for Linear and Nonlinear Equations. SIAM: Philadelphia, PA, 1995.
24. Mayo A. The fast solution of Poisson's and the biharmonic equations on irregular regions. SIAM Journal on Numerical Analysis 1984; 21(2):285-299.
25. Wiegmann A. The explicit jump immersed interface method and integral formulas. Technical Report LBNL-43566, Lawrence Berkeley National Laboratory, Berkeley, CA, June 1999.
26. Biros G, Ying L, Zorin D. A fast solver for Stokes equations with distributed forces in complex geometries. Journal of Computational Physics 2003; 193:317-348.
27. Wannier GH. A contribution to the hydrodynamics of lubrication. Quarterly of Applied Mathematics 1950; 8(1):1-32.
28. Calhoun D. A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular domains. Journal of Computational Physics 2002; 176(2):231-275.