A Cartesian grid embedded boundary method for the heat equation and Poisson's equation in three dimensions

Journal of Computational Physics

Volumn 211, Issue 2, 2006, Pages 531-550

  Schwartz, Peter ^a,b   Barad, Michael ^a   Colella, Phillip ^a,b   Ligocki, Terry ^b  

^a University of California   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

Heat equation; Multigrid methods; Poisson equation

Indexed keywords

FINITE VOLUME METHOD; HEAT TRANSFER;

ALGORITHM FOR SOLVING; CARTESIAN GRID; EMBEDDED BOUNDARY; EMBEDDED BOUNDARY METHODS; FINITE VOLUME DISCRETIZATIONS; HEAT EQUATION; IRREGULAR DOMAINS; MULTIGRID METHODS; SECOND ORDERS; THREE DIMENSIONS;

POISSON EQUATION;

EID: 26944447097     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.06.010     Document Type: Article

References (18)

1. Ann S. Almgren Thomas Buttke Phillip Colella A fast adaptive vortex method in three dimensions J. Comput. Phys. 113 1994 177-200
2. M. Barad P. Colella A fourth order accurate local refinement method for Poisson's equation J. Comput. Phys. 209 1 2005 1-18
3. P. Colella, D.T. Graves, B.J. Keen, D. Modiano, A Cartesian grid embedded boundary method for hyperbolic conservation laws, J. Comput. Phys., in press.
4. P. Colella Volume-of-fluid methods for partial differential equations in: E.F. Toro (eds) Godunov Methods: Theory and Applications 2001 Kluwer Academic/Plenum Publishers New York 3
5. Frederic Gibou Ronald Fedkiw A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains with applications to the Stefan problem J. Comput. Phys. 202 2005 577-601
6. Frederic Gibou Ronald Fedkiw Li-Tien Cheng Myungjoo Kang A second-order-accurate symmetric discretization of the Poisson equation on irregular domains J. Comput. Phys. 176 2002 205-227
7. H. Johansen P. Colella A Cartesian grid embedded boundary method for Poisson's equation on irregular domains J. Comput. Phys. 147 2 1998 60-85 December
8. Hans Svend Johansen, Cartesian Grid Embedded Boundary Finite Difference Methods for Elliptic and Parabolic Partial Differential Equations on Irregular Domains. Ph.D. Thesis, University of California, Berkeley, 1997.
9. M.P. Kirkpatrick S.W. Armfield J.H. Kent A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid J. Comput. Phys. 184 2003 1-36
10. Z. Li A fast iterative method for elliptic interface problems SIAM J. Numer. Anal. 35 1998 230
11. Peter McCorquodale Phillip Colella David P. Groteb Jean-Luc Vay A node-centered local refinement algorithm for Poisson's equation in complex geometries J. Comput. Phys. 201 2004 34-60
12. P. McCorquodale P. Colella H. Johansen A Cartesian grid embedded boundary method for the heat equation on irregular domains J. Comput. Phys. 173 2001 620-635
13. W.F. Noh Cel: A time-dependent, two-space-dimension, coupled Eulerian-Lagrange code SIAM J. Numer. Anal. 3 1964
14. Stephane Popinet Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries J. Comput. Phys. 190 2003 572-600
15. G.H. Shortley R. Weller The numerical solution of Laplace's equation J. Appl. Phys. 9 1938 334-344
16. 0-stable methods for the heat equation with time-dependent boundary conditions Adv. Comput. Math. 6 1996 333-352
17. H.S. Udaykumar R. Mittal P. Rampunggoon A. Khanna A sharp interface Cartesian grid method for simulating flows with complex moving boundaries J. Comput. Phys. 174 2001 345-380
18. David P. Young Robin G. Melvin Michael B. Bieterman Forrester T. Johnson Satish S. Samant John E. Bussoletti A locally refined rectangular grid finite element method: Application to computational fluid dynamics and computational physics J. Comput. Phys. 92 1991 1-66