A general fictitious domain method with immersed jumps and multilevel nested structured meshes

作者: Isabelle Ramière , Philippe Angot , Michel Belliard

DOI: 10.1016/J.JCP.2007.01.026

关键词: DiscretizationRobin boundary conditionDirichlet problemFinite volume methodBoundary value problemFictitious domain methodMathematicsMathematical analysisDirichlet conditionsNeumann boundary condition

摘要: This study addresses a new fictitious domain method for elliptic problems in order to handle general and possibly mixed embedded boundary conditions (E.B.C.): Robin, Neumann Dirichlet on an immersed interface. The main interest of this is use simple structured meshes, uniform Cartesian nested grids, which do not generally fit the interface but define approximate one. A cell-centered finite volume scheme with non-conforming mesh derived solve set equations additional algebraic transmission linking both flux solution jumps through Hence, local correction devised take account relative surface ratios each control Robin or condition. Then, numerical conserves first-order accuracy respect step. opens way combine E.B.C. multilevel refinement solver increase precision vicinity Such very efficient: L^2- L^~-norm errors vary like O(h"l"*) where h"l"* grid step finest level around until residual discretization error non-refined zone reached. results reported here convection-diffusion Dirichlet, (Dirichlet Robin) confirm expected as well performances present method.

参考文章(36)
K. Khadra, Ph. Angot, J. P. Caltagirone, P. Morel, Concept de zoom adaptatif en architecture multigrille locale ; étude comparative des méthodes L.D.C., F.A.C. et F.I.C. Mathematical Modelling and Numerical Analysis. ,vol. 30, pp. 39- 82 ,(1996) , 10.1051/M2AN/1996300100391
Zhilin Li, AN OVERVIEW OF THE IMMERSED INTERFACE METHOD AND ITS APPLICATIONS Taiwanese Journal of Mathematics. ,vol. 7, pp. 1- 49 ,(2003) , 10.11650/TWJM/1500407515
Robert Eymard, Thierry Gallouët, Raphaèle Herbin, Finite Volume Methods Handbook of Numerical Analysis. ,vol. 7, pp. 713- 1018 ,(2000) , 10.1016/S1570-8659(00)07005-8
Peter Schwartz, Michael Barad, Phillip Colella, Terry Ligocki, A Cartesian grid embedded boundary method for the heat equation and Poisson's equation in three dimensions Journal of Computational Physics. ,vol. 211, pp. 531- 550 ,(2006) , 10.1016/J.JCP.2005.06.010
Isabelle Ramière, Philippe Angot, Michel Belliard, A Fictitious domain approach with spread interface for elliptic problems with general boundary conditions Computer Methods in Applied Mechanics and Engineering. ,vol. 196, pp. 766- 781 ,(2007) , 10.1016/J.CMA.2006.05.012
Decheng Wan, Stefan Turek, Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method International Journal for Numerical Methods in Fluids. ,vol. 51, pp. 531- 566 ,(2006) , 10.1002/FLD.1129
Philippe Angot, Jean-Claude Latché, Xavier Coré, A multilevel local mesh refinement projection method for low Mach number flows Mathematics and Computers in Simulation. ,vol. 61, pp. 477- 488 ,(2003) , 10.1016/S0378-4754(02)00140-4
P. W. Hemker, W. Hoffman, M. H. Van Raalte, Discontinuous Galerkin discretization with embedded boundary conditions. Dedicated to Raytcho Lazarov. Computational methods in applied mathematics. ,vol. 3, pp. 135- 158 ,(2003) , 10.2478/CMAM-2003-0010
Patrick Joly, Leïla Rhaouti, Domaines fictifs, éléments finis H(div) et condition de Neumann: le problème de la condition inf-sup Comptes Rendus de l'Académie des Sciences - Series I - Mathematics. ,vol. 328, pp. 1225- 1230 ,(1999) , 10.1016/S0764-4442(99)80444-3
V. Girault, R. Glowinski, Error Analysis of a Fictitious Domain Method Applied to a Dirichlet Problem Japan Journal of Industrial and Applied Mathematics. ,vol. 12, pp. 487- 514 ,(1995) , 10.1007/BF03167240