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An efficient second‐order accurate cut‐cell method for solving the variable coefficient Poisson equation with jump conditions on irregular domains
Author(s) -
Ji Hua,
Lien FueSang,
Yee Eugene
Publication year - 2006
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1199
Subject(s) - discretization , poisson's equation , piecewise , mathematics , stencil , jump , solver , multigrid method , variable (mathematics) , mathematical analysis , poisson distribution , domain (mathematical analysis) , order of accuracy , partial differential equation , mathematical optimization , method of characteristics , statistics , physics , quantum mechanics , computational science
Abstract A numerical method is presented for solving the variable coefficient Poisson equation on a two‐dimensional domain in the presence of irregular interfaces across which both the variable coefficients and the solution itself may be discontinuous. The approach involves using piecewise cubic splines to represent the irregular interface, and applying this representation to calculate the volume and area of each cut cell. The fluxes across the cut‐cell faces and the interface faces are evaluated using a second‐order accurate scheme. The deferred correction approach is used, resulting in a computational stencil for the discretized Poisson equation on an irregular (complex) domain that is identical to that obtained on a regular (simple) domain. In consequence, a highly efficient multigrid solver based on the additive correction multigrid (ACM) method can be applied to solve the current discretized equation system. Several test cases (for which exact solutions to the variable coefficient Poisson equation with and without jump conditions are known) have been used to evaluate the new methodology for discretization on an irregular domain. The numerical solutions show that the new algorithm is second‐order accurate as claimed, even in the presence of jump conditions across an interface. Copyright © 2006 John Wiley & Sons, Ltd.