On Using a Fast Multipole Method-based Poisson Solver in anApproximate Projection Method

Williams, Sarah A. ; Almgren, Ann S. ; Puckett, E. Gerry

Lawrence Berkeley National Laboratory

关键词: Multipoles Projection Method Fast Multipole Method Approximateprojection;    Projection Method Fast Multipole Method Approximateprojection;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Approximations;    Laplacian;   

DOI  :  10.2172/898942
RP-ID  :  LBNL--59934
RP-ID  :  DE-AC02-05CH11231
RP-ID  :  898942

美国|英语

来源: UNT Digital Library

【 摘 要 】

Approximate projection methods are useful computational tools for solving the equations of time-dependent incompressible flow.Inthis report we will present a new discretization of the approximate projection in an approximate projection method. The discretizations of divergence and gradient will be identical to those in existing approximate projection methodology using cell-centered values of pressure; however, we will replace inversion of the five-point cell-centered discretization of the Laplacian operator by a Fast Multipole Method-based Poisson Solver (FMM-PS).We will show that the FMM-PS solver can be an accurate and robust component of an approximation projection method for constant density, inviscid, incompressible flow problems. Computational examples exhibiting second-order accuracy for smooth problems will be shown. The FMM-PS solver will be found to be more robust than inversion of the standard five-point cell-centered discretization of the Laplacian for certain time-dependent problems that challenge the robustness of the approximate projection methodology.