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

Abstract

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.

Authors:
; ;
Publication Date:
Research Org.:
Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
Sponsoring Org.:
USDOE Director. Office of Science. Office of AdvancedScientific Computing Research
OSTI Identifier:
898942
Report Number(s):
LBNL-59934
R&D Project: K11001; BnR: KJ0101010; TRN: US200708%%143
DOE Contract Number:  
DE-AC02-05CH11231
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ACCURACY; APPROXIMATIONS; INCOMPRESSIBLE FLOW; LAPLACIAN; MULTIPOLES; projection method fast multipole method approximateprojection

Citation Formats

Williams, Sarah A, Almgren, Ann S, and Puckett, E Gerry. On Using a Fast Multipole Method-based Poisson Solver in anApproximate Projection Method. United States: N. p., 2006. Web. doi:10.2172/898942.
Williams, Sarah A, Almgren, Ann S, & Puckett, E Gerry. On Using a Fast Multipole Method-based Poisson Solver in anApproximate Projection Method. United States. https://doi.org/10.2172/898942
Williams, Sarah A, Almgren, Ann S, and Puckett, E Gerry. Tue . "On Using a Fast Multipole Method-based Poisson Solver in anApproximate Projection Method". United States. https://doi.org/10.2172/898942. https://www.osti.gov/servlets/purl/898942.
@article{osti_898942,
title = {On Using a Fast Multipole Method-based Poisson Solver in anApproximate Projection Method},
author = {Williams, Sarah A and Almgren, Ann S and Puckett, E Gerry},
abstractNote = {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.},
doi = {10.2172/898942},
url = {https://www.osti.gov/biblio/898942}, journal = {},
number = ,
volume = ,
place = {United States},
year = {2006},
month = {3}
}