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

Technical Report · Tue Mar 28 04:00:00 UTC 2006

DOI:https://doi.org/10.2172/898942· OSTI ID:898942

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

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.

• Research Organization: Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director. Office of Science. Office of AdvancedScientific Computing Research
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 898942
• Report Number(s): LBNL--59934; BnR: KJ0101010
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACCURACY
APPROXIMATIONS
INCOMPRESSIBLE FLOW
LAPLACIAN
MULTIPOLES
projection method fast multipole method approximateprojection