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

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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 ... continued below

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Williams, Sarah A.; Almgren, Ann S. & Puckett, E. Gerry March 28, 2006.

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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.

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  • Report No.: LBNL--59934
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.2172/898942 | External Link
  • Office of Scientific & Technical Information Report Number: 898942
  • Archival Resource Key: ark:/67531/metadc883861

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  • March 28, 2006

Added to The UNT Digital Library

  • Sept. 22, 2016, 2:13 a.m.

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  • Sept. 22, 2017, 3:08 p.m.

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Williams, Sarah A.; Almgren, Ann S. & Puckett, E. Gerry. On Using a Fast Multipole Method-based Poisson Solver in anApproximate Projection Method, report, March 28, 2006; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc883861/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.