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

  • Author(s): Williams, Sarah A.
  • Almgren, Ann S.
  • Puckett, E. Gerry
  • et al.
Abstract

Approximate projection methods are useful computational tools for solving the equations of time-dependent incompressible flow.In this 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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