A Novel High-Order Accurate Compact Stencil Poisson Solver: Application to Cavity Flows

Author:

San Omer1

Affiliation:

1. Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg, Virginia 24061, USA

Abstract

In this paper, a fourth-order compact stencil finite difference scheme is developed for solving elliptic Poisson equation. The scheme presented here is based on a modular approach using a linear combination of compact difference algorithms that results in different discrete formulation than the well-known Mehrstellen scheme. An adjoint optimal V-cycle multigrid (MG) iterative solver are developed, implemented, and tested. The robustness of the adjoint Poisson solver is illustrated by solving incompressible Navier–Stokes equations in vorticity-stream function formulation. Using a fully implicit factorized delta-scheme algorithm for the time integration, benchmark quality results of the cavity flow problem are presented and compared to existing literature for various Reynolds numbers.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mechanical Engineering,Mechanics of Materials,General Materials Science

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