[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | All | Home ]

Preprint 2015-002

A fixed grid, shifted stencil scheme for inviscid fluid-particle interaction

John D. Towers

Abstract: This paper presents a finite volume scheme for the scalar one-dimensional fluid-particle interaction model proposed in [F. Lagoutière, N. Seguin, T. Takahashi. A simple 1D model of inviscid fluid-solid interaction. J. Differential Equations, 245: 3503–3544, 2008; MR2460032]. When devising a finite volume scheme for this model, one difficulty that arises is how to deal with the moving source term in the PDE while maintaining a fixed grid. The fixed grid requirement comes from the ultimate goal of accommodating two or more particles. The finite volume scheme that we propose addresses the moving source term in a novel way. We use a modified computational stencil, with the lower part of the stencil shifted during those time steps when the particle crosses a mesh point. We then employ an altered convective flux to compensate the stencil shifts. The resulting scheme uses a fixed grid, preserves total momentum, and enforces several stability properties in the single-particle case. The single-particle scheme is easily extended to multiple particles by a splitting method.

Paper:
Available as PDF (414 Kbytes).
Author(s):
John D. Towers
Submitted by:
; 2015-01-23.