A fixed grid, shifted stencil scheme for inviscid fluid-particle interaction. (English) Zbl 06638248

Towers, John D.

Appl. Numer. Math. 110, 26-40 (2016).

Summary: This paper presents a finite volume scheme for a scalar one-dimensional fluid-particle interaction model. 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.

MSC:

65	Numerical analysis

Keywords:

solid-fluid interaction; Burgers equation; finite volume scheme; singular source term; moving mesh scheme; well-balanced scheme; moving interface; PDE-ODE coupling

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