High-order finite-volume methods on locally-structured grids

Phillip  Colella

doi:10.3934/dcds.2016.36.4247

Article Contents

2016, Volume 36, Issue 8: 4247-4270. Doi: 10.3934/dcds.2016.36.4247

This issue Previous Article Sampling, feasibility, and priors in data assimilation Next Article Hyperbolic balance laws with relaxation

High-order finite-volume methods on locally-structured grids

Phillip Colella^1,

1.
Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

Received: June 2015

Revised: December 2015

Published: May 2017

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Abstract

We present an approach to designing arbitrarily high-order finite-volume spatial discretizations on locally-rectangular grids. It is based on the use of a simple class of high-order quadratures for computing the average of fluxes over faces. This approach has the advantage of being a variation on widely-used second-order methods, so that the prior experience in engineering those methods carries over in the higher-order case. Among the issues discussed are the basic design principles for uniform grids, the extension to locally-refined nest grid hierarchies, and the treatment of complex geometries using mapped grids, multiblock grids, and cut-cell representations.

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Mathematics Subject Classification: Primary: 65M08, 65N08.

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