# American Institute of Mathematical Sciences

August  2016, 36(8): 4247-4270. doi: 10.3934/dcds.2016.36.4247

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

 1 Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, United States

Received  June 2015 Revised  December 2015 Published  March 2016

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.
Citation: Phillip Colella. High-order finite-volume methods on locally-structured grids. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4247-4270. doi: 10.3934/dcds.2016.36.4247
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