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

Phillip Colella
2016 Discrete and Continuous Dynamical Systems. Series A  
We present an approach to designing arbitrarily high-order finitevolume 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
more » ... ciples 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. 2010 Mathematics Subject Classification. Primary: 65M08, 65N08.
doi:10.3934/dcds.2016.36.4247 fatcat:v4gaavefyzhy3kg3bnwpnogooe