Vol. 10, No. 1, 2015

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
High-accuracy embedded boundary grid generation using the divergence theorem

Peter Schwartz, Julie Percelay, Terry J. Ligocki, Hans Johansen, Daniel T. Graves, Dharshi Devendran, Phillip Colella and Eli Ateljevich

Vol. 10 (2015), No. 1, 83–96
Abstract

We present an algorithm to produce the necessary geometric information for finite volume calculations in the context of Cartesian grids with embedded boundaries. Given an order of accuracy for the overall calculation, we show what accuracy is required for each of the geometric quantities and we demonstrate how to calculate the moments using the divergence theorem. We demonstrate that, for a known flux, these moments can be used to create a flux divergence of the expected order.

Keywords
Cartesian grid embedded boundaries, grid generation, finite volume methods
Mathematical Subject Classification 2010
Primary: 65N12, 65N50, 65N08
Milestones
Received: 12 March 2014
Revised: 11 July 2014
Accepted: 16 October 2014
Published: 27 March 2015
Authors
Peter Schwartz
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road
Berkeley, CA 94720
United States
Julie Percelay
Lawrence Berkeley National Laboratory
1 Cyclotron Road
Berkeley, CA 94720
United States
Terry J. Ligocki
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road
Berkeley, CA 94720
United States
Hans Johansen
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road
Berkeley, CA 94720
United States
Daniel T. Graves
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road
Berkeley, CA 94720
United States
Dharshi Devendran
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road
Berkeley, CA 94720
United States
Phillip Colella
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road
Berkeley, CA 94720
United States
Eli Ateljevich
California Department of Water Resources
1416 9th Street
Sacramento, CA 95821
United States