Vol. 8, No. 1, 2013

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A cartesian grid embedded boundary method for the compressible Navier–Stokes equations

Daniel T. Graves, Phillip Colella, David Modiano, Jeffrey Johnson, Bjorn Sjogreen and Xinfeng Gao

Vol. 8 (2013), No. 1, 99–122
Abstract

We present an unsplit method for the time-dependent compressible Navier–Stokes equations in two and three dimensions. We use a conservative, second-order Godunov algorithm. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We solve for viscous and conductive terms with a second-order semiimplicit algorithm. We demonstrate second-order accuracy in solutions of smooth problems in smooth geometries and demonstrate robust behavior for strongly discontinuous initial conditions in complex geometries.

Keywords
Cartesian grid embedded boundaries, compressible Navier–Stokes, block-structured adaptive mesh refinement
Mathematical Subject Classification 2010
Primary: 76-04
Secondary: 35-04
Milestones
Received: 23 January 2013
Revised: 30 September 2013
Accepted: 8 October 2013
Published: 15 December 2013
Authors
Daniel T. Graves
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road
MS 50A-1148
Berkeley, CA 94720
United States
Phillip Colella
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road
MS 50A-1148
Berkeley, CA 94720
United States
David Modiano
Sanzaru Games, Inc.
323B Vintage Park Drive
Foster City, CA 94404
United States
Jeffrey Johnson
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road
MS 50A-1148
Berkeley, CA 94720
United States
Bjorn Sjogreen
Center for Applied Scientific Computing
Lawrence Livermore National Laboratory
Box 808, L-422
Livermore, CA 94551-0808
United States
Xinfeng Gao
Department of Mechanical Engineering
Colorado State University
Fort Collins, CO 80523
United States