Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 230, Issue 15, Pages 6023-6036Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.04.011
Keywords
Numerical boundary conditions; Complex moving boundaries; Inverse Lax-Wendroff procedure; Compressible inviscid flows; No-penetration conditions
Funding
- AFOSR [FA9550-09-1-0126]
- NSF [DMS-0809086]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0809086] Funding Source: National Science Foundation
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We develop a high order numerical boundary condition for compressible inviscid flows involving complex moving geometries. It is based on finite difference methods on fixed Cartesian meshes which pose a challenge that the moving boundaries intersect the grid lines in an arbitrary fashion. Our method is an extension of the so-called inverse Lax-Wendroff procedure proposed in [17] for conservation laws in static geometries. This procedure helps us obtain normal spatial derivatives at inflow boundaries from Lagrangian time derivatives and tangential derivatives by repeated use of the Euler equations. Together with high order extrapolation at outflow boundaries, we can impose accurate values of ghost points near the boundaries by a Taylor expansion. To maintain high order accuracy in time, we need some special time matching technique at the two intermediate Runge-Kutta stages. Numerical examples in one and two dimensions show that our boundary treatment is high order accurate for problems with smooth solutions. Our method also performs well for problems involving interactions between shocks and moving rigid bodies. (C) 2011 Elsevier Inc. All rights reserved.
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