Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
SIAM Journal on Scientific Computing
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A two-dimensional conservation laws scheme for compressible flows with moving boundaries
Journal of Computational Physics
A level set approach to Eulerian-Lagrangian coupling
Journal of Computational Physics
A conservative interface method for compressible flows
Journal of Computational Physics
A sharp interface immersed boundary method for compressible viscous flows
Journal of Computational Physics
An immersed boundary method for compressible flows using local grid refinement
Journal of Computational Physics
A high order ENO conservative Lagrangian type scheme for the compressible Euler equations
Journal of Computational Physics
Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws
Journal of Computational Physics
Uniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations
SIAM Journal on Scientific Computing
Efficient implementation of high order inverse Lax-Wendroff boundary treatment for conservation laws
Journal of Computational Physics
An accurate moving boundary formulation in cut-cell methods
Journal of Computational Physics
Hi-index | 31.46 |
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.