Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
An analysis of the discontinuous Galerkin method for wave propagation problems
Journal of Computational Physics
Numerical methods for ordinary differential equations in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
Journal of Computational Physics
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
Journal of Computational Physics
Metric Identities and the Discontinuous Spectral Element Method on Curvilinear Meshes
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Accurate interface-tracking for arbitrary Lagrangian-Eulerian schemes
Journal of Computational Physics
Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers
Boundary states at reflective moving boundaries
Journal of Computational Physics
High-Order Local Time Stepping on Moving DG Spectral Element Meshes
Journal of Scientific Computing
ALE-DGSEM approximation of wave reflection and transmission from a moving medium
Journal of Computational Physics
Hi-index | 31.46 |
We derive and evaluate high order space Arbitrary Lagrangian-Eulerian (ALE) methods to compute conservation laws on moving meshes to the same time order as on a static mesh. We use a Discontinuous Galerkin Spectral Element Method (DGSEM) in space, and one of a family of explicit time integrators such as Adams-Bashforth or low storage explicit Runge-Kutta. The approximations preserve the discrete metric identities and the Discrete Geometric Conservation Law (DGCL) by construction. We present time-step refinement studies with moving meshes to validate the approximations. The test problems include propagation of an electromagnetic gaussian plane wave, a cylindrical pressure wave propagating in a subsonic flow, and a vortex convecting in a uniform inviscid subsonic flow. Each problem is computed on a time-deforming mesh with three methods used to calculate the mesh velocities: from exact differentiation, from the integration of an acceleration equation, and from numerical differentiation of the mesh position.