Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
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
Journal of Computational Physics
On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
Journal of Computational Physics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Error estimation and adaptation for functional outputs in time-dependent flow problems
Journal of Computational Physics
Discontinuous Galerkin spectral element approximations on moving meshes
Journal of Computational Physics
Boundary states at reflective moving boundaries
Journal of Computational Physics
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
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 | 31.49 |
The formulation and implementation of higher-order accurate temporal schemes for dynamic unstructured mesh problems which satisfy the discrete conservation law are presented. The general approach consists of writing the spatially-discretized equations for an arbitrary-Lagrange-Eulerian system (ALE) as a non-homogeneous coupled set of ODE's where the dependent variables consist of the product of the flow variables with the control volume. Standard application of backwards difference (BDF) and implicit Runge-Kutta (IRK) schemes to these ODE's, when grid coordinates and velocities are known smooth functions of time, results in the design temporal accuracy of these schemes. However, in general, these schemes do not satisfy the GCL and are therefore not conservative. Using a suitable approximation of the grid velocities evaluated at the locations in time prescribed by the specific ODE time integrator, a GCL compliant scheme can be constructed which retains the design temporal accuracy of the underlying ODE time integrator. This constitutes a practical approach, since the grid velocities are seldom known as continuous functions in time. Numerical examples demonstrating design accuracy and conservation are given for one, two, and three-dimensional inviscid flow problems.