Adaptive multiresolution schemes for shock computations
Journal of Computational Physics
The numerical modeling of acoustic wave propagation using the multiple pressure variables approach
Computing and Visualization in Science
Fast high order ADER schemes for linear hyperbolic equations
Journal of Computational Physics
Journal of Computational Physics
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
ADER schemes on adaptive triangular meshes for scalar conservation laws
Journal of Computational Physics
TVD Fluxes for the High-Order ADER Schemes
Journal of Scientific Computing
Building Blocks for Arbitrary High Order Discontinuous Galerkin Schemes
Journal of Scientific Computing
MUSTA: a multi-stage numerical flux
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Spectral element method in time for rapidly actuated systems
Journal of Computational Physics
ADER schemes for the shallow water equations in channel with irregular bottom elevation
Journal of Computational Physics
Solvers for the high-order Riemann problem for hyperbolic balance laws
Journal of Computational Physics
Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant
Journal of Scientific Computing
Numerical solution for the wave equation
International Journal of Computer Mathematics
Journal of Computational Physics
Adaptive ADER Methods Using Kernel-Based Polyharmonic Spline WENO Reconstruction
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Comparison of solvers for the generalized Riemann problem for hyperbolic systems with source terms
Journal of Computational Physics
A sub-cell WENO reconstruction method for spatial derivatives in the ADER scheme
Journal of Computational Physics
Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes
Journal of Computational Physics
Hi-index | 0.06 |
The ADER scheme for solving systems of linear, hyperbolic partial differential equations in two-dimensions is presented in this paper. It is a finite-volume scheme of high order in space and time. The scheme is explicit, fully discrete and advances the solution in one single step. Several numerical tests have been performed. In the first test case the dissipation and dispersion behaviour of the schemes are studied in one space dimension. Dispersion as well as dissipation effects strongly influence the discrete wave propagation over long distances and are very important for, e.g., aeroacoustical calculations. The next test, the so-called co-rotating vortex pair, is a demonstration of the ideas of the two-dimensional ADER approach. The linearised Euler equations are used for the simulation of the sound emitted by a co-rotating vortex pair.