Invariance theorems concerning reflection at numerical boundaries
Journal of Computational Physics
Absorbing boundaries for wave propagation problems
Journal of Computational Physics
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
The numerical behavior of high-order finite difference methods
Journal of Scientific Computing
Far-field filtering operators for suppression of reflections from artificial boundaries
SIAM Journal on Numerical Analysis
Experiments with approximate radiation boundary conditions for computational aeroacoustics
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Cheap Error Estimation for Runge--Kutta Methods
SIAM Journal on Scientific Computing
Nonreflecting boundary conditions for the time-dependent wave equation
Journal of Computational Physics
A super-grid-scale model for simulating compressible flow on unbounded domains
Journal of Computational Physics
Stability of perfectly matched layers, group velocities and anisotropic waves
Journal of Computational Physics
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
A new absorbing layer for elastic waves
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Analysis and optimization of numerical sponge layers as a nonreflective boundary treatment
Journal of Computational Physics
Accurate absorbing boundary conditions for anisotropic elastic media. Part 1: Elliptic anisotropy
Journal of Computational Physics
Journal of Computational Physics
On the Accuracy and Stability of the Perfectly Matched Layer in Transient Waveguides
Journal of Scientific Computing
A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media
Journal of Computational Physics
Source Estimation by Full Wave Form Inversion
Journal of Scientific Computing
Hi-index | 31.48 |
We continue the development of the super-grid-scale model initiated in [T. Colonius, H. Ran, A super-grid-scale model for simulating compressible flow on unbounded domains, J. Comput. Phys. 182 (1) (2002) 191-212] and consider its application to linear hyperbolic systems. The super-grid-scale model consists of two parts: reduction of an unbounded to a bounded domain by a smooth coordinate transformation and a damping of those scales. For linear problems the super-grid scales are analogous to spurious numerical waves. We damp these waves by high-order undivided differences. We compute reflection coefficients for different orders of the damping and find that significant improvements are obtained when high-order damping is used. In numerical experiments with Maxwell's equations, we show that when the damping is of high order, the error from the boundary condition converges at the order of the interior scheme. We also demonstrate that the new method achieves perfectly matched layer-like accuracy. When applied to linear hyperbolic systems the stability of the super-grid-scale method follows from its construction. This makes our method particularly suitable for problems for which perfectly matched layers are unstable. We present results for two such problems: elastic waves in anisotropic media and isotropic elastic waves in wave guides with traction-free surfaces.