Wave propagation and reflection in irregular grids for hyperbolic equations
Applied Numerical Mathematics - Special issue on numerical fluid dynamics
Adaptive grid refinement for numerical weather prediction
Journal of Computational Physics
Spurious scattering from discontinuously stretching grids in computational fluid dynamics
Applied Numerical Mathematics
Numerical representation of geostrophic modes on arbitrarily structured C-grids
Journal of Computational Physics
A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid
Journal of Computational Physics
A method for reducing dispersion in convective difference schemes
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
High-order finite-volume methods for the shallow-water equations on the sphere
Journal of Computational Physics
Numerical wave propagation on non-uniform one-dimensional staggered grids
Journal of Computational Physics
Hi-index | 31.45 |
This paper examines high-order unstaggered symmetric and upwind finite-volume discretizations of the advection equation in the presence of an abrupt discontinuity in grid resolution. An approach for characterizing the initial amplitude of a parasitic mode as well as its decay rate away from a grid resolution discontinuity is presented. Using a combination of numerical analysis and empirical studies it is shown that spurious parasitic modes, which are artificially generated by the resolution discontinuity, are mostly undamped by symmetric finite-volume schemes but are quickly removed by upwind and semi-Lagrangian integrated mass (SLIM) schemes. Slope/curvature limiting is insufficient to completely remove these modes, especially at low forcing frequencies where the incident wave can act as a carrier of the parasitic mode. Increasing the order of accuracy of the reconstruction at the grid interface is effective at removing noise from the lowest-frequency incident modes, but insufficient at high frequencies. It is shown that this analysis can be extended to the 1D linear shallow-water equations via Riemann invariants.