Wave propagation and reflection in irregular grids for hyperbolic equations
Applied Numerical Mathematics - Special issue on numerical fluid dynamics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Journal of Computational Physics
Designing an efficient solution stragety for fluid flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Journal of Scientific Computing
Multidomain WENO Finite Difference Method with Interpolation at Subdomain Interfaces
Journal of Scientific Computing
Interface conditions for wave propagation through mesh refinement boundaries
Journal of Computational Physics
Accurate and stable grid interfaces for finite volume methods
Applied Numerical Mathematics
A node-centered local refinement algorithm for Poisson's equation in complex geometries
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
High Order Stable Finite Difference Methods for the Schrödinger Equation
Journal of Scientific Computing
Hi-index | 31.46 |
We present a class of energy stable, high-order finite-difference interface closures for grids with step resolution changes. These grids are commonly used in adaptive mesh refinement of hyperbolic problems. The interface closures are such that the global accuracy of the numerical method is that of the interior stencil. The summation-by-parts property is built into the stencil construction and implies asymptotic stability by the energy method while being non-dissipative. We present one-dimensional closures for fourth-order explicit and compact Padé type, finite differences. Tests on the scalar one- and two-dimensional wave equations, the one-dimensional Navier-Stokes solution of a shock and two-dimensional inviscid compressible vortex verify the accuracy and stability of this class of methods.