A class of energy stable, high-order finite difference interface schemes for adaptive mesh refinement of hyperbolic problems

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 implicit, Padé type, finite differences. Tests on the scalar wave equation and the one-dimensional Navier-Stokes solution of a shock verify the accuracy and stability of this class of methods. ∗ Corresponding author. Email address: [email protected] (R.M.J. Kramer). Preprint submitted to Elsevier Science 29 August 2006