Stable Coupling of Nonconforming, High-Order Finite Difference Methods

Stable High-Order Finite Difference Methods for Aerodynamics

Svärd, M. 2004. Stable High-Order Finite Difference Methods for Aerodynamics (Stabila högordnings finita differens-metoder för aerodynamik). Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1026. vii, 25 pp. Uppsala. ISBN 91-554-6063-1 In this thesis, the numerical solution of time-dependent partial differential equation...

High Order Stable Finite Difference Methods for the Schrödinger Equation

In this paper we extend the Summation–by–parts–simultaneous approximation term (SBP–SAT) technique to the Schrödinger equation. Stability estimates are derived and the accuracy of numerical approximations of interior order 2m, m = 1, 2, 3, are analyzed in the case of Dirichlet boundary conditions. We show that a boundary closure of the numerical approximations of order m lead to global accuracy...

High-Order Compact Finite Difference Methods

In this work we present a general approach for developing high-order compact differencing schemes by utilizing the governing differential equation to help approximate truncation error terms. As an illustrative application we consider the stream-function vorticity form of the Navier Stokes equations, and provide driven cavity results. Some extensions to treat non-constant metric coefficients res...

Stable high-order finite-difference methods based on non-uniform grid point distributions

It is well known that high-order finite-difference methods may become unstable due to the presence of boundaries and the imposition of boundary conditions. For uniform grids, Gustafsson, Kreiss, and Sundstrom theory and the summation-by-parts method provide sufficient conditions for stability. For non-uniform grids, clustering of nodes close to the boundaries improves the stability of the resul...

Energy Stable High Order Finite Difference Methods for Hyperbolic Equations in Moving Coordinate Systems