Stable high‐order finite‐difference methods based on non‐uniform grid point distributions
By Miguel Hermanns, J. A. Hernández. 2008
84 citations recorded by the source corpus.
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 Sundström 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 resulting finite‐difference operator. Several heuristic explanations exist for the goodness of the clustering, and attempts have been made to link it to the Runge phenomenon present in polynomial interpolations of high degree.
Subfields: Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/6257803688066bc3cf39f1fd99b240b7107fb920
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Citations in the corpus
- Laminar–turbulent transition induced by a discrete roughness element in a supersonic boundary layer (2013, methodology): “…domain is discretized, high-order finite difference numerical schemes of order q (FD-q) for non-symmetric domains, recently developed by Hermanns & Hernández (2008), are used in order to study the behaviour of symmetric and anti-symmetric modes (with respect to the roughness mid-plane…”