High Order Weighted Extrapolation for Boundary Conditions for Finite Difference Methods on Complex Domains with Cartesian Meshes

Fuente: arXiv
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Main Authors: Baeza, Antonio, Mulet, Pep, Zorío, David
Format: Preprint
Published: 2025
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author Baeza, Antonio
Mulet, Pep
Zorío, David
author_facet Baeza, Antonio
Mulet, Pep
Zorío, David
contents The design of numerical boundary conditions is a challenging problem that has been tackled in different ways depending on the nature of the problem and the numerical scheme used to solve it. In this paper we present a new weighted extrapolation technique which entails an improvement with respect to the technique that was developed in [1]. This technique is based on the application of a variant of the Lagrange extrapolation through the computation of weights capable of detecting regions with discontinuities. We also present a combination of the above technique with a least squares approach in order to stabilize the scheme in some cases where Lagrange extrapolation can turn the scheme mildly unstable. We show that this combined extrapolation technique can tackle discontinuities more robustly than the procedure introduced in [1].
format Preprint
id arxiv_https___arxiv_org_abs_2501_17106
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle High Order Weighted Extrapolation for Boundary Conditions for Finite Difference Methods on Complex Domains with Cartesian Meshes
Baeza, Antonio
Mulet, Pep
Zorío, David
Numerical Analysis
The design of numerical boundary conditions is a challenging problem that has been tackled in different ways depending on the nature of the problem and the numerical scheme used to solve it. In this paper we present a new weighted extrapolation technique which entails an improvement with respect to the technique that was developed in [1]. This technique is based on the application of a variant of the Lagrange extrapolation through the computation of weights capable of detecting regions with discontinuities. We also present a combination of the above technique with a least squares approach in order to stabilize the scheme in some cases where Lagrange extrapolation can turn the scheme mildly unstable. We show that this combined extrapolation technique can tackle discontinuities more robustly than the procedure introduced in [1].
title High Order Weighted Extrapolation for Boundary Conditions for Finite Difference Methods on Complex Domains with Cartesian Meshes
topic Numerical Analysis
url https://arxiv.org/abs/2501.17106