Spectral Difference Method with a Posteriori Limiting: III- Navier-Stokes Equations with Arbitrary High-Order Accuracy

Fuente: arXiv
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Main Authors: Velasco-Romero, David A., Teyssier, Romain
Format: Preprint
Published: 2026
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author Velasco-Romero, David A.
Teyssier, Romain
author_facet Velasco-Romero, David A.
Teyssier, Romain
contents We incorporate an arbitrarily high-order method for the Laplacian operator into the Spectral Difference method (SD). The resulting method is capable of capturing shocks thanks to its a-posteriori limiting methodology, and therefore it is able to survive scenarios in which the dissipative scales (viscous and diffusive) are not properly described. Moreover, it is capable of capturing these scales at lower resolution compared to lower-order methods and therefore attains convergence at lower resolution. We show that the method at hand has exponential convergence when describing smooth solutions and is able to recover a high-order solution when solving the dissipative scales.
format Preprint
id arxiv_https___arxiv_org_abs_2604_07339
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Spectral Difference Method with a Posteriori Limiting: III- Navier-Stokes Equations with Arbitrary High-Order Accuracy
Velasco-Romero, David A.
Teyssier, Romain
Instrumentation and Methods for Astrophysics
Numerical Analysis
We incorporate an arbitrarily high-order method for the Laplacian operator into the Spectral Difference method (SD). The resulting method is capable of capturing shocks thanks to its a-posteriori limiting methodology, and therefore it is able to survive scenarios in which the dissipative scales (viscous and diffusive) are not properly described. Moreover, it is capable of capturing these scales at lower resolution compared to lower-order methods and therefore attains convergence at lower resolution. We show that the method at hand has exponential convergence when describing smooth solutions and is able to recover a high-order solution when solving the dissipative scales.
title Spectral Difference Method with a Posteriori Limiting: III- Navier-Stokes Equations with Arbitrary High-Order Accuracy
topic Instrumentation and Methods for Astrophysics
Numerical Analysis
url https://arxiv.org/abs/2604.07339