Spectral Difference Method with a Posteriori Limiting: III- Navier-Stokes Equations with Arbitrary High-Order Accuracy
Instrumentation and Methods for Astrophysics
2026-04-09 v1 Numerical Analysis
Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2604.07339,
title = {Spectral Difference Method with a Posteriori Limiting: III- Navier-Stokes Equations with Arbitrary High-Order Accuracy},
author = {David A. Velasco-Romero and Romain Teyssier},
journal= {arXiv preprint arXiv:2604.07339},
year = {2026}
}
Comments
Submitted to MNRAS