An energy stable and accuracy-preserving finite volume scheme based on the SAV method with application to wall-distance computation
Abstract
A novel semi-implicit second-order finite volume scheme integrating the scalar auxiliary variable (SAV) approach is proposed for solving the pseudo-time Eikonal equation in wall-distance computation. Unconditional energy stability under zero boundary conditions is rigorously proved, eliminating the dependence of the time step on the grid scale and enabling large-time-step computation. The scheme is a priori accuracy-preserving, and its discretization matrix forms an M-matrix, thereby guaranteeing strict non-negativity of the numerical solution inherently. The framework extends readily to any non-conservative scalar equation and, being independent of the specific finite-volume reconstruction, is compatible with schemes of arbitrary order of accuracy. A vanishing artificial viscosity is introduced to smooth the solution without compromising formal accuracy, and upwinding is incorporated through directional weighting in the weighted least-squares (WLS) reconstruction. Numerical experiments confirm that the scheme achieves the designed accuracy and permits stable computations with uniformly large time steps. For complex configurations such as a three-element airfoil and the three-dimensional ONERA M6 wing, accurate results are obtained on high-aspect-ratio grids, with relative errors in the computed wall distance below 3\% relative to the search-based reference, except near geometric singularities.
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BibTeX
@misc{xu2026energy,
title = {{An energy stable and accuracy-preserving finite volume scheme based on the SAV method with application to wall-distance computation}},
author = {Xiaorui Xu and Qian Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16885},
eprint = {2609.16885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16885},
}
RIS
TY - UNPB
TI - An energy stable and accuracy-preserving finite volume scheme based on the SAV method with application to wall-distance computation
AU - Xiaorui Xu
AU - Qian Wang
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16885
UR - https://arxiv.org/abs/2609.16885
AB - A novel semi-implicit second-order finite volume scheme integrating the scalar auxiliary variable (SAV) approach is proposed for solving the pseudo-time Eikonal equation in wall-distance computation. Unconditional energy stability under zero boundary conditions is rigorously proved, eliminating the dependence of the time step on the grid scale and enabling large-time-step computation. The scheme is a priori accuracy-preserving, and its discretization matrix forms an M-matrix, thereby guaranteeing strict non-negativity of the numerical solution inherently. The framework extends readily to any non-conservative scalar equation and, being independent of the specific finite-volume reconstruction, is compatible with schemes of arbitrary order of accuracy. A vanishing artificial viscosity is introduced to smooth the solution without compromising formal accuracy, and upwinding is incorporated through directional weighting in the weighted least-squares (WLS) reconstruction. Numerical experiments confirm that the scheme achieves the designed accuracy and permits stable computations with uniformly large time steps. For complex configurations such as a three-element airfoil and the three-dimensional ONERA M6 wing, accurate results are obtained on high-aspect-ratio grids, with relative errors in the computed wall distance below 3\% relative to the search-based reference, except near geometric singularities.
ER -