基于SAV方法的能量稳定且精度保持的有限体积格式及其在壁面距离计算中的应用
An energy stable and accuracy-preserving finite volume scheme based on the SAV method with application to wall-distance computation
- Beijing Computational Science Research Center（北京计算科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种基于SAV方法的半隐式二阶有限体积格式，用于求解壁面距离计算中的Eikonal方程，具有无条件能量稳定、精度保持和非负性保证，并在复杂构型上实现了高精度大时间步长计算。
AI中文摘要：
本文提出了一种新颖的半隐式二阶有限体积格式，该格式集成了标量辅助变量（SAV）方法，用于求解壁面距离计算中的伪时间Eikonal方程。严格证明了在零边界条件下格式的无条件能量稳定性，消除了时间步长对网格尺度的依赖，从而实现了大时间步长计算。该格式具有先验的精度保持特性，其离散矩阵构成M-矩阵，从而从本质上保证了数值解的严格非负性。该框架可轻松推广到任何非守恒标量方程，并且由于不依赖于特定的有限体积重构，可与任意精度阶数的格式兼容。引入了一个消失的人工粘性项以平滑解而不损害形式精度，并通过加权最小二乘（WLS）重构中的方向加权实现了迎风性。数值实验证实，该格式达到了设计精度，并允许使用统一的大时间步长进行稳定计算。对于诸如三元素翼型和三维ONERA M6机翼等复杂构型，在高纵横比网格上获得了准确的结果，除几何奇点附近外，计算得到的壁面距离相对于基于搜索的参考值的相对误差低于3%。
英文摘要：
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.
