论文标题
浅水模型的三角形网格上的自适应中心风格方案
Adaptive Central-Upwind Scheme on Triangular Grids for the Shallow Water Model with variable density
论文作者
论文摘要
在本文中，我们在非结构化三角形网格上构建了强大的自适应中心风向方案，用于二维浅水方程，密度可变。该方法在曲线上均衡，具有阳性性且具有振荡性良好，并且在其中两种类型的流体合并。所提出的方法是在Epshteyn和Nguyen开发的自适应均衡，具有积极性的保护方案（Arxiv Preprint Arxiv：2011.06143，2020）。特别是，为了保留“湖泊”的稳态状态，我们使用适当旋转坐标的Riemann求解器来获得流体界面附近的点值。此外，为了提高自适应方法在多流体流中的效率，使用级别集合方法和音量分数方法重建密度不连续性的曲线。为了证明新的自适应中央上风方案的准确性，高分辨率和效率，对具有可变密度的浅水模型进行了一些具有挑战性的测试。
In this paper, we construct a robust adaptive central-upwind scheme on unstructured triangular grids for two-dimensional shallow water equations with variable density. The method is well-balanced, positivity-preserving, and oscillation-free at the curve where two types of fluid merge. The proposed approach is an extension of the adaptive well-balanced, positivity-preserving scheme developed in Epshteyn and Nguyen (arXiv preprint arXiv:2011.06143, 2020). In particular, to preserve "lake-at-rest" steady states, we utilize the Riemann Solver with appropriately rotated coordinates to obtain the point values in the neighborhood of the fluid interface. In addition, to improve the efficiency of an adaptive method in the multifluid flow, the curve of density discontinuity is reconstructed by using the level set method and volume fraction method. To demonstrate the accuracy, high resolution, and efficiency of the new adaptive central-upwind scheme, several challenging tests for Shallow water models with variable density are performed.
