三角形网格下二维浅水方程的高分辨率格式
A Non-Oscillatory Scheme for Shallow Water Equations on Triangular Meshes
DOI: 10.12677/IJFD.2019.71002, PDF,    科研立项经费支持
作者: 蔺彩凤*, 高 巍：内蒙古大学数学科学学院，内蒙古自治区 呼和浩特
关键词: 二维浅水方程；三角形网格；高分辨率格式；三角形网格下二维浅水方程的 高分辨率格式
摘要: 对于二维浅水方程问题，本文在三角网格下，基于CBC (Convection Boundedness Criterion)准则采用有限体积法离散建立了新的高分辨率NVSF (Normalized Variable and Space Formulation)格式，NVSF格式是为解决NVF高分辨率格式在不规则区域的应用所提出的，文章通过一些典型算例的精确解与数值解的比较，表明新构造的数值格式具有二阶精度，并且与准确解有很好的逼近效果，能很好地抑制在间断解处的非物理震荡。
Abstract: For the shallow water equations, a new finite volume NVSF (Normalized Variable and Space For-mulation) scheme is constructed under the triangular mesh. This scheme is based on the CBC (Convection Boundedness Criterion) criterion. NVSF scheme is adopted to solve the application of NVF high resolution scheme on triangular meshes, by comparing the exact solution of the typical example with the numerical solution. It is shown that the new numerical scheme has second order accuracy and has a good approximation near the exact solution. It can suppress the unphysical os-cillation of the discontinuity.
文章引用：蔺彩凤, 高巍. 三角形网格下二维浅水方程的高分辨率格式[J]. 流体动力学, 2019, 7(1): 11-22. https://doi.org/10.12677/IJFD.2019.71002

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