A HIGH-RESOLUTION GODUNOV-TYPE SCHEME IN FINITE VOLUMES FOR THE 2D SHALLOW-WATER EQUATIONS
A HIGH-RESOLUTION GODUNOV-TYPE SCHEME IN FINITE VOLUMES FOR THE 2D SHALLOW-WATER EQUATIONS
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DOI：
10.1002/fld.1650160604
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发表时间：
1993-03-30
影响因子：
1.8
通讯作者：
GARCIANAVARRO, P
中科院分区：
文献类型：
--
作者：
ALCRUDO, F;GARCIANAVARRO, P
提出了一种基于 MUSCL 变量外推和斜率限制器的高阶 Godunov 型方案，用于求解二维自由表面流方程。为了在贴体网格上应用有限体积积分技术，提出了法向通量函数的近似雅可比行列式（Roe 型）的构造。该过程允许对任意单元形状的方程进行保守的逆风离散化。该模型的主要优点源于网格对问题几何形状的适应性以及随后在边界附近产生正确结果的能力。通过与解析解的比较对该技术进行了验证，结果非常一致。给出了快速变化的二维流的三种情况，以显示该方法的效率和稳定性，该方法不包含依赖于可调参数的项。它可以被认为非常适合计算相当复杂的自由表面二维问题。
A high-order Godunov-type scheme based on MUSCL variable extrapolation and slope limiters is presented for the resolution of 2D free-surface flow equations. In order to apply a finite volume technique of integration over body-fitted grids, the construction of an approximate Jacobian (Roe type) of the normal flux function is proposed. This procedure allows conservative upwind discretization of the equations for arbitrary cell shapes. The main advantage of the model stems from the adaptability of the grid to the geometry of the problem and the subsequent ability to produce correct results near the boundaries. Verification of the technique is made by comparison with analytical solutions and very good agreement is found. Three cases of rapidly varying two-dimensional flows are presented to show the efficiency and stability of this method, which contains no terms depending on adjustable parameters. It can be considered well suited for computation of rather complex free-surface two-dimensional problems.