论文标题
欧拉和拉格朗日坐标的浅水方程的不变保守差异方案
Invariant conservative difference schemes for shallow water equations in Eulerian and Lagrangian coordinates
论文作者
论文摘要
考虑了欧拉坐标中的一维浅水方程。显示了对称和保护法的关系方程形式的关系，以及欧拉坐标中的对称性和保护法。构建了具有任意底部形状的Eulerian坐标方程的不变差异方案。它具有保护法的所有有限差异类似物。一些底部的地形需要在Eulerian坐标中移动网格，这些坐标是大量拉格朗日坐标中的固定网格。使用各种底部地形的流量示例对开发的不变的保守差异方案进行数值验证。
The one-dimensional shallow water equations in Eulerian coordinates are considered. Relations between symmetries and conservation laws for the potential form of the equations, and symmetries and conservation laws in Eulerian coordinates are shown. An invariant difference scheme for equations in Eulerian coordinates with arbitrary bottom topography is constructed. It possesses all the finite-difference analogues of the conservation laws. Some bottom topographies require moving meshes in Eulerian coordinates, which are stationary meshes in mass Lagrangian coordinates. The developed invariant conservative difference schemes are verified numerically using examples of flow with various bottom topographies.
