论文标题
拉格朗日坐标中（1+2） - 维度浅水方程的对称性，保护法和差异方案
Symmetries, conservation laws and difference schemes of the (1+2)-dimensional shallow water equations in Lagrangian coordinates
论文作者
论文摘要
考虑了Eulerian和Lagrangain坐标的二维浅水方程。给出了等式的拉格朗日式和哈密顿形式主义。映射具有圆形或平面底部的二维浅水方程中的二维浅水方程，以多变量指数$γ= 2 $的多变态气体的气体动力学方程。 考虑了方程的组属性，并进行了椭圆抛物面底部地形的组分类。 从离散的角度讨论了拉格朗日坐标中二维浅水方程的性质。构建了方程式及其一维降低的新的不变的保守有限差异方案。这些方案是通过扩展已知的一维方案或基于对能源保护法形式的一些假设来得出的。在拟议的方案中，有具有质量和能量保护定律的方案。
The two-dimensional shallow water equations in Eulerian and Lagrangain coordinates are considered. Lagrangian and Hamiltonian formalism of the equations is given. The transformations mapping the two-dimensional shallow water equations with a circular or plane bottom into the gas dynamics equations of a polytropic gas with polytropic exponent $γ=2$ is represented. Group properties of the equations are considered, and the group classification for the case of the elliptic paraboloid bottom topography is performed. The properties of the two-dimensional shallow water equations in Lagrangian coordinates are discussed from the discretization point of view. New invariant conservative finite-difference schemes for the equations and their one-dimensional reductions are constructed. The schemes are derived either by extending the known one-dimensional schemes or by direct algebraic construction based on some assumptions on the form of the energy conservation law. Among the proposed schemes there are schemes possessing conservation laws of mass and energy.
