一维浅水方程的强和谐Riemann求解器

处理底坡项是计算浅水动力学的重要任务之一。针对传统的底坡项处理技术在大起伏地形上的不足,通过计算底坡项对水深和动量通量的影响,并进行相应的分解,构造了集成底坡项的近似Riemann求解器。该求解器具有强和谐性,即能保持任意流速下的恒定流状态。同时,能保证水深计算值非负,有利于计算的稳定性。考虑了干湿界面中固壁、漫流等情况,适应动边界模拟。算例研究结果表明,该求解器能准确地处理底坡项,保证水深非负,和谐性好,激波捕获能力强,适应干湿界面计算,可模拟复杂混合流态问题,因而具有较好的推广应用价值。

A well-balanced Riemann solver for one-dimensional shallow water equations

The treatment of topography source terms (TST) is one of the important tasks in the computational shallow water dynamics. To overcome the shortage of conventional technology of dealing TST when facing big bottom step, An approximate Riemann solver was constructed,which integrates TST considering the influence of TST on both water depth and momentum flux, and then decompose them. The solver is well-balanced, which can preserve steady state under any water flow velocity. Meanwhile, it can guarantee nonnegative water depth that is preferable to keep computational stability. To treat with wetting/drying and achieve moving boundary simulation, some special methods are taken. Numerical results of some examples show that the solver can evaluate the effect of source terms accurately when maintaining depth nonnegative and is well-balanced. It also has an excellent shock-capturing ability, and can simulate the mixed flow exactly.