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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。
Handling slopes is one of the important tasks in the calculation of shallow hydrodynamics. Aiming at the shortcomings of traditional bottom slope processing technology on large undulating terrain, an approximate Riemann solver integrating bottom slope term is constructed by calculating the effect of bottom slope on water depth and momentum flux and corresponding decomposition. The solver has strong harmonics, ie a constant flow regime at any flow rate. At the same time, it can ensure that the calculated value of water depth is non-negative, which is in favor of the stability of calculation. Considering the dry wall interface, solid wall, and so on, to adapt to dynamic boundary simulation. The results of numerical examples show that the solver can deal with the slope term accurately, guarantee the non-negative water depth, have good harmony, strong shock-trapping ability, and adapt to the dry-wet interface calculation, which can simulate complex mixed flow problems. The promotion of application value.