二维溃坝问题的WAF算法及干湿边界研究

Application of WAF scheme based on unstructured mesh for 2D dam-break problem

利用平衡的二阶WAF算法研究了复杂地形上的二维溃坝问题.基于三角形网格建立了扩展平衡的有限体积格式,用WAF格式和HLLC Riemann求解器近似数值通量,中矩形公式离散地形源项,重新定义数值河床处理干湿边界问题,保证算法是平衡和扩展平衡的.利用WAF数值算法研究了复杂地形条件下的二维溃坝波演进问题,较好地模拟了溃坝波在传播中同固体壁面碰撞、反射的现象,计算数据和已有结果相符,证明WAF算法能有效处理溃坝间断解、复杂地形和干湿边界问题.

A well-balanced weighted average flux （WAF） scheme was proposed for the 2D shallow water equations with source terms based on the triangular mesh. Here, the WAF scheme with the HLLC solver was applied to approximate the intercell numerical flux at each interface. For the treat- ment of source terms, the rectangle formula was employed to approximate the line integral of the bed slope terms along the sides of each element. At the same time, the technique of redefinition of the dis- cretized bottom was carried out for the treatment of wet/dry fronts. Finally, the dam break of the shallow water flow with complex topography was studied by the WAF method. The numerical results agree with the existed results very well, including the collision of two shock wave meeting and reflec- tion of the shock wave hitting the solid wall. It is known that the problem of the shock wave, complex topography and wet/dry boundary can be deal with by the WAF method.