求解浅水波方程的熵相容格式

提出了一种求解浅水波方程组的熵相容格式．在熵稳定通量中添加特征速度差分绝对值的项来抵消解在跨过激波时所产生的熵增，从而实现熵相容．新的数值差分格式具有形式简单、计算效率高、无需添加任何的人工数值粘性的特点．数值算例充分说明了其显著的优点．利用新格式成功地模拟了不同类型溃坝问题的激波、稀疏波传播及溃坝两侧旋涡的形成，是求解浅水波方程组较为理想的方法.

An Entropy-Consistent Flux Scheme for Shallow Water Equations

An entropy-consistent flux scheme was developed for the shallow water equations. To offset the entropy increase with cubic order of the shock strength across shock waves, the term of absolute value of the characteristic velocity difference was added into the entropy stable flux, so as to achieve entropy consistency. The new numerical difference scheme featured extreme simplicity, high efficiency, and none additional artificial numerical viscous terms. Numerical experiments of the proposed scheme adequately demonstrated these advantages. The new scheme successfully simulates both the circular shock water wave propagations and the vortices formed on both sides of the breach in different kinds of dam break problems, thus makes a better method to solve the shallow water equations.