基于求解Riemann问题的界面处理方法

An Interface Treating Method Based on Riemann Problems

通过在界面处构造Riemann问题,根据流体的法向速度和压力在界面(接触间断)处连续的特性,利用Riemann问题的解不仅定义了ghost流体的值,而且对真实流体中邻近界面的点值进行了更新,使得在界面处的流体的状态满足接触间断的性质,给出了更加精确的界面边界条件,守恒误差分析表明该方法在界面计算过程中引入较小的误差.数值试验表明该方法能准确地捕捉界面和激波的位置.

By predicting the real fluid status rather than the ghost fluid status with a Riemann problem, a simple and efficient extension of the ghost fluid method in multi-dimension is introduced. Riemann problems are constructed at the interface and solved to define boundary conditions of fluid on both sides of the interface. Since the Riemann problem solvers describe fluid state reasonably and the normal velocity and pressure are continuous across the interface, a more accurate interface boundary condition is obtained. Conservation error shows that the method incurs minor errors. Numerical experiments show that this method captures the interface and shock waves correctly.