Level set方法在自适应Cartesian网格上的应用

采用基于自适应Cartesian网格的level set方法对多介质流动问题进行数值模拟。采用基于四叉树的方法来生成自适应Cartesian网格。采用有限体积法求解Euler方程，控制面通量的计算采用HLLC（Hartern, Lax, van Leer, Contact）近似黎曼解方法。level set方程也采用有限体积法求解，采用Lax-Friedchs方法计算通量，通过窄带方法来减少计算量，界面的处理采用ghost fluid方法。Runge-Kutta显式时间推进，时间、空间都是二阶精度。对两种不同比热比介质激波管问题进行数值模拟，其结果和精确解吻合；对空气/氦气泡相互作用等问题进行模拟，取得令人满意的结果。

Application of the level set method on adaptive cartesian grids

The level set method based on adaptive Cartesian grids is used to simulate multi-material flow problems.  An  quadtree-based algorithm is applied to generate adaptive Cartesian grids. The Euler equations are solved by the finite volume method and the flux of the control face is computed by the HLLC （Hartern, Lax, van Leer, Contact）approximate Riemann method. The level set equations are solved by the finite volume method and the flux is computed by the  Lax-Friedchs method. The narrow band method is used to reduce computational costs and the ghost fluid method is used to treat the interface. The explicit two-stage Runge-Kutta time-integration scheme can achieve second-order time-accuracy and the space accuracy is second order. The shock-tube problem containing two different ideal gases with different specific heat ratios is computed and the numerical results agree with the exact solution. Simulated results on interaction of air with helium bubble are satisfactory.