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.