Abstract: Level Set (LS) function for tracking multi-fluid interfaces and the different materials corresponding to different leves are applied.These LS equations together with fluid dynamic Euler equations are solved independently.An adaptive mesh refinement (AMR) method in the context of Cartesian grids is discussed at the same time.Such an approach can be automatically adaptive in that it chooses the regions of refinement based on the behavior of the solution while for time dependent problems the regions of refinement must change with time.There are two main strategies that have been used to handle the data structures involved when a rectangular grid is being refined.One approach is to refine individual grid cells as needed,typically by splitting a single cell in two dimensions into four pieces.Each of these pieces may be further subdivided recursively,depending on how many levels of refinement are allowed.High resolution results can be given by using this method,and it can also track the shock front adaptively and save CPU greatly.

Key words: multi-fluid, adaptive mesh refinement, wave propagation algorithm