A conservative interface method for compressible flows

In this work, we present a conservative interface method for both multi-fluid and complex boundary problems, in which the standard finite volume scheme on Cartesian grids is modified by considering computational cells being cut by interface. While the discretized governing equations are updated conservatively, the method treats the topological changes naturally by combining interface description and geometric operations with a level set technique. Extensive tests in 1D are carried out, and 2D examples suggest that the present scheme is able to handle multi-fluid and complex (static or moving) boundary problems in a straightforward way with good robustness and accuracy.