We describe in this paper the improvement on the numerical resolution of a fluid dynamics system by means of an Adaptive Mesh Refinement algorithm in order to handle an infinitely thin interface. This model is derived from the compressible Navier-Stokes equations in the case of diphasic flows for which both phases have a low Mach number. It consists of a coupled hyperbolic-elliptic system. The first part is numerically treated thanks to a hierarchical grid structure whereas we use the Local Defect Correction method to solve the second part.
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