Nonlinear finite volume method for the interface advection-compression problem on unstructured adaptive meshes

The paper is devoted to the nonlinear finite volume method applied for tracking interfaces on unstructured adaptive meshes. The fluid of volume approach is used. The interface location is described by the fraction of fluid in each computational cell. The interface propagation involves the simultaneous solution of the fraction advection and interface compression problems. The compression problem is solved to recover the interface (front) sharpness, which is smeared due to numerical diffusion. The problem discretization is carried out using the nonlinear monotone finite volume method. This method is applied to unstructured meshes with adaptive local refinement.