A multiphase level-set approach for all-Mach numbers

In this work, an alternate level-set-based approach is presented that applies uniformly to compressible and incompressible multiphase flows. Fundamental to this work, is the development of analytic transformations from a signed-distance function to species-mass conservation variables. Such transformations can be used to highlight compressible flow difficulties for level set methods, and develop interfacial reinitialization procedures based on different primitive variables. The proposed all-Mach method is based on preserving signed-distance functions within the context of a species-mass conservation equation to evolve the interface, and includes several reinitialization procedures that maintain the spirit of the signed distance function. In addition, we explore hybrid level-set reinitialization procedures that handle sub-grid-scale interfacial breakup. The model is demonstrated on concepts relevant to high-speed marine vehicles based on supercavitation, where a gaseous cavity surrounds a moving vehicle. Results indicate that the present algorithm preserves higher-order numerics, performs well on several incompressible and compressible validation cases, and extends to unsteady, three-dimensional flow.