A new algorithm for surface tension forces in the framework of the FVCF–ENIP method

This paper addresses a new scheme for the discretization of surface tension forces. This scheme is derived in the context of the Finite Volume with Characteristic Fluxes–Enhanced Natural Interface Positioning (FVCF–ENIP) method, a multimaterial solver for compressible flows with sharp interface capturing. Surface tension forces are discretized exactly along material interfaces without any approximation on the Dirac mass modeling the force, thanks to the explicit description of this latter in the FVCF–ENIP algorithm. An upwind strategy is applied in order to ensure, at the discrete level, a strict preservation of stationary solutions, which is the crux when dealing with numerical simulations involving surface tension forces. Strong instabilities, the so-called spurious currents, may indeed appear. Several numerical results attest the robustness of our method regarding these particular instabilities. Dynamical test-cases are presented, that show the good behavior of our method in terms of physics.