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The Navier-Stokes-Korteweg (NSK) equations are a classical diffuse-interfacemodel for compressible two-phase flow. As direct numerical simulations based onthe NSK system are quite expensive and in some cases even impossible, weconsider a relaxation of the NSK system, for which robust numerical methods canbe designed. However, time steps for explicit numerical schemes depend on therelaxation parameter and therefore numerical simulations in the relaxationlimit are very inefficient. To overcome this restriction, we propose animplicit-explicit asymptotic-preserving finite volume method. We prove that thenew scheme provides a consistent discretization of the NSK system in therelaxation limit and demonstrate that it is capable of accurately andefficiently computing numerical solutions of problems with realistic densityratios and small interfacial widths.

An Asymptotic-Preserving Method for a Relaxation of the Navier-Stokes-Korteweg Equations