An Asymptotic-Preserving Method for a Relaxation of the Navier-Stokes-Korteweg Equations
It addresses the computational bottleneck of simulating compressible two-phase flows with diffuse interfaces, where standard explicit schemes become inefficient due to relaxation parameter constraints.
The paper proposes an asymptotic-preserving finite volume method for a relaxation of the Navier-Stokes-Korteweg equations, enabling efficient numerical simulations with realistic density ratios and small interfacial widths.
The Navier-Stokes-Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flow. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a relaxation of the NSK system, for which robust numerical methods can be designed. However, time steps for explicit numerical schemes depend on the relaxation parameter and therefore numerical simulations in the relaxation limit are very inefficient. To overcome this restriction, we propose an implicit-explicit asymptotic-preserving finite volume method. We prove that the new scheme provides a consistent discretization of the NSK system in the relaxation limit and demonstrate that it is capable of accurately and efficiently computing numerical solutions of problems with realistic density ratios and small interfacial widths.