Surface tension for compressible fluids in ALE framework

We describe an Arbitrary-Lagrangian-Eulerian (ALE) method for the compressible Euler system with capillary force. The algorithm is split in two steps. First, the Lagrangian step is based on cell-centred schemes [9,20,46]. The surface tension force is discretized in order to exactly verify the Laplace law at the discrete level. We also provide a second-order spatial extension and a low-Mach correction, which do not break the well-balanced property of the scheme. The Lagrangian scheme is assessed on several problems, particularly on a linear Richtmyer-Meshkov instability which is the targeted application. The second step is the rezoning and remapping done thanks to a swept-region method using exact intersections near the interface. We use a Volume Of Fluid (VOF) method to track the interface. We describe the treatment of mixed-cells, and in particular the thermodynamics closure and the curvature calculation. The new scheme is used to investigate the influence of surface tension on a non-linear Richtmyer-Meshkov instability. (C) 2020 Elsevier Inc. All rights reserved.