A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows
Aude Bernard-Champmartin and Florian De Vuyst
Abstract: In 2002, Després and Lagoutière [Després and Lagoutière (2002)] proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solu tions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutière [Kokh and Lagoutière (2010)] in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, water-water impact and finally a case of Rayleigh–Taylor instability. One of the advantages of the present interface capturing solver is its natural implementation on parallel processors or computers. In particular, we are confident on its implementation on Graphics Processing Units (GPU) with high speedups.
Després, B., Lagoutière, F., 2002. Contact discontinuity capturing schemes for linear advection and compressible gas dynamics. J. Sci. Comput 16, 479–524. doi:10.1023/A:1013298408777
Kokh, S., Lagoutière, F., 2010. An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model. Journal of Computational Physics 229, 2773–2809. doi:10.1016/j.jcp.2009.12.003