Numerical Study On Euler-Lagrange Coupling With GEL Method In Multi-material Hydrodynamics

In the numerical simulation of multi-material hydrodynamics, Eulerian and Lagrangian methods have their own advantages and limitations. It is one of important fields how to effectively use these advantages in the multi-material hydrodynamic calculations. Based on Ghost Fluid method and Level Set function, GEL (Ghost-fluid Euler-Lagrange) method which couples Eulerian and Lagrangian calculations has been investigated in this paper. A two-dimensional code has also been developed.The main points of this work are as follows:1) Firstly, we briefly review Ghost Fluid Method for multi-material flows calculations in the paper.2) The basic theory of GEL method (Ghost-Fluid Euler-Lagrange Method) has been described in detail. Based on a finite difference Euler code (the two-order SCB scheme) and a 2-D finite element Code (DEFEL), a two-dimensional code, which can couple the Euler calculations and Lagrange calculations, has been developed in this paper. According to GEL method and the code, a flow chart is provided to show the course of connecting a standard Eulerian program with a standard Lagrangian code.3) Both an one-dimensional Riemann problem test and a two-dimensional test for moving boundaries (so-called cylinder lift-off problem), which are designed to measure the accuracy of the coupling method, are presented in the paper. The one-dimensional results using GEL method is in a good agreement with that using PPM method. The two-dimensional results using GEL method is also consistent with the results from the literature, thus validating the feasibility of GEL method used in the paper.Although GEL method is now used for one-dimensional and two-dimensional problems, it can be applied to three-dimensional problems without any difficulties theoretically.