Abstract

A three-dimensional Eulerian method is presented for the simulation of multi-components flows, from shock impacts between compressible fluids to fluid-structure interaction, with elastic-plastic deformations. The main purpose of that numerical method is to cope with the issues usually encountered during such interactions:

- keeping a sharp interface even when large deformations occur during impacts problems;

- nonlinear wave-propagation in the different media;

- accurate modeling of the constitutive properties of the solid medium under strong shock, and calculation of its elasto-plastic behavior in an Eulerian frame.

The interface tracking between materials relies on the use of level-set functions. A new conservative technique has been developed, where cut-cells at the interface are identified and treated specifically. As such cells might have extremely small volume fractions, the CFL condition required for stability might become extremely small as well, driving the simulation to a potentially infinitely long computational time. To overcome this problem, a mass, momentum, and energy redistribution among the neighboring cells is used, ensuring simultaneously conservation. This approach had been previously investigated and implemented in 2D, and is here extended to 3D.

Each phase, except at the neighbourhood of the interface, is treated independently with traditional shock-capturing schemes. High-order accuracy is achieved by incorporating the weighted-essentially non-oscillatory (WENO) method, and Runge-Kutta time integration. For solid/fluid problems, a dedicated Riemann solver has also been developed to comply to the interface treatment.

This whole numerical scheme is demonstrated using 1D, 2D and 3D calculations. This includes initial values problems for 1D testcases, whilst the 2D and 3D problems come essentially from previous numerical studies, whether for strong fluid/fluid and fluid/solid interaction.