Modelling and numerical simulation of plasma flows with two-fluid mixing

For the modelling of plasma flows at very high temperature such as the ones produced by laser beams, one must account for a bi-temperature compressible Euler system coupled to electron thermal conduction and radiative conduction. Moreover, mixing of two different fluids can occur, the two fluids occupying the same volume. For modelling such a phenomenon, instead of dealing with the conservation of mass, momentum and energy for each fluid, we propose here a simplified model which will be easier to implement in a multi-physics Lagrangian 2D code. The principle is to use a closure for expressing the relative velocity between the two fluids with the help of the gradient of the concentration. So, besides the classical system, the final model consists in a nonlinear diffusion equation for the concentration and an equation for the mixing kinetic energy (analogous to the one used in turbulence models). We present also first numerical 2D simulations using this model.