A Numerical Adaptative Method For Solving Kinetic Equations Based On Local Velocity Grids

摘要

The aim of this paper is to present a new numerical deterministic method for solving kinetic equations using local dynamical grids for the velocity variable. Indeed, classical methods are based on a global velocity grid constructed according to initial conditions. But these classical methods present a huge computational cost and realistic cases are difficult to simulate. In the present method, the dynamical grids are constructed by solving firstly a system of conservation laws and next by considering a projection of the distribution function on the new grid. The projection is performed by using interpolation procedures involving essentially non oscillatory techniques to diminish oscillations. During the presentation, we will show that this method is in particular well adapted to physical situations with sharp gradients of temperatures.