Seminario - Asymptotic Preserving IMEX Deferred Correction Residual Distribution Schemes

giovedì 7/6/2018, alle 16:30 il Dott. Davide Torlo terrà un seminario in Aula Anile.

Titolo: Asymptotic Preserving IMEX Deferred Correction Residual Distribution Schemes

Abstract: The class of schemes presented can be used to solve hyperbolic systems with relaxation source terms. In particular, we will focus on kinetic models leaded by a relaxation parameter. To solve the stiffness of the relaxation terms in macroscopic regime, we adopted an IMEX scheme, implicit for the stiff source term and explicit for the convection term, which ensures good performance without resorting to discretization scales of the size of the mean free path. The spatial discretization is performed by Residual distribution technique, that are based on finite element method and can be shaped into well known finite element, finite volume and discontinuous Galerkin schemes. For time discretization we use the Deferred Correction procedure, which is a way to combine two methods: the first, which is stable and low order (the IMEX scheme), and the second one, more difficult to solve, but high order. This iterative method can reach the order of the second scheme with few steps, solving implicitly only the stable one.
Some numerical tests are shown in 1D and 2D to prove the quality of the scheme and the correct order of accuracy.