Periodic Reporting for period 1 - HNSKMAP (High-order Numerical Schemes for Kinetic Models with Applications in Plasma Physics)
Periodo di rendicontazione: 2016-02-01 al 2018-01-31
On the one hand, we want to propose and analyse systematic numerical methods for nonlinear kinetic models which have some challenging difficulties such as physical conservations, asymptotic regimes and stiffness. On the other hand, applications to plasma physics will be investigated, which are mainly high dimensional problems with multi-scale and complex geometries. Moreover collisions between particles for large time scale simulation need to be taken into account.
We would like to develop a class of less dissipative high order Hermite methods together with weighted essentially non-oscillatory (WENO) reconstructions to control spurious numerical oscillations, and high order asymptotic preserving (AP) discontinuous Galerkin (DG) schemes with implicit-explicit (IMEX) time discretizations for multi-scale stiff problems under unresolved meshes. More importantly, these developed numerical methods would satisfy the positivity preserving (PP) principle, such as positive density distribution functions for kinetic descriptions, which is often violated by high order numerical methods with physical meaningless values.
More precisely, the first semester is devoted to the modeling part where we have derived a reduced kinetic model starting to the 2Dx3D Vlasov-Maxwell system in the presence of a large external magnetic field. Then the goal is to perform some numerical simulations and to validate our approach on suitable numerical tests. The main problem is that there are really few results in the literature on this topic therefore the numerical validation is crucial here.
To reduce the cost of numerical simulations, it is classical to derive asymptotic models with a smaller number of variables than the kinetic description.