Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space
Résumé
A new scheme for solving the Vlasov equation using an unstructured mesh for the phase space is proposed. The algorithm is based on the semi-Lagrangian method which exploits the fact that the distribution function is constant along the characteristic curves. We use different local interpolation operators to reconstruct the distribution function f , some of which need the knowledge of the gradient of f .We can use limiter coefficients to maintain the positivity and the L1 bound of f and optimize these coefficients to ensure the conservation of the L1 norm, that is to say the mass by solving a linear programming problem. Several numerical results are presented in two and three (axisymmetric case) dimensional phase space. The local interpolation technique is well suited for parallel computation.