Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space

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 L^∞ 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.