Conservative Numerical Schemes for the Vlasov Equation

A new scheme for solving the Vlasov equation using a phase space grid is proposed. The algorithm is based on the conservation of the flux of particles, and the distribution function is reconstructed using various techniques that allow control of spurious oscillations or preservation of the positivity. Several numerical results are presented in two- and four-dimensional phase space and the scheme is compared with the semiLagrangian method. This method is almost as accurate as the semiLagrangian one, and the local reconstruction technique is well suited for parallel computation.