Conservative numerical schemes for the Vlasov equation

A new scheme for solving the Vlasov equation using a phase space grid is pr oposed. The algorithm is based on the conservation of the flux of particles , and the distribution function is reconstructed using various techniques t hat allow control of spurious oscillations or preservation of the positivit y. Several numerical results are presented in two- and four-dimensional pha se space and the scheme is compared with the semiLagrangian method. This me thod is almost as accurate as the semiLagrangian one, and the local reconst ruction technique is well suited for parallel computation. (C) 2001 Academi c Press.