Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov—Poisson equation in phase space Original Research Article

A new numerical scheme for solving the hyper-dimensional Vlasov—Poisson equation in phase space is described. At each time step, the distribution function and its first derivatives are advected in phase space by the Cubic Interpolated Propagation (CIP) scheme. Although a cell within grid points is interpolated by a cubic-polynomial, any matrix solutions are required. The scheme guarantees exact mass conservation. The numerical results show good agreement with the theory. Even if we reduce the number of grid points in the v-direction, the scheme still gives stable, accurate and reasonable results with memory storage comparable to particle simulations. Owing to this fact, the scheme has succeeded to be generalized in a straightforward way to deal with six-dimensional, or full-dimensional problems.