Constructing the six-dimensional Vlasov solver using Constrained Interpolation Profile scheme

A new numerical scheme for solving the hyper-dimensional Vlasov equation in phase space is proposed. At each time step, the distribution function and its first derivatives are advected in phase space by the Constrained Interpolation Profile (CIP) scheme. Although a cell within grid points is interpolated by a cubic-polynomial, any matrix solutions are not required. The scheme guarantees the exact conservation of the mass. Even if we reduce the number of grid points in v-direction, the scheme still give the 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 the six-dimensional, or full-dimensional problems.