Finite volume-complete flux scheme for plasma simulation

In fluid models of plasmas, the transports of species and electron energy are described by continuity equations and drift-diffusion momentum transport equations. These equations are usually discretized with the exponential scheme in literature. We present a new scheme, named finite volume-complete flux (FV-CF) scheme, which is second order accurate, even for dominant advection problems. The flux is based on the solution of a local boundary value problem (BVP) for the entire equation, including the source term, therefore it consists of two parts, homogeneous flux and inhomogeneous flux, corresponding to the homogeneous and particular solution of the BVP, respectively. The inhomogeneous numerical flux turns out to be very important for dominant drift, since it ensures that the flux approximation remains second order accurate. An example is presented to compare the accuracy between FV-CF scheme and exponential scheme.