Numerical integration of the plasma fluid equations with a modification of the second-order Nessyahu–Tadmor central scheme and soliton modeling

Here we outline a modification of the second order central difference scheme based on staggered spatial grids due to Nessyahu and Tadmor [H. Nessyahu, E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys. 87 (1990) 408] to a non-staggered scheme for one-dimensional hyperbolic systems which can additionally include source terms. With this modification we integrate the one-dimensional electrostatic plasma fluid-Poisson equations to illustrate ion-acoustic soliton formation and propagation. This application is interesting because, to our knowledge, it is the first time that a high-resolution scheme has been employed on the plasma fluid equations, where in particular, we test its ability to handle a coupled fluid-Poisson system and also, we examine its performance on very long time integrations involving thousands of time steps. As a check on the accuracy of the modified scheme we perform tests on a shock capturing problem in a Broadwell gas, and in both cases, the results obtained are compared with those from previously reported schemes.