A comparison between the discontinuous galerkin method and the high resolution wave propagation method for the full two-fluid plasma system

Abstract

Summary form only given. The Runge-Kutta discontinuous Galerkin method and the high resolution wave propagation method are compared for applications of the full two-fluid plasma model. The two-fluid plasma equations have hyperbolic parts, therefore both the algorithms are applicable to solve the equation set. For the discontinuous Galerkin algorithm, the conserved variable is defined as a linear combination of a set of basis functions and the selection of these basis functions sets the spatial order of the solution. A Runge-Kutta time integration scheme is used with this method. The high resolution wave propagation algorithm is a finite volume method that uses cell averages to define the conserved variable and it is essentially similar to a low order discontinuous Galerkin method. Both methods compute the numerical flux at the cell edges with an approximate Riemann solver. The two algorithms are compared for stability, accuracy, convergence and computational expense when applied to the hyperbolic set of two-fluid equations. An electron acoustic square pulse is simulated and the results obtained from the two algorithms are compared to the analytical solution. The comparison between the algorithms is verified with the ion soliton propagation and the electron Weibel instability simulations