Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation (Communications in Computational Physics, 2014)
A globally hyperbolic moment system up to arbitrary order for the Wignerequation was derived in [6]. For numerically solving the high order hyperbolic moment system therein, we in this paper develop a preliminary numerical method forthis system following the NR$xx$ method recently proposed in [8], to validate the moment system of the Wigner equation. The developed method can keep both mass andmomentum conserved, and the variation of the total energy under control though itis not strictly conservative. We systematically study the numerical convergence of thesolution to the moment system both in the size of spatial mesh and in the order ofthe moment expansion, and the convergence of the numerical solution of the momentsystem to the numerical solution of the Wigner equation using the discrete velocitymethod. The numerical results indicate that the high order moment system in [6] isa valid model for the Wigner equation, and the proposed numerical method for themoment system is quite promising to carry out the simulation of the Wigner equation.