TY - JOUR
T1 - Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation
AU - Ruo Li, Tiao Lu, Yanli Wang & Wenqi Yao
JO - Communications in Computational Physics
VL - 3
SP - 569
EP - 595
PY - 2014
DA - 2014/03
SN - 15
DO - http://doi.org/10.4208/cicp.091012.120813a
UR - https://global-sci.org/intro/article_detail/cicp/7106.html
KW - 
AB - <p style="text-align: justify;">A globally hyperbolic moment system up to arbitrary order for the Wigner
equation was derived in [6]. For numerically solving the high order hyperbolic moment system therein, we in this paper develop a preliminary numerical method for
this system following the NR$xx$ method recently proposed in [8], to validate the moment system of the Wigner equation. The <span style="text-align: justify;">developed&nbsp;</span>method can keep both mass and
momentum conserved, and the variation of the total energy under control though it
is not strictly conservative. We systematically study the numerical convergence of the
solution to the moment system both in the size of spatial mesh and in the order of
the moment expansion, and the convergence of the numerical solution of the moment
system to the numerical solution of the Wigner equation using the discrete velocity
method. The numerical results indicate that the high order moment system in [6] is
a valid model for the Wigner equation, and the proposed numerical method for the
moment system is quite promising to carry out the simulation of the Wigner equation.</p>