(13)
where
represents the characteristic speed component by Roe's average state between element
and 1;
denotes the average wave strength component;
is a limiter. The MUSCL type limiter of Van Leer is used, which has moderate dissipative and compressible performance;
is a dissipative function put forward by Harten. The definitions of all these variables are given in Ref.[10]. The ratio between time and space is
(14)
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