Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cures for the Expansion Shock and the Shock Instability of the Roe
  Scheme   A common defect of the Roe scheme is the production of non-physical expansion
shock and shock instability. An improved method with several advantages was
presented to suppress the shock instability. However, this method cannot
prevent expansion shock and is incompatible with the traditional curing method
for expansion shock. Therefore, the traditional curing mechanism is analyzed.
The discussion explains the effectiveness of the traditional curing method and
identifies several defects, one of which leads to incompatibility between
curing the shock instability and expansion shock. Consequently, a new improved
Roe scheme is proposed in this study. This scheme is concise, easy to
implement, low computational cost, and robust. More importantly, the scheme can
simultaneously cure the shock instability and expansion shock without
additional costs.

4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an