Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Truly multi-dimensional all-speed schemes for the Euler equations on
  Cartesian grids   Finite volume schemes often have difficulties to resolve the low Mach number
(incompressible) limit of the Euler equations. Incompressibility is only
non-trivial in multiple spatial dimensions. Low Mach fixes, however generally
are applied to the one-dimensional method and the method is then used in a
dimensionally split way. This often reduces its stability. Here, it is
suggested to keep the one-dimensional method as it is, and only to extend it to
multiple dimensions in a particular, all-speed way. This strategy is found to
lead to much more stable numerical methods. Apart from the conceptually
pleasing property of modifying the scheme only when it becomes necessary, the
multi-dimensional all-speed extension also does not include any free parameters
or arbitrary functions, which generally are difficult to choose, or might be
problem dependent. The strategy is exemplified on a Lagrange Projection method
and on a relaxation solver.

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The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
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The categories of this paper are: adap-org