Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-Lagrangian lattice Boltzmann method for compressible flows   This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM)
solver for compressible flows. In contrast to other LBM for compressible flows,
the vertices are organized in cells, and interpolation polynomials up to fourth
order are used to attain the off-vertex distribution function values. Differing
from the recently introduced Particles on Demand (PoD) method, the method
operates in a static, non-moving reference frame. Yet the SLLBM in the present
formulation grants supersonic flows and exhibits a high degree of Galilean
invariance. The SLLBM solver allows for an independent time step size due to
the integration along characteristics and for the use of unusual velocity sets,
like the D2Q25, which is constructed by the roots of the fifth-order Hermite
polynomial. The properties of the present model are shown in diverse example
simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a
two-dimensional Riemann problem and a shock-vortex interaction. It is shown
that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev
support points allow for spatially high-order solutions and minimize the mass
loss caused by the interpolation. Transformed grids in the shock-vortex
interaction show the general applicability to non-uniform grids.

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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: stat