Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A discontinuous Galerkin spectral element method for a nonconservative
  compressible multicomponent flow model   In this work, we propose an accurate, robust, and stable discretization of
the gamma-based compressible multicomponent model by Shyue [J. Comput. Phys.,
142 (1998), 208-242] where each component follows a stiffened gas equation of
state (EOS). We here extend the framework proposed in Renac [J. Comput. Phys.
382 (2019), 1-26] and Coquel et al. [J. Comput. Phys. 431 (2021) 110135] for
the discretization of hyperbolic systems, with both fluxes and nonconservative
products, to unstructured meshes with curved elements in multiple space
dimensions. The framework relies on the discontinuous Galerkin spectral element
method (DGSEM) using collocation of quadrature and interpolation points. We
modify the integrals over discretization elements where we replace the physical
fluxes and nonconservative products by two-point numerical fluctuations. The
contributions of this work are threefold. First, we analyze the semi-discrete
DGSEM discretization and prove that the scheme is high-order accurate,
free-stream preserving, and entropy stable when excluding material interfaces.
Second, we design a three-point scheme with a HLLC solver that does not require
a root-finding algorithm for approximating the nonconservative products. The
scheme is proved to be robust and entropy stable for convex entropies,
preserves uniform states across material interfaces, satisfies a discrete
minimum principle on the specific entropy and maximum principles on the EOS
parameters. Third, the HLLC solver is applied at interfaces in the DGSEM
scheme, while we consider two kinds of fluctuations in the integrals over
discretization elements: material interface preserving and entropy
conservative. Time integration is performed using SSP Runge-Kutta schemes. The
high-order accuracy, nonlinear stability, and robustness of the present scheme
are assessed through several numerical experiments in one and two space
dimensions.

11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ