This paper is devoted to the simulation of the two-dimensional gas flows with oscillations and discontinuities using the Runge — Kutta Discontinuous Galerkin (RKDG) method, that has been implemented in the code prototype written in C++. It implements the HLLC numerical flux, the KXRCF troubled cells indicator, the WENO S limiter with the local characteristic decomposition approach and algorithm of dynamic time step control. The computations could be performed on unstructured meshes with mixed cell types (quadrangular and triangular) which can be built in any mesh bulder in IDEAS UNV format (i.e. SALOME). The code is verified on the common numerical tests such as pulsating and vibrating cylinders, Sod-like cylindrical explosion, forward-facing step, blast wave problem. Comparison between analytical solution and numerical results obtained with the in-house code and the open-source OpenFOAM package is presented.

1.
R. E.
Harris
,
E. M.
Collins
,
A.
Sescu
,
E. A.
Luke
,
L. L.
Strutzenberg
, and
J. S.
West
, “High-order discontinuous galerkin and hybrid rans/les method for prediction of launch vehicle lift-off acoustic environments,” in
20th AIAA/CEAS Aeroacoustics Conference
(
Atlanta
,
GA
,
2014
).
2.
T.
Toulorge
, “
Efficient runge-kutta discontinuous galerkin methods applied to aeroacoustics
,” Ph.D. thesis,
Kathlieke Universiteit, Leuvene
,
2012
.
3.
C. K. W.
Tam
and
J. C.
Webb
,
J. of Comp. Phys.
107
,
262
281
(
1993
).
4.
I. S.
Bosnyakov
,
S. V.
Lyapunov
,
A. I.
Troshin
,
V. V.
Vlasenko
, and
A. V.
Wolkov
, “
A high-order discontinuous galerkin method for external aerodynamics
,” in
32nd AIAA Applied Aerodynamics Conferencee
(
2014
).
5.
V. D.
Galepova
,
V. V.
Lukin
,
I. K.
Marchevsky
, and
I. N.
Fufaev
,
Preprints of Keldysh IAP
131
(
2017
), .
6.
J.
Qiu
and
C.-W.
Shu
,
SIAM J. Sci. Comput.
26
,
907
929
(
2006
).
7.
X.
Zhong
and
C.-W.
Shu
,
J. Comp. Phys.
232
,
397
415
(
2013
).
8.
E. F.
Toro
,
Riemann Solvers and Numerical Methods for Fluid Dynamics
(
Springer
,
Berlin
,
2009
).
9.
B.
Cockburn
and
C.-W.
Shu
,
Math. Comp.
52
,
411
435
(
1989
).
10.
B.
Cockburn
,
Lecture Notes in Mathematics
1697
,
151
268
(
1998
).
11.
J.
Zhu
,
X.
Zhong
,
C.-W.
Shu
, and
J.-X.
Qiu
,
Communications in Computational Physics
19
,
944
969
(
2016
).
12.
L.
Krivodonova
,
J.
Xin
,
J. F.
Remacle
,
N.
Chevaugeon
, and
J. E.
Flaherty
,
Applied Numerical Mathematics
48
,
323
338
(
2004
).
13.
Openfoam free cfd software
(https://openfoam.org/, accessed: 2018-06-10).
14.
M. J.
Crocker
, ed.,
Handbook of Acoustics
(
Wiley-Interscience
,
1998
).
15.
V.
Korchagova
,
I.
Fufaev
,
S.
Sautkina
, and
V.
Lukin
,
Proceedings of ISP RAS
30
,
285
300
(
2018
).
16.
M.
Kraposhin
,
A.
Bovtrikova
, and
S.
Strijhak
,
Procedia Computer Science
66
,
43
52
(
2015
).
This content is only available via PDF.