The current work presents a parallel formulation using the MPI protocol for an adaptive high order finite difference scheme to solve 2D conservation laws. Adaptivity is achieved at each time iteration by the application of an interpolating wavelet transform in each space dimension. High order approximations for the numerical fluxes are computed by ENO and WENO schemes. Since time evolution is made by a TVD Runge-Kutta space splitting scheme, the problem is naturally suitable for parallelization. Numerical simulations and speedup results are presented for Euler equations in gas dynamics problems.

1.
B.
Cockburn
,
C.
Johnson
,
C.-W.
Shu
, and
E.
Tadmor
,
Advanced numerical approximation of nonlinear hyperbolic equations
.,
Springer-Verlag
,
Milan
,
1998
, pp.
1
450
.
2.
A.
Kozakevicius
, and
L. C.
de Castro Santos
,
Applied Numerical Mathematics
59
,
2337
2355
(
2009
).
3.
R.
Bürger
, and
A.
Kozakevicius
,
Journal of Computational Physics
224
,
1190
1222
(
2007
).
4.
S.
Berres
,
R.
Bürger
, and
A.
Kozakevicius
,
Advances in Applied Mathematics and Mechanics
1
,
581
614
(
2009
).
5.
E. S.
de Góes Maciel
,
A. P.
Pimenta
,
E. M.
Ferreira
, and
N. E.
Mastorakis
, “
TVD and ENO Applications to Supersonic Flows in 2D
,” in
2014 International Conference on Mathematics and Computers in Sciences and in Industry
,
2014
, pp.
1
23
.
6.
A.
de Jesus Kozakevicius
, and
A. A.
Schmidt
,
AIP Conference Proceedings
2
,
1158
1161
(
2009
).
7.
M. O.
Domingues
,
S.
Gomes
,
O.
Roussel
, and
K.
Schneider
,
Applied Numerical Mathematics
59
,
2303
2321
(
2009
).
8.
Z.-N.
Wu
, and
H.
Zou
,
Journal of Computational Physics
187
,
683
715
(
2003
).
9.
M.
Nordén
,
S.
Holmgren
, and
M.
Thuné
, OpenMP versus MPI for PDE Solvers Based on Regular Sparse Numerical Operators,
ICCS 2002 - Lecture Notes in Computer Science
,
Springer
-
Berlin-Heidelberg
,
2002
, vol.
2331
, pp.
681
690
.
10.
P.
Kestener
,
F.
Château
, and
R.
Teyssier
, Accelerating Euler Equations Numerical Solver on GPU,
Algorithms and Architectures for Parallel Processing - Lecture Notes in Computer Science
,
Berlin-Heidelberg
,
2010
, pp.
281
288
.
11.
C.
Wang
,
X.
Dong
, and
C.-W.
Shu
,
Journal of Computational Physics
298
,
161
175
(
2015
).
12.
A.
Kurganov
, and
E.
Tadmor
,
Numer. Methods Partial Differential Equations
18
,
548
608
(
2000
).
This content is only available via PDF.
You do not currently have access to this content.