TY - JOUR
T1 - SUPG finite element computation of compressible flows with the entropy and conservation variables formulations
AU - Le Beau, G. J.
AU - Ray, S. E.
AU - Aliabadi, S. K.
AU - Tezduyar, T. E.
N1 - Funding Information:
Correspondence to: Tayfun E. Tezduyar, Minnesota Supercomputer Institute, University of Minnesota, 1200 Washington Avenue South, Minneapolis, MN 55415, USA. ’ This research was sponsored by NASA-Johnson Space Center under grant NAG 9-449 and by NSF under grant MSM-8796352. Partial support for this work has also come from the Army Research Office contract number DAAL03-89-C-0038 with the Army High-Performance Computing Research Center at the University of Minnesota.
PY - 1993/5
Y1 - 1993/5
N2 - SUPG-stabilized finite element formulations of compressible Euler equations based on the conservation and entropy variables are investigated and compared. The formulation based on the conservation variables consists of the formulation introduced by Tezduyar and Hughes plus a shock capturing term. The formulation based on the entropy variables is the same as the one by Hughes, Franca and Mallet, which has a shock capturing term built in. These formulations are tested on several subsonic, transonic and supersonic compressible flow problems. It is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables. Furthermore, the solutions obtained using the two formulations are very close and in some cases almost indistinguishable. Consequently, it can be deduced that the relative merits of these two formulations will continue to remain under debate.
AB - SUPG-stabilized finite element formulations of compressible Euler equations based on the conservation and entropy variables are investigated and compared. The formulation based on the conservation variables consists of the formulation introduced by Tezduyar and Hughes plus a shock capturing term. The formulation based on the entropy variables is the same as the one by Hughes, Franca and Mallet, which has a shock capturing term built in. These formulations are tested on several subsonic, transonic and supersonic compressible flow problems. It is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables. Furthermore, the solutions obtained using the two formulations are very close and in some cases almost indistinguishable. Consequently, it can be deduced that the relative merits of these two formulations will continue to remain under debate.
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U2 - 10.1016/0045-7825(93)90033-T
DO - 10.1016/0045-7825(93)90033-T
M3 - Article
AN - SCOPUS:0027593720
SN - 0374-2830
VL - 104
SP - 397
EP - 422
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 3
ER -