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Summary of Test Case C1.5
Radial expansion wave (2D/3D)
1
1
st
International High-Order CFD Workshop
Jan, 7-8, 2012, Nashville, TN
Contributing groups:
Fidkowski, Galbraith, Gassner,
Mavriplis, Van Leer, Z.J. Wang
P =2
P = 3
P =4
2D:
Error vs. DOF
•
Expected order: 2P+1 on rectangles,
P+1 on triangles.
•
Order short of 2P +1 on rectangles.
•
Cause: unexpected lack of solution
smoothness at larger times.
•
All results for t=2,
γ
=3, for greatest
smoothness.
•
Van Leer has lowest error.
2D: Error vs. Work
P =2
P = 3
P =4
P =2
P = 3
P =4
•
Galbraith most efficient owing to use of
analytical integration rather than
Gaussian quadrature.
•
Van Leer second best.
3D: Error vs. DOF
P =2
P = 3
P =4
•
Only regular hexahedral
elements used.
•
Results even further below
expected order due to lack of
solution smoothness.
•
All results for t=2,
γ
=3.
•
Van Leer has lowest error.
P =2
P = 3
P =4
3D: Error vs. Work
•
Only regular hexahedral
elements used
•
Van Leer most efficient.
Conclusions
•
Before order of accuracy 2P+1 can be reached
with any DG method, the problem of the non-
smoothness of the solution must be fixed,
possibly by adding a manufactured source term.
•
The consistently low errors of Van Leer et al.
may be owing to high-order Gaussian quadrature
used in anticipation of order of accuracy 2P+1.
sdsd
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Presentation Transcript
1st International High-Order CFD Workshop Jan, 7-8, 2012, Nashville, TN Summary of Test Case C1.5 Radial expansion wave (2D/3D) Contributing groups: Fidkowski, Galbraith, Gassner, Mavriplis, Van Leer, Z.J. Wang 1st International Workshop on High-Order CFD Methods 1
2D: Error vs. DOF Expected order: 2P+1 on rectangles, P+1 on triangles. Order short of 2P +1 on rectangles. Cause: unexpected lack of solution smoothness at larger times. All results for t=2, =3, for greatest smoothness. Van Leer has lowest error. P =2 P = 3 P =4 C1.5 Radial expansion wave
2D: Error vs. Work P =2 P =2 Galbraith most efficient owing to use of analytical integration rather than Gaussian quadrature. Van Leer second best. P = 3 P =4 P = 3 P =4 C1.5 Radial expansion wave
3D: Error vs. DOF Only regular hexahedral elements used. Results even further below expected order due to lack of solution smoothness. All results for t=2, =3. Van Leer has lowest error. P =2 P = 3 P =4 C1.5 Radial expansion wave
3D: Error vs. Work Only regular hexahedral elements used P =2 Van Leer most efficient. P = 3 P =4 C1.5 Radial expansion wave
Conclusions Before order of accuracy 2P+1 can be reached with any DG method, the problem of the non- smoothness of the solution must be fixed, possibly by adding a manufactured source term. The consistently low errors of Van Leer et al. may be owing to high-order Gaussian quadrature used in anticipation of order of accuracy 2P+1. C1.5 Radial expansion wave
