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Summary of Test Case C1.5 Radial expansion wave (2D/3D)

1 st 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 . 2D: Error vs. DOF. P =2.

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Summary of Test Case C1.5 Radial expansion wave (2D/3D)

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  1. 1st International High-Order CFD Workshop Jan, 7-8, 2012, Nashville, TN Summary of Test Case C1.5Radial expansion wave (2D/3D) Contributing groups: Fidkowski, Galbraith, Gassner, Mavriplis, Van Leer, Z.J. Wang

  2. 2D: Error vs. DOF P =2 • 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. P = 3 P =4

  3. 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

  4. 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, γ=3. • Van Leer has lowest error. P =2 P = 3 P =4

  5. 3D: Error vs. Work • Only regular hexahedral elements used • Van Leer most efficient. P =2 P = 3 P =4

  6. 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.

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