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An adaptive finite element scheme for transient problems in CFD. (English) Zbl 0611.73079
An adaptive finite element scheme for transient problems is presented. The classic h-enrichment/coarsening is employed in conjunction with a triangular finite element discretization in two dimensions. A mesh change is performed every n timesteps, depending on the Courant number employed and the number of ’projective layers’ added ahead of the refined region. In order to simplify the refinement/coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved on the CRAY XMP 12 at NRL. Several examples involving shock-shock interactions and the impact of shocks on structures demonstrate the performance of the method, indicating that considerable savings in CPU time and storage can be realized even for strongly unsteady flows.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
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[1] Glaz, H.M.; Colella, P.; Glass, I.I.; Deschambault, R.L., A numerical study of oblique shock-wave reflections with experimental comparisons, (), 117-140
[2] Fry, M.; Tittsworth, J.; Kuhl, A.; Book, D.L.; Boris, J.P.; Picone, M., Transport algorithms with adaptive gridding, (), 376-384
[3] Kailasanath, K.; Oran, E.S.; Boris, J.P.; Young, T.R., Determination of detonation cell size and the role of transverse waves in two-dimensional detonations, Combustion and flame, 61, 199-209, (1985)
[4] Peters, N.; Warnatz, J., Numerical methods in laminar flame propagation, ()
[5] Ewing, R.E., Special issue on oil reservoir simulation, Comput. meths. appl. mech. engrg., 47, (1984)
[6] O.C. Zienkiewicz, private communication.
[7] Gnoffo, P.A., A finite-volume, adaptive grid algorithm applied to planetary entry flowfields, Aiaa j, 21, 1249-1254, (1983) · Zbl 0526.76073
[8] Nakahashi, K.; Deiwert, G.S., A three-dimensional adaptive grid method, Aiaa-85-0486, (1985)
[9] Berger, M.J.; Oliger, J., Adaptive mesh refinement for hyperbolic partial differential equations, J. comput. phys., 53, 484-512, (1984) · Zbl 0536.65071
[10] Smooke, M.D.; Koszykowsky, M.L., Two-dimensional fully adaptive solutions of solid-solid alloying reactions, J. comput. phys., 62, 1-25, (1986) · Zbl 0588.65086
[11] Dannenhoffer, J.F.; Baron, J.R., Adaptive procedure for steady state solution of hyperbolic equations, Aiaa-84-0005, (1984)
[12] Dannenhoffer, J.F.; Baron, J.R., Grid adaptation for the 2-D Euler equations, Aiaa-85-0484, (1985)
[13] Dannenhoffer, J.F.; Baron, J.R., Robust grid adaptation for complex transonic flows, Aiaa-86-0495, (1986)
[14] Löhner, R.; Morgan, K.; Zienkiewicz, O.C., An adaptive finite element procedure for high speed flows, Comput. meths. appl. mech. engrg., 51, 441-465, (1985) · Zbl 0568.76074
[15] Löhner, R.; Morgan, K.; Zienkiewicz, O.C., Adaptive grid refinement for the compressible Euler equations, (), 281-297, Ch. 15
[16] Löhner, R.; Morgan, K., Improved adaptive refinement strategies for finite element aerodynamic computations, Aiaa-86-499, (1986)
[17] Palmerio, B.; Billey, V.; Dervieux, A.; Periaux, J., Self-adaptive mesh refinements and finite element methods for solving the Euler equations, () · Zbl 0606.76076
[18] Angrand, F.; Billey, V.; Dervieux, A.; Periaux, J.; Pouletty, C.; Stoufflet, B., 2-D and 3-D Euler flow calculations with a second-order accurate Galerkin finite element method, Aiaa-85-1706, (1985)
[19] Oden, J.T., Notes on grid optimization and adaptive methods for finite element methods, () · Zbl 0615.73083
[20] Oden, J.T.; Devloo, P.; Strouboulis, T., Adaptive finite element methods for the analysis of inviscid compressible flow: part I. fast refinement/unrefinement and moving mesh methods for unstructured meshes, Comput. meths. appl. mech. engrg., 59, 327-362, (1986) · Zbl 0593.76080
[21] Löhner, R.; Morgan, K.; Vahdati, M.; Boris, J.P.; Book, D.L., FEM-FCT; combining high resolution with unstructured grids, J. comput. phys., (1986), to appear. · Zbl 0659.65085
[22] Zienkiewicz, O.C.; Morgan, K., Finite elements and approximation, (1983), Wiley New York · Zbl 0582.65068
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