A Comparison of Explicit Time Integration Techniques for the Finite Element Shock Wave Equations.
NAVAL RESEARCH LAB WASHINGTON DC
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Numerical studies of three explicit, two-step time integration techniques for the one dimensional, finite element shock wave equations have been conducted. One of these integration techniques, the Godunov scheme, is first order accurate in time while the other, the Lax-Wendroff scheme, is second order accurate in time. The results show that overall, the best numerical solutions were obtained by the standard Godunov scheme, with either linear or parabolic spatial element. A central weighted first-step Godunov time integration provided results nearly as good. The results of the condensed mass matrix formulation were clearly not as good as the results for the full matrix. Results for the Lax-Wendroff time integration showed severe oscillations in the solution, and consequently were not as good as the Godunov time integration. The present finite element results compare quite favorably with results from standard finite-difference methods. Author
- Numerical Mathematics
- Fluid Mechanics