A class of implicit upwind schemes for Euler simulations with unstructured meshes

作者: L. Fezoui , B. Stoufflet

DOI: 10.1016/0021-9991(89)90187-3

关键词: Explicit and implicit methodsApplied mathematicsEuler equationsMathematicsEuler's formulaMathematical optimizationFinite element methodRate of convergencePartial differential equationUpwind schemeLinearization

摘要: Abstract A class of implicit finite element upwind schemes for solving Euler equations is presented. Steady flows with extreme conditions such as high Mach numbers or/and large angles attack on unstructured meshes can be simulated. Upwind methods are used the spatial approximation. Higher rates convergence obtained by using an scheme relying a linearization fluxes and partial resolution systems Gauss-Seidel algorithm. The that we get more efficient robust than explicit time integration.

参考文章(9)
Joseph L Steger, R.F Warming, Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods Journal of Computational Physics. ,vol. 40, pp. 263- 293 ,(1981) , 10.1016/0021-9991(81)90210-2
H.C. Yee, Linearized form of implicit TVD schemes for the multidimensional Euler and Navier-Stokes equations Computers & Mathematics With Applications. ,vol. 12, pp. 413- 432 ,(1986) , 10.1016/0898-1221(86)90172-0
Françoise Angrand, Alain Dervieux, Some explicit triangular finite element schemes for the Euler equations International Journal for Numerical Methods in Fluids. ,vol. 4, pp. 749- 764 ,(1984) , 10.1002/FLD.1650040804
Richard M Beam, R.F Warming, An implicit finite-difference algorithm for hyperbolic systems in conservation-law form Journal of Computational Physics. ,vol. 22, pp. 87- 110 ,(1976) , 10.1016/0021-9991(76)90110-8
Computing Methods in Applied Sciences and Engineering, 1977, II Mathematics of Computation. ,vol. 41, pp. 384- ,(1974) , 10.1007/3-540-06769-8
G. Vijayasundaram, Transonic flow simulations using an upstream centered scheme of Godunov in finite elements Journal of Computational Physics. ,vol. 63, pp. 416- 433 ,(1986) , 10.1016/0021-9991(86)90202-0
D. JESPERSEN, T. PULLIAM, Flux vector splitting and approximate Newton methods 6th Computational Fluid Dynamics Conference Danvers. pp. 535- 543 ,(1983) , 10.2514/6.1983-1899