A two-point difference scheme for computing steady-state solutions to the conservative one-dimensional Euler equations. (English) Zbl 0563.76023

Wornom, Stephen F.

Comput. Fluids 12, 11-30 (1984).

An implicit finite-difference method is presented for obtaining steady- state solutions to the time dependent Euler equations, written in the conservation form, for flow containing shocks. The method uses a two- difference scheme for flux derivatives at subsonic points, at supersonic points, dissipation is added by retarded density concept, and the difference equations involve three points. However, the overall method retains the nice feature of the general two-point method as regards boundary conditions. Application of the method to quasi-one-dimensional nozzle flow equations is introduced for five different test cases, combining subsonic and supersonic boundary conditions. Some comparison with three-point method is made. Calculated results show the method’s advantages. Residuals can be reduced to machine zero in approximately 35 time steps for 50 mesh points. For one-dimensional Euler calculations, the scheme offers two advantages; the first is in regard to application of boundary conditions, the second is that the two-point algorithm is well-conditioned for large time steps.

Reviewer: G.C.Ling

MSC:

76B99	Incompressible inviscid fluids
76M99	Basic methods in fluid mechanics

Keywords:

implicit finite-difference method; steady-state solutions; time dependent Euler equations; flow containing shocks; dissipation; retarded density concept; two-point method; quasi-one-dimensional nozzle flow

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