Flux-difference Splitting Research Articles

A multigrid method for the Cauchy-Riemann equations based on flux-difference splitting and its extension to the steady Euler equations

Flux-vector splitting and flux-difference splitting techniques are applied to the Cauchy-Riemann equations. It is shown that the discrete equations obtained by both techniques can be solved by relaxation methods, which can be used in the multigrid technique. The flux-difference splitting technique is applied to the steady one-dimensional Euler equations and the resulting set of discrete equations is solved by a relaxation algorithm. The solution for transonic flow is free of transition points in the shock region. By analogy with the Cauchy-Riemann equations, it is concluded that] this technique is extendable to two dimensions and that it can be used in the multigrid method.

Computation of steady supersonic flows by a flux-difference/splitting method

A “flux-difference splitting” method has been conceived for the numerical solution of hyperbolic problems and successfully implemented for unsteady flows. It aims to describe the propagation of waves and to respect the domains of dependence. Shock waves are captured numerically very neatly. Here an extension is proposed for the prediction of two-dimensional or axisymmetric steady supersonic flows. Numerical examples are shown to validate the capabilities of the method.

A Contribution to the Numerical Prediction of Unsteady Flows

Methods based on flux-differe nce splitting are investigated with reference to the prediction of unsteady compressible flows. They combine the feature of taking into account the wake-like nature of these flows and the capability of correctly capturing shock waves. Two recently proposed approaches and a third one suggested here are compared for one-dimensional flow, with particular reference to the means of operating the splitting. They are extended to the cases of variable-area ducts and a general transformation of the independent variables. Firstand second-order accurate schemes are presented and procedures for the computation at the boundaries are shown. Finally, numerical experiments are reported and discussed.