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Implicit upwind residual-distribution Euler and Navier-Stokes solver on unstructured meshes

par Issman, Emmanuel ;Degrez, Gérard ;Deconinck, Herman
Référence AIAA journal, 34, 10, page (2021-2028)
Publication Publié, 1996-10

Article révisé par les pairs

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Résumé :

Implicit iterative solution techniques are considered for application to a compressible Euler and Navier-Stokes solver using upwind residual-distribution schemes on unstructured meshes. Numerical evaluation of the complete Jacobian matrix needed for the linearization process is achieved at low cost, either by finite difference approximation or by Broyden's update. It enables nonlinear solution strategies such as Newton iterative methods where linear systems are solved approximately using an accelerated iterative scheme. The linearized backward Euler scheme is used to integrate the discretized equations in time, together with a simple time-step evolution strategy. Alternatively, when this strategy fails, it is possible to use a fixed-point acceleration method that has proven quite robust. Numerical applications show the efficiency of the iterative strategy for various flow conditions.