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Upwind relaxation methods for the Navier-Stokes equations using inner iterations. (English) Zbl 0741.76053

An upwind line relaxation algorithm for the Navier-Stokes equations which employs inner iterations is applied to a supersonic and a subsonic test problem. The purpose of using inner iterations is to accelerate the convergence to steady-state solutions, thereby reducing the overall CPU time. A convergence criterion is developed to assist in automating the inner iterative procedure. The ability of the line inner iterative procedure to mimic the quadratic convergence of the direct solver method is confirmed in both test problems.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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