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The fringe region technique and the Fourier method used in the direct numerical simulation of spatially evolving viscous flows. (English) Zbl 0930.35015
For numerical simulations of a flow in infinite domains these domains must be made finite. Information from the solution of a corresponding initial boundary value problem in the exterior domain is transferred via the artificial boundary conditions. To eliminate the difficulties with boundary conditions and facilitate the use of Fourier method the fringe region (or filter, damping layer) technique has been used in direct simulations of transitional and turbulent boundary layers.
The thoretical basis of the fringe region technique is given in the present paper. The energy estimates are obtained for the deviation between an exact solution of the Navier-Stokes equations and the approximate solution computed using the fringe region technique. The results of the paper indicate that it is possible to use the fringe region technique in combination with the Fourier method to obtain accurate numerical solutions to the inflow-outflow problem associated with the Navier-Stokes equations. This conclusion is illustrated by some numerical examples.

MSC:
35A35 Theoretical approximation in context of PDEs
35R30 Inverse problems for PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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