Non-Reflecting Boundary Conditions for DNS in Curvilinear Coordinates

High-order non-reflecting boundary conditions in a generalized curvilinear coordinate system for solving the time-dependent Navier-Stokes equations in complex geometry have been developed based on the characteristic analysis and the modified Navier-Stokes equation. Viscous terms are taken into account to include the viscous effect near the wall. All boundary conditions are added implicitly to the equations of interior points to ensure the stability of this scheme. The computational results show that the non-reflecting boundary conditions are compatible to the sixth- or fourth-order compact central difference scheme and maintain a high-order accuracy for the global solution. The non-reflecting boundary conditions work surprisingly well without any artificial buffer or sponge. No visible reflected wave was found from either inflow, outflow, far-field, or solid surface. The computational solution is found quite accurate comparing with valid data.

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