A Brief Note on Implementing Boundary Conditions at a Solid Wall Using the FCT Algorithm
NAVAL RESEARCH LAB WASHINGTON DC
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The implementation of boundary conditions at a solid wall using the flux-corrected transport FCT algorithm has been studied. We found that extrapolating the interior points to obtain the pressure at the wall may introduce instability. Instead, the given physical conditions at the wall, such as the continuity equation and the given thermal conditions, should he used to evaluate the pressure at the wall. Since the viscous diffusion and other source terms can be calculated from flow variables at interior points and the wall surface, the need to specify the guard-cell values at a solid wall is only required by the numerical diffusion embedded in FCT. Guard-cell values may interfere with the activation of the flux limiter near the wall, introducing either numerical instability or producing unphysical numerical results. Several approaches have been proposed to control this interference, such as turning off numerical diffusion at the first cell near the wall, or introducing extra numerical diffusion in the momentum equation at the wall to suppress the instability.
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