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In the three-dimensional curvilinear coordinates, a fifth-order numerical scheme (FVM-QSI scheme) is proposed for convection equations which are discretized with a finite volume method. In the FVM-QSI scheme, fluxes on the cell boundaries are evaluated with quintic spline functions. In order to prevent numerical oscillations, the calculated fluxes are corrected with the flux control techniques (DC and FP methods), which are newly proposed in the 3D space in this paper. As a result of the computations of cubic cavity flows and its scalar convections, it was shown that the FVM-QSI scheme with the DC method enables us to obtain conservative and accurate results without numerical oscillations.

FIFTH-ORDER CONSERVATIVE SCHEME WITH FLUX CONTROL FOR CONVECTION EQUATIONS ON 3D CURVILINEAR COORDINATES