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The collocation method uses the Rhie-Chow scheme to find the cell interfacevelocity by pressure-weighted interpolation. The accuracy of this interpolationmethod in unsteady flows has not been fully clarified. This study constructs afinite difference scheme for incompressible fluids using a collocated grid in ageneral curvilinear coordinate system. The velocity at the cell interface isdetermined by weighted interpolation based on the pressure difference toprevent pressure oscillations. The Poisson equation for the pressure correctionvalue is solved with the cross-derivative term omitted to improve calculationefficiency. In addition, simultaneous relaxation of velocity and pressure isapplied to improve convergence. Even without the cross-derivative term,calculations can be stably performed, and convergent solutions are obtained. Inunsteady inviscid flow, the conservation of kinetic energy is excellent even ina non-orthogonal grid, and the calculation result has second-order accuracy totime. In viscous analysis at a high Reynolds number, the error decreasescompared with that of the Rhie-Chow interpolation method. The present numericalscheme improves calculation accuracy in unsteady flows. The possibility ofapplying this computational method to high Reynolds number flows isdemonstrated through several analyses.

Energy-conserving finite difference scheme based on velocity interpolation applicable to unsteady flows using collocated grids