An extended Finite Variable Difference Method with application to QUICK scheme. Optimized QUICK

A Finite Variable Difference Method (FVDM) proposed previously by the author for locally exact numerical schemes is extended so as to be applicable to polynomial expansion schemes. This extended FVDM is applied to the QUICK scheme. The optimum differencing points are analytically derived in terms of mesh Reynolds numbers so that the variance of the numerical solution is minimized under the condition that roots of the resulting characteristic equation are nonnegative to insure the numerical stability. This optimized scheme coincides with the original QUICK scheme at Rm=8/3, which is the critical value of its stability, and complements a stable scheme for Rm greater than 8/3. This optimization improves the numerical solution for the steady and unsteady convection-diffusion equations without numerical oscillations. In the same manner as the previous result for the locally exact numerical schemes, it has been made clear based on the extended FVDM that optimum differencing points from the view point of numerical stability and accuracy exist for the polynomial expansion schemes. (author)