Calculation of governing equations and geometry parameter for FV-TVD scheme

Since governing equations are discretized using a finite volume method for FV TVD scheme, we use integral governing equations to solve the flow field. We achieve N S equations in terms of cylinder coordinate velocity components in an arbitrary curvilinear coordinate using a tensor analytic method to the integral governing equations. It's also testified that term g which include Jacobian can be reduced when governing equations are discretized on an infinitesimal small control volume. Numerical calculations indicated that this scheme can capture shocks and contact discontinuities exactly and the solution with this treatment is in good agreement with the experimental data.