Performances of Numerical and Analytical Jacobians in Flow and Sensitivity Analysis

Abstract

The effects of flux Jacobian evaluation on flow and sensitivity analysis are studied. A cell centered finite volume method with various upwinding schemes is used. A Newton’s method is applied for flow solution, and the resulting spa rse matrix is solved by LU factorization. Flux Jacobians are evaluated both numerically and analytically. The sources of the error in numerical Jacobian calculation are studied. The optimum finite difference perturbation magnitude that minimizes the error is searched. The effects of error numerical Jacobians on the convergence of flow solver are studied. The sen sitivities of the flow variables are evaluated by direct-differentiation method. The Jac obian matrix which is constructed in the flow solution is also used in sensitivity calculati on. The influence of errors in numerical Jacobians on the accuracy of sensitivities is analy zed. Results showed that, the error in Jacobians significantly affects the convergence of flow analysis and accuracy of sensitivities. Approximately the same optimum perturbation magnitude enables the most accurate numerical flux Jacobian and sensitivity calculation s.