COMPARISON OF NUMERICAL AND ANALYTICAL JACOBIANS

The results are presented of a comparison between numerical and analyt ical approaches for forming the Jacobian matrices that arise from impl icit discretizations of the governing equations. The derivation of the exact analytical Jacobians using the MACSYMA symbolic manipulation ex pert system is discussed in detail. The numerical differentiation proc edure used to develop the numerical Jacobians is described, The Jacobi an entries obtained from the preceding approaches were tested by compa ring the density residuals obtained for selected test cases. The test cases include supersonic flat plate and compression corner geometries. The results indicate that the two approaches are virtually identical, although the numerical Jacobian approach may have some implementation advantages over the exact analytical approach.