Comparison of numerical and analytical Jacobians
作者： Kirk J. Vanden , Paul D. Orkwis
DOI: 10.2514/3.13202
关键词: Jacobian matrix and determinant 、 Numerical analysis 、 Symbolic computation 、 Navier–Stokes equations 、 Calculus 、 Applied mathematics 、 Test case 、 Continuity equation 、 Incompressible flow 、 Numerical differentiation 、 Mathematics 、 Aerospace engineering
摘要: The results are presented of comparison between numerical and analytical approaches for forming the Jacobian matrices that arise from implicit discretizations governing equations derivation exact Jacobians using MACSYMA symbolic manipulation expert system is discussed in detail. differentiation procedure used to develop described. entries obtained preceding were tested by comparing density residuals selected test cases. cases include supersonic flat plate compression corner geometries. indicate two virtually identical, although approach may have some implementation advantages over approach.
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