Effects of the Jacobian evaluation on Newton's solution of the Euler equations

Date

2005-09-20

Author

Onur, O
Eyi, Sinan

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Newton's method is developed for solving the 2-D Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes. Both analytical and numerical methods are used for Jacobian calculations. Although the numerical method has the advantage of keeping the Jacobian consistent with the numerical residual vector and avoiding extremely complex analytical differentiations, it may have accuracy problems and need longer execution time. In order to improve the accuracy of numerical Jacobians, detailed error analyses are performed. Results show that the finite-difference perturbation magnitude and computer precision are the most important parameters that affect the accuracy of numerical Jacobians. A method is developed for calculating an optimal perturbation magnitude that can minimize the error in numerical Jacobians. The accuracy of the numerical Jacobians is improved significantly by using the optimal perturbation magnitude. The effects of the accuracy of numerical Jacobians on the convergence of the flow solver are also investigated. In order to reduce the execution time for numerical Jacobian evaluation, flux vectors with perturbed flow variables are calculated only for neighbouring cells. A sparse matrix solver that is based on LU factorization is used. Effects of different flux splitting methods and higher-order discretizations on the performance of the solver are analysed. Copyright (c) 2005 John Wiley & Sons, Ltd.

Subject Keywords

Mechanical Engineering, Mechanics of Materials, Applied Mathematics, Computational Mechanics, Computer Science Applications

URI

https://hdl.handle.net/11511/43593

Journal

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

DOI

https://doi.org/10.1002/fld.996

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Department of Aerospace Engineering, Article

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Citation Formats

O. Onur and S. Eyi, “Effects of the Jacobian evaluation on Newton’s solution of the Euler equations,” INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, pp. 211–231, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43593.