Effect of the Jacobian evalution on direct solutions of the Euler equations

Download

index.pdf

Date

2003

Author

Onur, Ömer

Metadata

Show full item record

Item Usage Stats

265
views

0
downloads

A direct method is developed for solving the 2-D planar/axisymmetric Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes, and the resulting nonlinear system of equations are solved using Newton̕s Method. Both analytical and numerical methods are used for Jacobian calculations. Numerical method has the advantage of keeping the Jacobian consistent with the numerical flux vector without extremely complex or impractical analytical differentiations. However, numerical method may have accuracy problem and may need longer execution time. In order to improve the accuracy of numerical method detailed error analyses were performed. It was demonstrated that the finite-difference perturbation magnitude and computer precision are the most important parameters that affect the accuracy of numerical Jacobians. A relation was developed for optimum perturbation magnitude that can minimize the error in numerical Jacobians. Results show that very accurate numerical Jacobians can be calculated with optimum perturbation magnitude. The effects of the accuracy of numerical Jacobians on the convergence of flow solver are also investigated. In order to reduce the execution time for numerical Jacobian evaluation, flux vectors with perturbed flow variables are calculated for only related cells. A sparse matrix solver based on LU factorization is used for the solution, and to improve the Jacobian matrix solution some strategies are considered. Effects of different flux splitting methods, higher-order discretizations and several parameters on the performance of the solver are analyzed.

Subject Keywords

Aerospace engineering, Direct flow solution, 2-D planar

URI

http://etd.lib.metu.edu.tr/upload/2/1098268/index.pdf
https://hdl.handle.net/11511/13777

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Effects of the Jacobian evaluation on Newton's solution of the Euler equations Onur, O; Eyi, Sinan (Wiley, 2005-09-20) 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 accurac...
Effects of the Jacobian evaluation on Newton's solution of the Euler equations Onur, O.; Eyi, Sinan (null; 2005-12-01) A 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 accur...
Two-dimensional unsteady Navier-Stokes solution method with moving overset grids Tuncer, İsmail Hakkı (American Institute of Aeronautics and Astronautics (AIAA), 1997-03-01) A simple numerical algorithm to localize intergrid boundary points and to interpolate unsteady solution variables across two-dimensional, structured overset grids is presented. Overset grids are allowed to move in time relative to each other. Intergrid boundary points are localized in a triangular stencil on the donor grid by a directional search algorithm. The final parameters of the search algorithm give the interpolation weights at the intergrid boundary point. Numerical results are presented for steady ...
NEW FAMILY OF MODAL METHODS FOR CALCULATING EIGENVECTOR DERIVATIVES AKGUN, MA (American Institute of Aeronautics and Astronautics (AIAA), 1994-02-01) A new family of modal methods for the calculation of eigenvector derivatives in non-self-adjoint systems with a singular coefficient matrix is developed. The family contains the modal and modified modal methods as a subset. In the family, the component of the mth eigenvector in the expansion of the derivative of the jth eigenvector is multiplied by various powers of the eigenvalue ratio lambda(i)/lambda(m), thereby accelerating convergence. The family of methods is applied to a self-adjoint example problem,...
Nonlinear flutter calculations using finite elements in a direct Eulerian-Lagrangian formulation Seber, Guclu; Bendiksen, Oddvar O. (American Institute of Aeronautics and Astronautics (AIAA), 2008-06-01) A fully nonlinear aeroelastic formulation of the direct Eulerian-Lagrangian computational scheme is presented in which both structural and aerodynamic nonlinearities are treated without approximations. The method is direct in the sense that the calculations are done at the finite element level, both in the fluid and structural domains, and the fluid-structure system is time-marched as a single dynamic system using a multistage Runge-Kutta scheme. The exact nonlinear boundary condition at the fluid-structure...

Citation Formats

Ö. Onur, “Effect of the Jacobian evalution on direct solutions of the Euler equations,” M.S. - Master of Science, Middle East Technical University, 2003.