Sensitivity analysis using finite difference and analytical Jacobians

Download
index.pdf
2009
Ezertaş, Ahmet Alper
Show full item record
195
views
413
downloads
The Flux Jacobian matrices, the elements of which are the derivatives of the flux vectors with respect to the flow variables, are needed to be evaluated in implicit flow solutions and in analytical sensitivity analyzing methods. The main motivation behind this thesis study is to explore the accuracy of the numerically evaluated flux Jacobian matrices and the effects of the errors in those matrices on the convergence of the flow solver, on the accuracy of the sensitivities and on the performance of the design optimization cycle. To perform these objectives a flow solver, which uses exact Newton’s method with direct sparse matrix solution technique, is developed for the Euler flow equations. Flux Jacobian is evaluated both numerically and analytically for different upwind flux discretization schemes with second order MUSCL face interpolation. Numerical flux Jacobian matrices that are derived with wide range of finite difference perturbation magnitudes were compared with analytically derived ones and the optimum perturbation magnitude, which minimizes the error in the numerical evaluation, is searched. The factors that impede the accuracy are analyzed and a simple formulation for optimum perturbation magnitude is derived. The sensitivity derivatives are evaluated by direct-differentiation method with discrete approach. The reuse of the LU factors of the flux Jacobian that are evaluated in the flow solution enabled efficient sensitivity analysis. The sensitivities calculated by the analytical Jacobian are compared with the ones that are calculated by numerically evaluated Jacobian matrices. Both internal and external flow problems with varying flow speeds, varying grid types and sizes are solved with different discretization schemes. In these problems, when the optimum perturbation magnitude is used for numerical Jacobian evaluation, the errors in Jacobian matrix and the sensitivities are minimized. Finally, the effect of the accuracy of the sensitivities on the design optimization cycle is analyzed for an inverse airfoil design performed with least squares minimization.
Aerospace engineering., Engineering Analysis.
http://etd.lib.metu.edu.tr/upload/12611067/index.pdf
https://hdl.handle.net/11511/18829
Graduate School of Natural and Applied Sciences, Thesis

Suggestions

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...
Time-domain calculation of sound propagation in lined ducts with sheared flows
Özyörük, Yusuf (American Institute of Aeronautics and Astronautics (AIAA), 2000-05-01)
A recent application of the time-domain equivalent of the classical acoustic impedance condition, i.e., the particle displacement continuity equation, to numerical simulations of a Bow-impedance tube in the time domain yielded reasonably good results with uniform mean flows. The present paper extends this application to include sheared mean-flow effects on sound propagation over acoustically treated walls. To assess the prediction improvements with sheared flows, especially at relatively high Mach numbers, ...
Computational study of subsonic flow over a delta canard-wing-body configuration
Tuncer, İsmail Hakkı (American Institute of Aeronautics and Astronautics (AIAA), 1998-07-01)
Subsonic flowfields over a close-coupled, delta canard-wing-body configuration at angles of attack of 20, 24,2, and 30 deg are computed using the OVERFLOW Navier-Stokes solver Computed flowfields are presented in terms of particle traces, surface streamlines, and leeward-side surface pressure distributions for the canard-on and -off configurations. The interaction between the canard and the wing vortices, wing vortex breakdown, and the influence of the canard on vortex breakdown are identified, The comparis...
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,...
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 ...
Citation Formats
A. A. Ezertaş, “Sensitivity analysis using finite difference and analytical Jacobians,” M.S. - Master of Science, Middle East Technical University, 2009.
METU IIS - Integrated Information Service open@metu.edu.tr