Theses and Dissertations
Issuing Body
Mississippi State University
Advisor
Cinnella, Pasquale
Committee Member
Janus, Jonathan Mark
Committee Member
Warsi, Z.U.A
Date of Degree
8-2-2003
Document Type
Graduate Thesis - Open Access
Major
Aerospace Engineering
Degree Name
Master of Science
College
James Worth Bagley College of Engineering
Department
Department of Aerospace Engineering
Abstract
This study seeks to validate a recently introduced global preconditioning technique for the Euler equations. Energy and enthalpy equations are nondimensionalized by means of a reference enthalpy, resulting in increased numerical accuracy for low-speed flows. A cellbased, finite volume formulation is used, with Roe flux difference splitting and both explicit and implicit time integration schemes. A Newton-linearized iterative implicit algorithm is implemented, with Symmetric Gauss-Seidel (LU/SGS) nested sub-iterations. This choice allows one to retain time accuracy, and eliminates approximate factorization errors, which become dominant at low speed flows. The linearized flux Jacobians are evaluated by numerical differentiation. Higher-order discretization is constructed by means of the MUSCL approach. Locally one-dimensional characteristic variable boundary conditions are implemented at the farfield boundary. The preconditioned scheme is successfully applied to the following traditional test cases used as benchmarks for local preconditioning techniques: point disturbance, flow angle disturbance, and stagnation point arising from the impingement of two identical jets. The flow over a symmetric airfoil and a convergentdivergent nozzle are then simulated for arbitrary Mach numbers. The preconditioned scheme greatly enhances accuracy and convergence rate for low-speed flows (all the way down to M ≈ 10E − 4). Some preliminary tests of fully unsteady flows are also conducted.
URI
https://hdl.handle.net/11668/20287
Recommended Citation
Yildirim, B. Gazi, "A Global Preconditioning Method for the Euler Equations" (2003). Theses and Dissertations. 150.
https://scholarsjunction.msstate.edu/td/150
