Numerical Solution of the Euler and the Navier-Stokes Equations for a Compressible Flow Problem
Lee, Seung Ho
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https://hdl.handle.net/2142/70622
Description
Title
Numerical Solution of the Euler and the Navier-Stokes Equations for a Compressible Flow Problem
Author(s)
Lee, Seung Ho
Issue Date
1983
Department of Study
Aeronautical and Astronautical Engineering
Discipline
Aeronautical and Astronautical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Aerospace
Abstract
An implicit noniterative finite difference method in conservative form has been used to solve numerically the Euler and the Navier-Stokes equations for the compressible flow over a triconic body. The numerical solutions were obtained for the Euler equations for subsonic, transonic and supersonic flows. For the Navier-Stokes equations, solutions were obtained for subsonic and transonic flows. The grid system was generated using an algebraic method. The longitudinal gridlines are parallel to the surface of the body, and the transverse gridlines are either orthogonal or near-orthogonal to the longitudinal gridlines. The distribution of grid spacings is designed to accommodate the curvature of the body surface as well as the gradients of the flow variables. Numerical experiments were conducted to test the validity of the implementation of the wall boundary conditions for both inviscid and viscous flow problems. The adiabatic wall condition gives the best fidelity for these problems. The solution is initialized by imposing the wall boundary condition slowly. To stabilize the computation, fourth order artificial dissipation is explicitly added to the numerical scheme. Experiments were performed to find the smallest artificial dissipation which gives an accurate numerical solution. The rate of convergence of the solution was significantly increased by initializing the flow field with values linearly extrapolated from the solution of the lower Mach number for the Euler solution and of Reynolds number for the Navier-Stokes solution. The surface pressure distributions are in agreement with experimental results for the entire range of Mach numbers considered. A supersonic bubble, a separation bubble, and a shock induced separation were observed from the calculations of the flow properties in the flow field.
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