Advances in Engineering Advances in Engineering features breaking research judged by Advances in Engineering advisory team to be of key importance in the Engineering field. Papers are selected from over 10,000 published each week from most peer reviewed journals.
International Journal for Numerical Methods in Fluids, Volume 72, Issue 2, pages 157–176, 20 May 2013.
Joe Iannelli.
School of Engineering, Grand Valley State University, Grand Rapids, MI 49504, USA
Abstract
An exact similarity solution of the compressible-flow Navier–Stokes equations is presented, which embeds supersonic, transonic, and subsonic regions. Describing the viscous and heat-conducting high-gradient flow in a shock wave, the solution accommodates non-linear temperature-dependent viscosity as well as heat-conduction coefficients and provides the variation of all the flow variables and their derivatives. Also presented are methods to obtain time-dependent and/or multi-dimensional solutions as well as verification benchmarks of increasing severity. Comparisons between the developed analytical solution and CFD solutions of the Navier–Stokes equations, with determination of convergence rates and orders of accuracy of these solutions, illustrate the utility of the developed exact solution for verification purposes. Copyright © 2012 John Wiley & Sons, Ltd.
Copyright © 2012 John Wiley & Sons, Ltd.
Additional information:
“This is a new exact solution of the compressible-flow Navier-Stokes equations, a solution that may be expressed as a time-dependent and / or multi-dimensional solution, accommodates both constant and temperature-dependent coefficients of viscosity and thermal conductivity, and embeds supersonic, transonic, and subsonic flows. The solution is cast in non-dimensional form and depends on the free-stream Mach number and Reynolds number, which control the severity of the solution gradients. This is a complete solution in that it provides the flow density, velocity, energy, pressure, and temperature as well as the gradients of these flow variables. It is thus valuable for both theoretical investigations of shocked flows and verification protocols for CFD codes for compressible flows. The author may be contacted at [email protected].
