An investigation of genuinely multidimensional schemes for the Euler equations
Abstract
Efforts to improve algorithms which are used to obtain solutions to the Euler equations have resulted in the development of genuinely multidimensional schemes. These differ from classical operatorsplit schemes by allowing the wave components of the numerical model to propagate independently of the underlying grid geometry. While genuinely multidimensional solvers show high resolution of flowfield features, they lack the robustness of the classical methods. This work has sought to develop a more robust genuinely multidimensional scheme. The result of this investigation is a new genuinely multidimensional scheme which makes use of gradient data taken from the flowfield. The numerical model consists of five waves which are elementary solutions to the Euler equations. These waves are used with a newly developed flux formulation which models the effect of the passage of the waves over a portion of the domain. It is these flux values which are used to obtain the flowfield solution. An evaluation of the method was conducted by using it to solve a wide variety of two dimensional flow problems and then comparing the results to those obtained using a classical solution technique. This comparison showed that the present scheme always improved resolution of flowfield features for supersonic flows while maintaining nearlymonotone strong shock transitions. The method displayed no such improvements for the subsonic and transonic flow cases investigated. While the present method did exhibit an improvement in convergence to steady state over that seen by similar methods, it still does not meet a rigorous convergence criterion. Recommendations are made for continuing research with the present method together with suggestions for possible improvements to it.
 Publication:

Ph.D. Thesis
 Pub Date:
 1992
 Bibcode:
 1992PhDT........41M
 Keywords:

 Computational Fluid Dynamics;
 Euler Equations Of Motion;
 Flow Distribution;
 Mathematical Models;
 Supersonic Flow;
 Two Dimensional Flow;
 Robustness (Mathematics);
 Steady State;
 Subsonic Flow;
 Transonic Flow;
 Fluid Mechanics and Heat Transfer