Investigation of Roe's 2D wave decomposition models for the Euler equations
Abstract
A new technique to solve the two dimensional (2D) Euler equations by modeling the solution with a discrete number of simple waves is implemented. The global solution is obtained by superposition of elementary solutions consisting of plane waves. The traveling directions of these waves are not fixed in advance but depend on the local flow gradient at each time step. Three different wave decomposition models were considered and implemented based on four acoustic waves: (1) one entropy wave and respective vorticity; (2) one shear wave propagating in the perpendicular direction to the streamlines; and (3) one shear wave propagating in the direction of the pressure gradient. Different first order upwind fluctuation splitting schemes were tested both for triangular and quadrilateral cells. Different test cases were solved with the new method: shear flow, oblique shock reflection, ramp flow, nozzle flow; a comparison among the results obtained with the different decomposition models and numerical schemes is presented.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 July 1990
 Bibcode:
 1990STIN...9123436D
 Keywords:

 Euler Equations Of Motion;
 Flow Equations;
 Mathematical Models;
 Sound Waves;
 Two Dimensional Models;
 Wave Degradation;
 Finite Volume Method;
 Nozzle Flow;
 Oblique Shock Waves;
 Shear Flow;
 Fluid Mechanics and Heat Transfer