Embedded mesh solution of the 2D Euler equations  Evaluation of interface formulations
Abstract
Solution of the steady 2D Euler equations using mesh embedding, or local grid refinement, with a cellcentered finite volume scheme is investigated. Embedded regions which are topologically similar to the global grid are considered. An isoenergetic model for the governing equations is used in Jameson's finite volume multistage scheme with modifications to the boundary conditions and smoothing. A detailed study of the embedding interface flux and smoothing formulations is conducted. Taylor expansion analysis reveals that local second order spatial accuracy is not possible if a conservative interface flux formulation is used. The analysis also gives constraints for local first order accuracy. An energy stability analysis indicates that downwind weighting of interface fluxes causes local instabilities. Analysis shows that conservative interface smoothing formulations must have a locally convective component, but that correct interface formulations allow globally dissipative smoothing. Embedded mesh solutions obtained with this scheme are presented for a transonic airfoil. They show that if embedding interfaces are close to the shocks, then small modifications in the interface location can have large effects on converge and solution accuracy.
 Publication:

24th AIAA Aerospace Sciences Meeting
 Pub Date:
 January 1986
 Bibcode:
 1986aiaa.meetT....A
 Keywords:

 Computational Fluid Dynamics;
 Computational Grids;
 Error Analysis;
 Euler Equations Of Motion;
 Finite Volume Method;
 Transonic Flow;
 Boundary Conditions;
 Boundary Value Problems;
 Interfaces;
 Time Marching;
 Viscosity;
 Fluid Mechanics and Heat Transfer