MOST OF THE NUMERICAL CODES FOR SOLVING THE COMPRESSIBLE NAVIER-STOKES EQUATIONS OR THE EULER EQUATIONS IN USE TODAY ARE BASED ON FINITE DIFFERENCE SCHEMES.

MOST OF THE NUMERICAL CODES FOR SOLVING THE COMPRESSIBLE NAVIER-STOKES EQUATIONS OR THE EULER EQUATIONS IN USE TODAY ARE BASED ON FINITE DIFFERENCE SCHEMES. MOST OF THESE SCHEMES ARE LINEAR. NONLINEAR SCHEMES, HOWEVER, HAVE MORE DESIRABLE PROPERTIES SUCH AS MONOTONE PRESERVING, INCREASED ACCURACY, AND IMPROVED STABILITY. THUS NUMERICAL SOLUTIONS BASED ON THE NONLINEAR SCHEMES AVOID THE SPURIOUS OSCILLATIONS AT SHOCK WAVES. FOR LINEAR SCHEMES SUCH AS MACCORMACK'S SCHEME, ARTIFICIAL DISSIPATION IS REQUIRED FOR STABILITY AND TO DAMP OUT THE SPURIOUS OSCILLATIONS. WHILE NONLINEAR SCHEMES ARE SUPERIOR TO LINEAR SCHEMES, THEY ARE ALSO MUCH MORE EXPENSIVE TO EXECUTE ON A COMPUTER. TYPICALLY, A NONLINEAR SCHEME REQUIRES ABOUT AN ORDER OF MAGNITUDE MORE COMPUTER TIME THAN A LINEAR SCHEME. IT IS THIS INCREASED COST THAT HAS PREVENTED THE DEVELOPMENT AND UTILIZATION OF BETTER NONLINEAR SCHEMES. THIS PROJECT CONCERNS A PROGRAM TO DEVELOP A PROCEDURE WHEREBY THE EXECUTION OF A NONLINEAR SCHEME CAN BE MADE JUST AS RAPIDLY AND EFFICIENTLY AS FOR A LINEAR SCHEME.