SOLUTIONS INCREASING THE CONVERGENCE RATE FOR EULER EQUATION

EXISTING METHODS OF NUMERICALLY SOLVING THE EULER EQUATIONS EXISTING METHODS OF NUMERICALLY SOLVING THE EULER EQUATIONS USE A LINEARIZATION IN EITHER REAL OR ARTIFICIAL TIME SO THAT AT EACH STEP OF THE SOLUTION PATH WELL KNOWN TECHNIQUESCAN BE USED. THIS LINEARIZATION IS PERFORMED ABOUT THE SOLUTION OBTAINED AT THE PREVIOUS STEP AND SUCH A SOLUTION SATISFIES THE PHYSICAL BOUNDARY CONDITIONS. SPECIAL TREATMENT MAY BE EQUIRED NEAR SHOCK WAVES. AN ALTERNATIVE, NOVEL CONCEPT IS THAT THE LINEARIZATION SHOULD BE PERFORMED ABOUT SOME FUNCTION SET THAT SPEEDS CONVERGENCE, DOES NOT REQUIE SPECIAL TREATMENT OF THE SHOCK AND IS NOT NECESSARILY RELATED TO THE PHYSICAL SOLUTION. THIS PHASE I EFFORT CONCERNS A PROGRAM TO ESTABLISH SOME GUIDELINES ABOUT THE CHOICE OF THIS FUNCTION SET SO THAT OPTIMUM USE CAN BE MADE OF THE GENERAL CONCEPT.