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THIS WORK DEVELOPS NEW APPROXIMATIONS FOR THE EXPONENTIAL INTERPOLATION FUNCTIONS WHICH ARE USED IN POWER-LAW SCHEME (PLS) AND WUDS. THESE APPROXIMATIONS ALLOW ACCURATE RESULTS FOR NEAR ZERO GRID PÉCLET NUMBERS AND REDUCE THE SCHEME TO UPWIND INTERPOLATION FOR A PÉCLET NUMBER ABOUT 9. THE COMPUTATIONAL COST OF THESE FUNCTIONS IS COMPARABLE TO THE USUAL APPROXIMATION USED IN PLS AND IS LESS EXPENSIVE THAN THE COMMON APPROXIMATIONS USED IN WUDS. THE SOLUTION OF ONE-DIMENSIONAL AND TWO-DIMENSIONAL CONVECTION-DIFFUSION PROBLEMS ARE USED TO SHOW THE GOOD CONVERGENCE CHARACTERISTICS OF THE NEW APPROXIMATIONS FOR THE INTERPOLATION FUNCTIONS. QUESTIONS CONCERNING THE USAGE OF NONUNIFORM GRIDS AND EXPONENTIAL-BASED SCHEMES WITH SOURCE TERM (WUDS-E, PLS-E AND LOADS) ARE ALSO ADDRESSED.
KEYWORDS: INTERPOLATION, FINITE-VOLUMES, EXPONENTIAL SCHEMES, ACCURACY, GRID INDEPENDENCE
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