| Abstract: | In this paper we demonstrate the accuracy and robustness of combining the
advection upwind splitting method (AUSM), specifically AUSM+-UP 9], with high-order upwind-biased interpolation procedures, the weighted essentially non-oscillatory
(WENO-JS) scheme 8] and its variations 2, 7], and the monotonicity preserving (MP)
scheme 16], for solving the Euler equations. MP is found to be more effective than the
three WENO variations studied. AUSM+-UP is also shown to be free of the so-called "carbuncle" phenomenon with the high-order interpolation. The characteristic variables are preferred for interpolation after comparing the results using primitive and
conservative variables, even though they require additional matrix-vector operations.
Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison. In addition, four reflective boundary
condition implementations are compared for their effects on residual convergence and
solution accuracy. Finally, a measure for quantifying the efficiency of obtaining high
order solutions is proposed; the measure reveals that a maximum return is reached
after which no improvement in accuracy is possible for a given grid size. |
