Commun. Comput. Phys., 12 (2012), pp. 1096-1120.

AUSM-Based High-Order Solution for Euler Equations

Angelo L. Scandaliato 1, Meng-Sing Liou 2*

1 Ohio Aerospace Institute, Cleveland, OH, 44142, USA. Currently, University of California at San Diego.
2 NASA Glenn Research Center, Cleveland, OH, 44135, USA.

Received 25 March 2011; Accepted (in revised version) 8 December 2011
Available online 17 April 2012


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.

AMS subject classifications: 65, 76

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Key words: Shock capturing, advection upwind splitting, Euler equations, weighted essentially non-oscillatory, monotonicity preserving.

*Corresponding author.
Email: (A. L. Scandaliato), (M.-S. Liou)

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