AUSM-Based High-Order Solution for Euler Equations

作者：Scandaliato Angelo L; Liou Meng Sing^*

来源：Communications in Computational Physics, 2012, 12(4): 1096-1120.

DOI：10.4208/cicp.250311.081211a

• Shock capturing
• advection upwind splitting
• Euler equations
• weighted essentially non-oscillatory
• monotonicity preserving

In this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method (AUSM), specifically AUSM(+)-UP 191, with high-order upwind-biased interpolation procedures, the weighted essentially non-oscillatory (WENO-JS) scheme 181 and its variations 12,71, and the monotonicity preserving (MP) scheme 1161, for solving the Euler equations. MP is found to be more effective than the three WEN 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.

• 出版日期2012-10