Volume 12, Issue 4
AUSM-Based High-Order Solution for Euler Equations

Angelo L. Scandaliato & Meng-Sing Liou

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

Published online: 2012-12

Preview Full PDF 116 1062
Export citation
  • 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.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-12-1096, author = {}, title = {AUSM-Based High-Order Solution for Euler Equations}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {4}, pages = {1096--1120}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.250311.081211a}, url = {http://global-sci.org/intro/article_detail/cicp/7326.html} }
TY - JOUR T1 - AUSM-Based High-Order Solution for Euler Equations JO - Communications in Computational Physics VL - 4 SP - 1096 EP - 1120 PY - 2012 DA - 2012/12 SN - 12 DO - http://dor.org/10.4208/cicp.250311.081211a UR - https://global-sci.org/intro/article_detail/cicp/7326.html KW - AB -

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.

Angelo L. Scandaliato & Meng-Sing Liou. (2020). AUSM-Based High-Order Solution for Euler Equations. Communications in Computational Physics. 12 (4). 1096-1120. doi:10.4208/cicp.250311.081211a
Copy to clipboard
The citation has been copied to your clipboard