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

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  • Abstract

In this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method (AUSM), specifically AUSM+-UP [9], with highorderupwind-biasedinterpolationprocedures,theweightedessentially 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 approximateRiemann 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. 

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@Article{CiCP-12-1096, author = {Angelo L. Scandaliato and Meng-Sing Liou}, 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 highorderupwind-biasedinterpolationprocedures,theweightedessentially 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 approximateRiemann 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 AU - Angelo L. Scandaliato & Meng-Sing Liou 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/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 highorderupwind-biasedinterpolationprocedures,theweightedessentially 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 approximateRiemann 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. (1970). AUSM-based High-order Solution for Euler Equations. Communications in Computational Physics. 12 (4). 1096-1120. doi:10.4208/cicp.250311.081211a
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