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国际计算热科学期刊
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN 打印: 1940-2503
ISSN 在线: 1940-2554

国际计算热科学期刊

DOI: 10.1615/ComputThermalScien.2013006746
pages 503-520

FALSE DIFFUSION PRODUCED BY FLUX LIMITERS

Vincent H. Chu
Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke St. West, Montreal, Quebec H3A0C3, Canada
Congwei Gao
Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, Quebec H3A 0C3, Canada

ABSTRACT

The false diffusions of six flux limiters were examined in a series of advection simulation experiments conducted for different flow directions and Courant numbers. The rate of deviation from the exact solution determines the false-diffusion coefficients that are defined by the Lagrangian diffusion equation. Occasional intervention by downgrading high-order schemes to a lower order produces a false-diffusion error that is linearly in proportion to the size of the computation grid. The dimensionless coefficient normalized by the grid size oscillates with time. The amplitude of the oscillations is evaluated as an indicator of computational instability. Some flux limiters, such as MINMOD, produce computationally stable results. However, the simulation by MINMOD is diffusive. Other flux limiters such as ULTRA-QUICK and ULTRA-CD are more accurate and not as diffusive, but computationally are not as stable. This study found that the false-diffusion coefficients of the flux limiters became independent of the Courant number when the fourth-order Runge−Kutta method was used for time integration. Using fourth-order time integration, the flux limiter SUPERBEE was nine times less diffusive than MINMOD, and 49 times less diffusive than the first-order upwind scheme.


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