年間 6 号発行
ISSN 印刷: 1940-2503
ISSN オンライン: 1940-2554
Indexed in
FALSE DIFFUSION PRODUCED BY FLUX LIMITERS
要約
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.