作者: Pavel Tkalich
关键词: Interpolation 、 Courant–Friedrichs–Lewy condition 、 Diffusion (business) 、 Advection 、 Applied mathematics 、 Mathematical optimization 、 Mathematics 、 Range (mathematics) 、 Upwind scheme 、 Linear combination 、 Order of accuracy
摘要: Using the interpolation polynomial method, major upwind explicit advection–diffusion schemes of up to fifth-order accuracy are rederived and their properties explored. The trend emerges that higher order an advection scheme, easier is task scheme stabilization wiggling suppression. Thus, for a certain range turbulent diffusion coefficient, stability interval third- up-upwind can be extended three units Courant number ð0 # c 3Þ: Having good phase behavior, odd-order stable within single computational cell 1Þ: By contrast, even-order two consecutive grid-cells 2Þ; but exhibit poor dispersive properties. Stemming from finding considered higher-order (even, in particular) expressed as linear combination lower-order ones (odd this case), best qualities odd- evenorder algorithms blended mixed-order schemes. To illustrate idea, Second-Order Reduced Dispersion (SORD) marching Fourth-Order (FORD) developed. Computational tests demonstrate favorable performance In spite previous practice restricting usage (fourth-order particular), they potential stand among popular hydraulics.