Derivation of high-order advection-diffusion schemes

作者: Pavel Tkalich

DOI: 10.2166/HYDRO.2006.008

关键词: InterpolationCourant–Friedrichs–Lewy conditionDiffusion (business)AdvectionApplied mathematicsMathematical optimizationMathematicsRange (mathematics)Upwind schemeLinear combinationOrder 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.

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