NUMERICAL ADVECTION EXPERIMENTS1

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Abstract
First, second, and fourth order finite difference approximations to the color equation in both advection and conservation form are considered in one and two space dimensions. All schemes considered are based on forward time differences and most involve centered space differences. All are shown to be numerically stable for |uΔt/Δx| ≤ 1. Test calculations indicate that for the same order of accuracy, the conservation form produces more accurate solutions than the advection form. For either conservation or advection form, fourth order schemes are shown to be more accurate than second or first order schemes in terms of both amplitude and phase errors. Abstract First, second, and fourth order finite difference approximations to the color equation in both advection and conservation form are considered in one and two space dimensions. All schemes considered are based on forward time differences and most involve centered space differences. All are shown to be numerically stable for |uΔt/Δx| ≤ 1. Test calculations indicate that for the same order of accuracy, the conservation form produces more accurate solutions than the advection form. For either conservation or advection form, fourth order schemes are shown to be more accurate than second or first order schemes in terms of both amplitude and phase errors.

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