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Comparison of truncation error of finite-difference and finite-volume formulations of convection terms. (English) Zbl 0798.76053
Summary: This paper explains significant differences in spatial truncation error between formulations of convection involving a finite-difference approximation of the first derivative, on the one hand, and a finite- volume model of flux differences across a control volume cell on the other. The difference between the two formulations involves a second- order truncation error term (proportional to the third derivative of the convected variable). Hence, for example, a third- (or higher) order finite-difference approximation for the first-derivative convection term is only second-order accurate when written in conservative control volume form as a finite-volume formulation, and vice versa.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76R99 Diffusion and convection
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[1] Leonard, B.P., Comp. methods appl. mech. eng., 19, 59, (1979)
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