Comparison of truncation error of finite-difference and finite-volume formulations of convection terms.

*(English)*Zbl 0798.76053Summary: 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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\textit{B. P. Leonard}, Appl. Math. Modelling 18, No. 1, 46--50 (1994; Zbl 0798.76053)

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##### References:

[1] | Leonard, B.P., Comp. methods appl. mech. eng., 19, 59, (1979) |

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