Mixed analytical/numerical method for flow equations with a source term.

*(English)*Zbl 1048.76044Summary: A mixed analytical/numerical approach is studied for flow problems described by partial differential equations with source terms which are analytically integrable and which may involve a time scale (\(S\)-scale) much smaller than the mean flow time scale (\(M\)-scale). A rigorous error analysis based on the modified equation is conducted for a linear model equation, and it is shown, both analytically and numerically, that the mixed scheme is more accurate than a conventional numerical method. Most interestingly, the mixed approach has a good accuracy for the \(M\)-scale structure even though the time step is larger than the \(S\)-scale, while a conventional scheme fails to work in this case by producing errors of order \(O(1)\) or larger.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76N15 | Gas dynamics, general |

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\textit{T. Du} et al., Comput. Fluids 32, No. 5, 659--690 (2003; Zbl 1048.76044)

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