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**Comparison study on the performances of finite volume method and finite difference method.**
*(English)*
Zbl 1275.65053

Summary: The vorticity-stream function method and MAC algorithm are adopted to systemically compare the finite volume method (FVM) and finite difference method (FDM). Two typical problems – lid-driven flow and natural convection flow in a square cavity – are taken as examples to compare and analyze the calculation performances of FVM and FDM with variant mesh densities, discrete forms, and treatments of boundary condition. It is indicated that FVM is superior to FDM from the perspective of accuracy, stability of the convection term, robustness, and calculation efficiency. Particularly, when the mesh is coarse and taken as \(20 \times 20\), the results of FDM suffer severe oscillation and even lose physical meaning.

### MSC:

65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

35K20 | Initial-boundary value problems for second-order parabolic equations |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |

### Keywords:

vorticity-stream function method; MAC algorithm; finite volume method; finite difference method; stability
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\textit{R. Liu} et al., J. Appl. Math. 2013, Article ID 596218, 10 p. (2013; Zbl 1275.65053)

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