Abstract
The purpose of the present work was to evaluate the importance of formal accuracy and of the conservation property in the numerical computation of incompressible flows with arbitrary free boundaries, such as occur in wave-breaking problems. Four spatial discretization methods were implemented in a computer code based on the VOF method for tracking free surfaces: a non-conservative four-point scheme, the conservative quadratic upstream interpolation method, the conservative linear extrapolation method and a lower-order conservative scheme based on the power-law discretization. The performance of the four schemes was evaluated in three test problems: the propagation of a solitary wave of high amplitude, the propagation of an undular hydraulic jump and the flow resulting from a breaking hydraulic jump. The main conclusion obtained in the present work was that discrete momentum conservation is more important than the formal accuracy of the spatial discretization scheme, particularly when there is recirculation and breaking.
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