Semi-implicit numerical modeling of nonhydrostatic free-surface flows for environmental problems.

*(English)*Zbl 1027.76034Summary: We describe a semi-implicit numerical model for three-dimensional Navier-Stokes equations on unstructured grids. The governing differential equations are discretized by a finite difference-finite volume algorithm which is robust, efficient, and applies to barotropic and baroclinic, hydrostatic and nonhydrostatic, and one-, two-, and three-dimensional flow problems. The resulting model is relatively simple, mass-conservative, and unconditionally stable with respect to the gravity wave speed, wind stress, vertical viscosity, and bottom friction.

##### MSC:

76M20 | Finite difference methods applied to problems in fluid mechanics |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

76M12 | Finite volume methods applied to problems in fluid mechanics |

##### Keywords:

Finite difference-finite volume algorithm; Unstructured grids; Semi-implicit model; Three-dimensional Navier-Stokes equations##### Software:

GENSMAC
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\textit{V. Casulli} and \textit{P. Zanolli}, Math. Comput. Modelling 36, No. 9--10, 1131--1149 (2002; Zbl 1027.76034)

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##### References:

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