Abstract
A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k − ɛ equations in this model. The eddy viscosity is calculated from the k − ɛ turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field, and then applied to simulate the tidal flow in the Bohai Sea.
Similar content being viewed by others
References
Casulli, V. and Zanolli, P., 2002. Semi-implicit numerical modeling of non-hydrostatic free-surface flows for environmental problems, Mathematical and Computer Modelling 36(9–10): 1131–1149.
Ford, R., Pain, C. C., Piggott, M. D., Goddard, A. J. H., de Oliveira, C. R. E. and Umpleby, A. P., 2004. A nonhydrostatic finite-element model for three-dimensional stratified oceanic flow, Month Weather Review 312(9): 2816–2831.
Fringer, O. B., Gerritsen, M. and Street, R. L., 2006. An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator, Ocean Modelling 14(3): 139–173.
Ham, D. A., Pietrzak, J. and Stelling, G. S., 2005. A scalable unstructured grid 3-dimensional finite volume model for the shallow water equations, Ocean Modelling 10(1–2): 153–169.
Ham, D. A., Pietrzak, J. and Stelling, G. S., 2006. A streamline tracking algorithm for semi-Lagrangian advection schemes based on the analytic integration of the velocity field, Journal of Computational and Applied Mathematics 192(1): 168–174.
Leupi, C. and Altinakar, M. S., 2005. Finite element modeling of free-surface flows with non-hydrostatic pressure and k − ɛ turbulence model, International Journal for Numerical Methods in Fluids 49(2): 1145–1162.
Lu, B., Jin, S. and Ai, C. F., 2010. A conservative unstructured staggered grid scheme for incompressible Navier-Stokes eqauations, Journal of Hydrodynamics, Ser. B 22(2): 173–184.
Perot, B., 2000. Conservation properties of unstructured staggered mesh schemes, Journal of Computational Physics 159(1): 58–89.
Wang, K., Jin, S. and Liu, G., 2009. An efficient hydrodynamic model for surface waves, China Ocean Eng. 23(1): 145–156.
Wang, Z. L. and Geng, Y. F., 2013. A three-dimensional semi-implicit unstructured grid finite volume ocean model, Acta Oceanologica Sinica 32(2): 68–78.
Yuan, H. and Wu, C. H., 2004. An implicit three-dimensional fully non-hydrostatic model for free-surface flows, International Journal for Numerical Methods in Fluids 46(7): 709–733.
Zijlema, M. and Stelling, G. S., 2008. Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure, Coast. Eng. 55(10): 780–790.
Author information
Authors and Affiliations
Additional information
This project was financially supported by the Science and Technology Project of the Ministry of Transport (Grant No. 2011329224170).
Rights and permissions
About this article
Cite this article
Lü, B. A new efficient finite volume modeling of small amplitude free surface flows with unstructured grid. China Ocean Eng 27, 509–522 (2013). https://doi.org/10.1007/s13344-013-0043-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13344-013-0043-7