Semi-implicit subgrid modelling of three-dimensional free-surface flows. (English) Zbl 1316.76018
Summary: A semi-implicit numerical model for two- and three-dimensional free-surface flows will be formulated in such a fashion as to intrinsically account for subgrid bathymetric details. It will be shown that with the proposed subgrid approach the model accuracy can be substantially improved without increasing the corresponding computational effort.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
subgrid resolution; semi-implicit methods; free-surface; shallow water; wetting and drying; finite volumeReferences:
| [1] | Leendertse, RM-6230-RC 1 (1970) |
| [2] | Stelling GS On the construction of computational methods for shallow water equations 1984 |
| [3] | Casulli, Semi-implicit finite difference methods for the two-dimensional shallow water equations, Journal of Computational Physics 86 pp 56– (1990) · Zbl 0681.76022 · doi:10.1016/0021-9991(90)90091-E |
| [4] | Casulli, Semi-implicit finite difference methods for three-dimensional shallow water flow, International Journal for Numerical Methods in Fluids 15 pp 629– (1992) · Zbl 0762.76068 · doi:10.1002/fld.1650150602 |
| [5] | Casulli, An unstructured grid, three-dimensional model based on the shallow water equations, International Journal for Numerical Methods in Fluids 32 pp 331– (2000) · Zbl 0965.76061 · doi:10.1002/(SICI)1097-0363(20000215)32:3<331::AID-FLD941>3.0.CO;2-C |
| [6] | Mason, Floodplain friction parameterization in two-dimensional river flood models using vegetation heights derived from airborne scanning laser altimetry, Hydrological Processes 17 pp 1711– (2003) · doi:10.1002/hyp.1270 |
| [7] | Nikora, Double-averaging concept for rough-bed open-channel and overland flows: theoretical background, Journal of Hydraulic Engineering 133 pp 873– (2007) · doi:10.1061/(ASCE)0733-9429(2007)133:8(873) |
| [8] | Nikora, Double-averaging concept for rough-bed open-channel and overland flows: applications, Journal of Hydraulic Engineering 133 pp 884– (2007) · doi:10.1061/(ASCE)0733-9429(2007)133:8(884) |
| [9] | Casulli, A high-resolution wetting and drying algorithm for free-surface hydrodynamics, International Journal for Numerical Methods in Fluids 60 pp 391– (2009) · Zbl 1161.76034 · doi:10.1002/fld.1896 |
| [10] | Casulli, Stability, accuracy and efficiency of a semi-implicit method for three-dimensional shallow water flow, Computers and Mathematics with Applications 27 pp 99– (1994) · Zbl 0796.76052 · doi:10.1016/0898-1221(94)90059-0 |
| [11] | Stelling, A staggered conservative scheme for every Froude number in rapidly varied shallow water flows, International Journal for Numerical Methods in Fluids 43 pp 1329– (2003) · Zbl 1062.76541 · doi:10.1002/fld.537 |
| [12] | Ham, The symmetry and stability of unstructured mesh C-grid shallow water models under the influence of Coriolis, Ocean Modelling 16 pp 47– (2007) · doi:10.1016/j.ocemod.2006.05.008 |
| [13] | Kleptsova, On the accurate and stable reconstruction of tangential velocities in C-grid ocean models, Ocean Modelling 28 pp 118– (2009) · doi:10.1016/j.ocemod.2008.12.007 |
| [14] | Lesser, Development and validation of a three-dimensional morphological model, Coastal Engineering 51 pp 883– (2004) · doi:10.1016/j.coastaleng.2004.07.014 |
| [15] | Casulli, High resolution methods for multidimensional advection-diffusion problems in free-surface hydrodynamics, Ocean Modelling 10 pp 137– (2005) · doi:10.1016/j.ocemod.2004.06.007 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
