A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment

作者：Hou Jingming^*; Liang Qiuhua; Simons Franz; Hinkelmann Reinhard

来源：Advances in Water Resources, 2013, 52: 107-131.

DOI：10.1016/j.advwatres.2012.08.003

• Shallow water equations (SWEs)
• Second order reconstruction
• Well-balanced scheme
• Wet-dry fronts
• Slope source terms
• Unstructured grids

Within the framework of the Godunov-type cell-centered finite volume (CCFV) scheme, this paper proposes a 2D well-balanced shallow water model for unstructured grids. In this model, the face-based van Albada limiting scheme is employed in conjunction with a directional correction to reconstruct second order spatial values at the midpoint of the considered face. The Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored (HLLC) is applied to compute the fluxes of mass and momentum, while the splitting implicit method is utilized to solve the friction source terms. The novel aspects of the model include the new limited directional correction with which the new local extrema caused by the unlimited correction are prevented efficiently, the simplified non-negative water depth reconstruction used to get rid of numerical instabilities and in turn to preserve mass conservation at wet-dry interfaces and the novel slope source term treatment which suits complex unstructured grids well by transforming the slope source of a cell into fluxes at its faces. This model is able to preserve the C-property and mass conservation, to achieve good convergence to steady state, to capture discontinuous flows and to handle complex flows involving wetting and drying over uneven beds on unstructured grids with poor connectivity in an accurate, efficient and robust way. These capabilities are verified against analytical solutions, numerical results of alternative models and experimental and field data.

• 出版日期2013-2