A hybrid 1D-2D Lagrangian solver with moving coupling to simulate dam-break flow

Abstract

In dam-break problems, two-dimensional (2D) models on the vertical plane appropriately capture the non-hydrostatic pressure distribution but with a high computational cost. This study presents a hybrid Lagrangian solver of one-dimensional (1D) shallow water flow and a 2D large-eddy simulation with a sub-particle scale to simulate dam-break flows over frictional beds. The proposed 1D-2D hybrid scheme is a useful trade-off between the accuracy of the 2D models on the vertical plane and the computational efficiency of 1D shallow water equations models. The configuration of sub-domains is established so that the 1D solves the regions with dominantly hydrostatic pressure, while the 2D solver accounts for the non-hydrostaticity. A moving coupling method is introduced based on two-layer shallow water equations with a uniform velocity distribution that constructs two sub-domains, including inner and outer zones in the section coupling model (SCM), or upper and lower layers within the layer coupling model (LCM). Then, the region with high vertical accelerations is substituted by the 2D model in the SCM or mixed SCM-LCM in which the overlapping zone and boundary interface move with time, based on the 1D flow feature. Also, a new method is proposed to deal with irregular boundary interfaces in the LCM while satisfying the momentum transfer. The present hybrid model is advantageous as it meets mass conservation, and there is no need for typical inflow/outflow boundary conditions at the coupling interfaces for simulating dam-break waves. Moving particle simulation (MPS) is utilized to solve the Lagrangian equations, which is advantageous in dealing with free-surface problems with large deformation. The model validation reveals that the hybrid results of water depths are in very good agreement with observed data and those obtained from the 2D model for selected dam-break flows with the ratio of initial depths downstream to upstream up to 0.4. In this respect, the average root-mean-square-error (RMSE) is computed at 8.09 mm in the SCM, 8.16 mm in the mixed SCM-LCM, and 7.48 mm in the pure 2D model, while both hybrid models save the computational time by 55% compared to the 2D model. Moreover, the mixed SCM-LCM preserves the nonlinearity of the wavefront over long times, whereas the SCM converts the wavefront into a shockwave considering the same number of fluid particles.