Three-Dimensional Simulation of Scalar Transport in Large Shallow Water Systems Using Flux-Form Eulerian–Lagrangian Method

Abstract

This study is devoted to advancing hydroenvironmental modeling of large-scale shallow water systems to the times of three-dimensional (3D) simulations, where the solution of advective transport of scalar is the focus. The solution to the transport model is demonstrated using a semi-implicit hydrostatic 3D flow model, which uses an Eulerian–Lagrangian method (ELM) and a prediction-correction method. A new 3D scalar advection scheme, the 3D flux-form ELM (FFELM), is proposed based on layer-integrated advection subequations. The new scheme allows large time steps for which the Courant number is greater than 1 and is parallelizable. A grid sensitivity study is performed using a solid-body rotation experiment, in which the FFELM is indicated to achieve the performance of second-order accuracy advection schemes and run stably under a time step for which the Courant number is much larger than 1. Moreover, a nested FFELM (FFELM-N) is proposed, in which the trajectory-tracking information of the ELM in the 3D flow model is reused to reduce the startup cost of the transport model. The new model is also tested using the real Jing-Dongting (JDT) river–lake system, for which the computational domain (3,900 km2 in the horizontal) is divided by a computational grid of 327,820×10 cells. A parallel run of the transport model (using 16 cores) is approximately 10 times faster than a sequential run. The runtime of the transport model using the FFELM-N is reduced to one-third that using the FFELM in both sequential and parallel tests. Using 16 cores, it takes 6.02 days to complete the calculation of a one-year unsteady process of flow and scalar transport in the JDT system, for which the runtime of the transport model using the FFELM-N is only 1.28 days.