Abstract: A 3D hydrodynamic model that calculates advection terms with an Eulerian-Lagrangian method (ELM) can maintain numerical stability at large time steps, while its linear interpolation generates a significant amount of additional numerical resistance, restricting its application in river engineering. Spectral element method (SEM) is a high-order method suitable for irregular domain calculations. This paper uses SEM to replace linear interpolation with polynomial interpolation in vertical direction, and develops a new 3D shallow water model by combining with ELM. Numerical experiment on open-channel flow shows that this 3D model, taking advantage of the spectral element method and ELM, is capable of breaking through the Courant number constraint on its time steps, and eliminates most of the numerical resistance of a classical ELM, thus improving its accuracy by an order of magnitude.

Key words: spectral element method, 3D shallow water model, Eulerian-Lagrangian method, numerical resistance