A GPU-accelerated numerical model for nearshore scalar transport by dispersive shallow water flows

A GPU-accelerated nearshore scalar transport model with the Boussinesq-type wave solver is introduced. The depth-integrated advection-diffusion equation is implemented into Celeris Advent, the firstly-developed open-source Boussinesq wave model equipped with an interactive system supporting simultaneous visualization and data exchange between a user and the computing unit. A hybrid finite volume-finite difference scheme is adopted to discretize the governing equations, and the modified HLL Riemann solver for satisfying the conservation property of the scalar concentration is applied for an accurate approximation of scalar numerical flux. A source-function wavemaker in conjunction with alongshore periodic boundary conditions and a wave-breaking model are implemented to more precisely replicate the nearshore hydrodynamic processes. Several numerical tests using analytical solutions and experimental data are performed to validate the model. Finally, field-scale dye release experiments are reproduced numerically, assessing the applicability of the proposed model in predicting nearshore scalar transport by dispersive hydrodynamics. The proposed model is expected to serve as an advanced tool for real-time assessment and mitigation of marine pollution incidents. Program summary: Program Title: Celeris-with-scalar-transport CPC Library link to program files: https://doi.org/10.17632/bk7v57wsxj.1 Developer's repository link: https://doi.org/10.5281/zenodo.10609197 Licensing provisions: GNU General Public License 3 Programming language: C++, HLSL Supplementary material: Movies 1-4 Nature of problem: Nearshore scalar transport phenomena have generally been investigated through the numerical models that solve the shallow water equations and the advection-diffusion equation due to their high computational efficiency. However, these models are incapable of simulating the dispersive effects of the waves, which are significant in nearshore hydrodynamics. The scalar transport model with a Boussinesq-type solver can precisely approximate the nearshore scalar transport processes, but its application has been limited by the heavy computational load, which hinders real-time simulations. Building on previous work (Celeris Advent), this software enables real-time numerical simulation of nearshore scalar transport as well as simultaneous visualization. It also supports an interactive environment, allowing the user to change the water surface, bathymetry, and scalar concentration while the model is running. Solution method: A hybrid finite volume-finite difference scheme is used to solve the extended Boussinesq equations and the advection-diffusion equation. Various components, including the modified HLL Riemann solver, an eddy-viscosity type wave-breaking model, and a source-function wavemaker with periodic boundary conditions, have been newly implemented for better approximations of scalar transport processes governed by breaking dispersive shallow water waves in nearshore regions.