Abstract
In this study, a meshless particle method, smoothed particle hydrodynamics (SPH), is adopted to solve the shallow water equations (SWEs) and the advection diffusion equations (ADEs) for simulating solute transport processes under 1D/2D conditions with steep gradients. A new SPH-SWEs-ADEs model is herein developed to focus on the numerical performance of solute transport in flows with steep velocity and concentration gradients, since the traditional mesh-based methods have numerical difficulties on solving such steep velocity/concentration gradient flows. The present model is validated by six benchmark study cases, including three steep concentration gradient cases and three coupled steep concentration/velocity gradient cases. The comparison between the simulated results and the exact solutions for the former three cases shows that complete mass concentration conservation in pure advection-dominated flows is preserved. The numerical oscillation in concentration and the negative concentration resulted from the discretization of the advection term of ADEs can be totally avoided. The other three cases confirm that this model can also well capture coupled steep gradients of velocities and concentrations. It is demonstrated that the presented solver is an effective and reliable tool to investigate solute transports in complex flows incorporating steep velocity gradients.
Highlights
Numerical computation of solute transport processes in water bodies is essential for many hydraulic and environmental research fields
This study develops a new smoothed particle hydrodynamics (SPH)‐shallow water equations (SWEs)‐advection–diffusion equations (ADEs) model and shows its numerical advantages to
This study develops a new SPH-SWEs-ADEs model and shows its numerical advantages to solve solve steep gradient or discontinuous solutions in ADEs
Summary
Numerical computation of solute transport processes in water bodies is essential for many hydraulic and environmental research fields. Such computation is based on solving the advection–diffusion equations (ADEs). As solving ADEs, some difficulties are always encountered due to their dual nature of mixing parabolic and hyperbolic systems [1]. When solute transport processes are advection-dominated, these equations are a first-order hyperbolic type. If solute transport processes are diffusion-dominated, they behave as second-order parabolic type. Many grid-based numerical methods attempted to handle the above dual characteristic challenge, especially the advection-dominated challenge resulting from the non-linear advection term in ADEs
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