Two-phase SPH modelling of advective diffusion processes

Abstract

This paper deals with a two-dimensional numerical model based on the smoothed particle hydrodynamics (SPH) technique for the evaluation of the concentration field of pollutants in water. A SPH model is formulated to solve the fickian diffusion equation applied to pollutants with the same density as the water. A lagrangian SPH formalism of the advective diffusion equation is also developed for pollutant-water, taking into account the effects of molecular diffusion and natural advection induced by differences between the fluid densities. These equations are coupled with the fluid mechanics equations. Attention is paid to the numerical aspects involved in the solution procedure and to the optimization of the model parameters. Environmental engineering problems concerning diffusion and natural advection phenomena occur in the presence of a pollutant in still water. Numerical tests referring to a strip and a bubble of contaminant in a water tank with different initial concentration laws have been carried out. The results obtained by the proposed SPH models are compared with other available SPH formulations, showing an overall better agreement with standard analytical solutions in terms of spatial evolution of the concentration values. Capabilities and limits of the proposed SPH models to simulate advective diffusion phenomena for a wide range of density ratios are discussed.

SPH Simulations of Solute Transport in Flows with Steep Velocity and Concentration Gradients

“…It can be found that the moving speed of the leading edge of Figure 3c owing to the effects of advection and diffusion is larger than the one of Figure 3a resulting from the effect of pure advection. Furthermore, the simulated results show good agreement against the exact solutions obtained in [33]. It can be concluded that the present model is capable of solving steep gradient or discontinuous solutions in concentration fields of advection-dominated, advection-diffusion, and diffusion-dominated problems.…”

“…Equation (28) can be obtained with different derivations [29,31,33]. It is also suitable for the situations that the diffusion processes is anisotropic or inhomogeneous, and in such situations, the coefficient D u will be a tensor and has the elements of D uxx , D uxy , D uyx , and D uyy [30].…”

“…To update particle positions, velocities and other physical variables, the leap-frog integration scheme is used due to its symplectic nature, which conserves the energy of dynamics systems, i.e., Equations (29)- (33).…”

Numerical Simulation of Hydrodynamics and Reaeration over a Stepped Spillway by the SPH Method

“…To date, different SPH models have been widely studied and applied in the field of fluid mechanics. Recently, SPH methods have been widely applied in single-phase flows [12][13][14][15], multiphase flows [16][17][18], and diffusion processes between different density flows [19,20]. Compared to the Euler method, the existing Lagrangian SPH method has performed well in simulating the motion characteristic of particles.…”

Free-Surface Flow Simulations with Smoothed Particle Hydrodynamics Method using High-Performance Computing

“…Since then, it has been used in several research areas, e.g. coastal engineering [3][4][5][6][7], flooding forecast [8][9][10][11], solid body transport [12][13][14][15], soil mechanics [16][17][18][19][20], sediment erosion or entrainment processes [21][22][23][24], fastmoving non-Newtonian flows [25][26][27][28][29][30][31][32][33], flows in porous media [34][35][36], solute transport [37][38][39], turbulent flows [40][41][42] and multiphase flows [43][44][45][46][47], not to mention manifold industrial applications (see, for instance [48][49][50]…”