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

Chang, Yu-Hern; Chang, Tsang‐Jung

doi:10.3390/w9020132

Cited by 13 publications

(10 citation statements)

References 40 publications

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“…In combination of the modified velocity-Verlet numerical algorithm that was used in most DPD simulation 20 and the leap-frog numerical algorithm that was applied in SPH simulation 33 , following numerical algorithm was implemented in the present work, where the iterations of velocity and solute concentration were divided into two half steps separated by the acceleration iteration.where is the acceleration of particle i and Δ t is the time step.…”

Section: Methodsmentioning

confidence: 99%

Mesoscale modelling of miscible and immiscible multicomponent fluids

Zhao

Moat

Qin

2019

Sci Rep

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A mesoscopic simulation method based on the integration of dissipative particle dynamics (DPD), smoothed particle hydrodynamics (SPH) and computational thermodynamics (CT) has been developed. The kinetic behaviours of miscible and immiscible fluids were investigated. The interaction force between multicomponent mesoscopic particles is derived from the system free energy. The diffusivity of the components in non-ideal solution is determined by the chemical potential. The proposed method provides convincing predictions to the effects of convection, diffusion and microscopic interaction on the non-equilibrium evolution of engineering fluids, and demonstrates a potential to simulate more complicated phenomena in materials processing.

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Section: Methodsmentioning

confidence: 99%

Mesoscale modelling of miscible and immiscible multicomponent fluids

Zhao

Moat

Qin

2019

Sci Rep

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“…Chaniotis et al (2002) approximated the diffusion terms by directly discretizing the second-order derivatives, but this approach is sensitive to particle disorder, then particle remeshing schemes have to be added. Most of the studies (Cleary and Monaghan, 1999;Shao and Lo, 2003;Aristodemo et al, 2010;Ryan et al, 2010;Chang and Chang, 2017;Zheng et al, 2018) adopted a scheme that can be regarded as the hybrid of SPH and difference method. In this scheme, the simulation of diffusion terms merely includes the first-order derivative approximation of SPH.…”

Section: Introductionmentioning

confidence: 99%

SPH modeling of substance transport in flows with large deformation

Liu

Hou²,

Lei³

et al. 2022

Front. Environ. Sci.

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The velocity field in coastal and oceanic currents is mostly non-uniform, which will result in irregular particle distribution when the fluid is represented by an amount of moving discrete particles as in smoothed particle hydrodynamics (SPH). When the non-uniformity of the flow is big, i.e., with large deformation, the conventional SPH method can hardly solve the associated advection-diffusion process (e.g., substance transport). To accurately simulate the substance transport in flows with large deformation, two types of particle shifting techniques (PSTs) are incorporated into the conventional SPH in this paper. One is based on current particle distance, and the other is based on Fick’s law. In the second type, the repulsive force (RF) term for suppressing the paring instability that occurs in particle shifting technique (PST) is studied and the effect of the kernel function is examined. By introducing a particle disorder measurement, the simulated results of SPH with the two types of PSTs and their modifications are evaluated and the influence of the shifting magnitude is analyzed. The suggestions for how to set reasonable parameters in PSTs are provided by a systematic parametric study. For further illustration, the simulation of the anisotropic diffusion is also examined. To give reliable reference solutions, the high-resolution modified total variation diminishing Lax Friedrichs scheme with Superbee limiter (MTVDLF-Superbee) with fine mesh is also implemented. The validated Lagrangian particle model with optimized PST is applied to a practical application.

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“…They also conducted a series of comparisons between various approximate Riemann Solvers with multiple frictionless flow cases and documented the new stabilization technique’s efficiency. The capability of the SPH‐SWE model was well explained in coupling systems with the advection‐diffusion equation (Chang & Chang, 2017) and Navier‐Stokes equations (Ni et al., 2020) for modeling solute transport and non‐linear hydrodynamics, respectively.…”

Section: Introductionmentioning

confidence: 99%

MPS‐Based Model to Solve One‐Dimensional Shallow Water Equations

Sarkhosh

Jin

2021

Water Resources Research

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Two meshless (or mesh-free) methods that are widely employed in hydrodynamic modeling of problems with steep gradients and large deformation are smoothed particle hydrodynamics (SPH) and moving particle simulation (MPS) that are classified into two categories of incompressible and weakly compressible fluids (Gotoh & Khayyer, 2016). Although SPH was initially introduced for astrophysical applications (Gingold & Monaghan, 1977), in the scope of hydrodynamics, SPH and MPS were developed by Monaghan (1992) and Koshizuka and Oka (1996), respectively, for solving the free-surface incompressible flow using Navier-Stokes equations. Gotoh et al. ( 2001) presented a sub-particle scale closure model for closing large eddy simulation (LES) to simulate turbulence fluctuations in the MPS method. The theory of a weakly compressible flow was adopted by Monaghan (1994) in SPH and Shakibaeinia and Jin (2010) in MPS using a thermodynamic equation of state for calculating the pressure instead of resorting to the Poisson equation.The main difference between SPH and MPS arises from different differential operators employed in the spatial integration of the partial differential equations. In SPH, the differential operators are obtained from the differentiation of a weighted average function, the so-called kernel, without directly applying differencing schemes for flow variables. The superposition of the kernels then computes flow variables' derivatives (Liu & Liu, 2010). In contrast, MPS is the extension of the finite volume method to a mesh-free approach in which the spatial discretization is obtained based on the differentiation of flow variables. The weighted average of physical quantities derivatives of neighboring particles is applied to the target particle. However, unlike the finite volume method in which the velocity divergence is used for pressure calculation, the particle number density is adopted in MPS. The particle number density indicating the number of particles surrounding a particle is a key variable in MPS that is straightforward to fulfill flow incompressibility (Koshizuka et al., 2018).

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

Cited by 13 publications

References 40 publications

Mesoscale modelling of miscible and immiscible multicomponent fluids

Mesoscale modelling of miscible and immiscible multicomponent fluids

SPH modeling of substance transport in flows with large deformation

MPS‐Based Model to Solve One‐Dimensional Shallow Water Equations

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