Weakly Compressible Smoothed Particle Hydrodynamics Research Articles

Flow under long two-dimensional dam sluice gate using WSPH

An application of the weakly compressible Smoothed Particle Hydrodynamics (WSPH) numerical method is presented here for the case of two-dimensional flow in a long channel with a partially open sluice gate. The results are compared with an analytical solution provided by shallow water equations (SWE) and available experimental data. Of particular interest is the application of this numerical method to a sluice gate case with a high ratio of channel length to depth, which tends to amplify the effects of the chosen numerical resolution. Good model congruence was observed even for relatively low vertical resolution, and the effects of the equations used to describe the boundary conditions were identified.

Smoothed Particle Hydrodynamics Simulations of Turbulent Flow in Curved Pipes With Different Geometries: A Comparison With Experiments

Abstract The swirling secondary flow in curved pipes is studied in three-space dimensions using a weakly compressible smoothed particle hydrodynamics (WCSPH) formulation coupled to new nonreflecting outflow boundary conditions. A large eddy simulation (LES) model for turbulence is benchmarked with existing experimental data. After validation of the present model against experimental results for a 90 deg pipe bend, a detailed numerical study aimed at reproducing experimental flow measurements for a wide range of Reynolds numbers has been performed for different pipe geometries, including U pipe bends, S-shaped pipes, and helically coiled pipes. In all cases, the SPH calculated behavior shows reasonably good agreement with the measurements across and downstream the bend in terms of streamwise velocity profiles and cross-sectional contours. Maximum mean-root-square deviations from the experimentally obtained profiles are always less than ∼1.8%. This combined with the very good matching between the SPH and the experimental cross-sectional contours shows the uprising capabilities of the present scheme for handling engineering applications with streamline curvature, such as flows in bends and manifolds.

An arbitrary Lagrangian Eulerian smoothed particle hydrodynamics (ALE-SPH) method with a boundary volume fraction formulation for fluid-structure interaction

We present a new weakly-compressible smoothed particle hydrodynamics (SPH) method capable of modeling non-slip fixed and moving wall boundary conditions. The formulation combines a boundary volume fraction (BVF) wall approach with the transport-velocity SPH method. The resulting method, named SPH-BVF, offers detection of arbitrarily shaped solid walls on-the-fly, with small computational overhead due to its local formulation. This simple framework is capable of solving problems that are difficult or infeasible for standard SPH, namely flows subject to large shear stresses or at moderate Reynolds numbers, and mass transfer in deformable boundaries. In addition, the method extends the transport-velocity formulation to reaction-diffusion transport of mass in Newtonian fluids and linear elastic solids, which is common in biological structures. Taken together, the SPH-BVF method provides a good balance of simplicity and versatility, while avoiding some of the standard obstacles associated with SPH: particle penetration at the boundaries, tension instabilities and anisotropic particle alignments, that hamper SPH from being applied to complex problems such as fluid-structure interaction in a biological system.

A Local Semi-Fixed Ghost Particles Boundary Method for WCSPH

Due to the convenience and flexibility in modeling complex geometries and deformable objects, local ghost particles methods are becoming more and more popular. In the present study, a novel local semi-fixed ghost particles method is proposed for weakly compressible smoothed particle hydrodynamics (WCSPH). In comparison with the previous local ghost particles methods, the new boundary method can effectively reduce spurious pressure oscillations and smooth the flow field. Besides, the new generation mechanism of fictitious particles is simple and robust, which is suitable for all kinds of kernel functions with different sizes of the support domain. The numerical accuracy and stability of the new smoothed particle hydrodynamics (SPH) scheme are validated for several typical benchmark cases. A detailed investigation into the pressure on solid walls and the surface elevation in dynamic simulations is also conducted. A comparison of numerical results shows that the new boundary method helps reduce the oscillations in the numerical solutions and improves the numerical accuracy of the pressure field.

Implicit molecular stresses in weakly compressible particle-based discretization methods for fluid flow.

Weakly compressible particle-based discretization methods, utilized for the solution of the subsonic Navier-Stokes equation, are gaining increasing popularity in the fluid dynamics community. One of the most popular among these methods is the weakly compressible smoothed particle hydrodynamics. Since the dynamics of a single numerical particle is determined by fluid dynamic transport equations, the particle per definition should represent a homogeneous fluid element. However, it can be easily argued that a single particle behaves only pseudo-Lagrangian as it is affected by volume partition errors and can hardly adapt its shape to the actual fluid flow. Therefore, we will assume that the kernel support provides a better representative of an actual fluid element. By means of nonequilibrium molecular dynamics (NEMD) analysis, we derive isothermal transport equations for a kernel-based fluid element. The main discovery of the NEMD analysis is a molecular stress tensor, which may serve to explain current problems encountered in applications of weakly compressible particle-based discretization methods.

On the use of multibody dynamics techniques to simulate fluid dynamics and fluid–solid interaction problems

A multibody dynamics-based solution to the fluid dynamics problem is compared herein to two established Lagrangian-based techniques used by the computational fluid dynamics (CFD) community. The multibody dynamics-based solution has two salient attributes: it enforces the incompressibility condition through bilateral kinematic constraints, and it treats the coupling with the solid phase via unilateral kinematic constraints. The multibody dynamics-based solution, called herein the Kinematically Constrained Smoothed Particle Hydrodynamics (KCSPH) method, is a Lagrangian approach to solving the CFD problem. It relies on the Smoothed Particle Hydrodynamics (SPH) method to discretize the spatial differential operators in the Navier–Stokes equations, and on the Newton–Euler equations of multibody dynamics to convect the SPH particles forward in time. We show that the multibody dynamics-based approach is efficient and accurate by comparing its performance with the two most commonly used SPH algorithms in the CFD community: the weakly compressible SPH (WCSPH), and the implicit SPH (ISPH) methods. The comparison is carried out in conjunction with four tests: an incompressibility benchmark test, dam break, floating cylinder, and sloshing tank. We conclude that KCSPH is a robust alternative to conventional CFD approaches for fluid–solid interaction (FSI) problems with complex/moving boundaries. The solvers and models used herein are publicly available in an open-source software called Chrono; the implementations use GPU (for WCSPH and ISPH), and multicore CPU (for KCSPH) parallel computing.

Wave Propagation Studies in Numerical Wave Tanks with Weakly Compressible Smoothed Particle Hydrodynamics

Generation and propagation of waves in a numerical wave tank constructed using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) are considered here. Numerical wave tank simulations have been carried out with implementations of different Wendland kernels in conjunction with different numerical dissipation schemes. The simulations were accelerated by using General Process Graphics Processing Unit (GPGPU) computing to utilize the massively parallel nature of the simulations and thus improve process efficiency. Numerical experiments with short domains have been carried out to validate the dissipation schemes used. The wave tank experiments consist of piston-type wavemakers and appropriate passive absorption arrangements to facilitate comparisons with theoretical predictions. The comparative performance of the different numerical wave tank experiments was carried out on the basis of the hydrostatic pressure and wave surface elevations. The effect of numerical dissipation with the different kernel functions was also studied on the basis of energy analysis. Finally, the observations and results were used to arrive at the best possible numerical set up for simulation of waves at medium and long distances of propagation, which can play a significant role in the study of extreme waves and energy localizations observed in oceans through such numerical wave tank simulations.

A Comparison Between Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) and Moving Particle Semi-Implicit (MPS) Methods for 3D Dam-Break Flows

Lagrangian particle-based methods have opened new perspectives for the investigation of complex problems with large free-surface deformation. Some well-known particle-based methods adopted to solve non-linear hydrodynamics problems are the smoothed parti- cle hydrodynamics (SPH) and the moving particle semi-implicit (MPS). Both methods model the continuum by a system of Lagrangian particles (points), but adopting distinct approaches for the numerical operators, pressure calculation, and boundary conditions. Despite the ability of the particle-based methods in modeling highly nonlinear hydrodynamics, some shortcomings, such as unstable pressure computation and high computational cost remain. In order to assess the performance of these two methods, the weakly-compressible SPH (WCSPH) parallel solver, DualSPHysics, and an in-house incompressible MPS solver are adopted in this work. Two test cases consisting of three-dimensional (3D) dam-break problems are simulated, and wave heights, pressures and forces are compared with the available experimental data. The influence of the artificial viscosity on the accuracy of WCSPH is investigated. Computational times of both solvers are also compared. Finally, the relative benefits of the methods for solving free-surface problems are discussed, therefore providing directions of their applicability.

Interaction of a pair of in-line bubbles ascending in an Oldroyd-B liquid: A numerical study

In this paper, the interaction between two initially circular in-line bubbles during their rise in a viscoelastic liquid under gravity is numerically simulated by weakly compressible smoothed particle hydrodynamics (WC-SPH). The background fluid is assumed to obey Oldroyd-B rheological model and the surface tension between two phases is evaluated by continuum surface tension (CST) method. First, it is shown that the obtained results for two benchmark problems, including two rising bubbles in a Newtonian fluid and a single rising bubble in a viscoelastic fluid, are in good agreement with previously published results. Then, together ascending of two unequal in-line bubbles in an Oldroyd-B viscoelastic liquid is simulated. Two different configurations are considered for the position of larger bubble and the center-of-mass of the bubbles and its velocity are presented for each case. Also, the differences of velocity and stress distributions in the background liquid are evaluated for two configurations. Based on the obtained results, it could be said that when the larger bubble is placed above the smaller one, merging does not occurred and the upper bubble has a dual cusped trailing edge. In addition, the effects of Deborah number, polymer concentration, density and viscosity ratios, Reynolds number, and Bond number are investigated on rising bubbles. To the best of authors’ knowledge, it is the first time the simultaneous rising of two bubbles in Oldroyd-B fluids is investigated.

Post-Failure Dynamics of Rainfall-Induced Landslide in Oltrepò Pavese

Prediction of landslide hazard risk at hill slope induced by intense rainfall requires the appropriate modeling of the interactions between soil and weather phenomena, leading to failure as well as a reliable prediction of post-failure dynamics. In the peculiar case of fast shallow landslides behaving like dense granular flows, a suitable modeling approach for large and rapid deformations is necessary to estimate potential related damage. The impact force exerted by the leading edge of the earth-flow on the downstream structure should be estimated for both damage prediction and design of effective protection measures. In this paper, a free open source 3D research code based on standard weakly compressible smoothed particle hydrodynamics (WCSPH) method is validated by modeling a full-scale rainfall-induced shallow landslide which occurred in Oltrepò Pavese (Northern Italy). The code allows resolving the vertical velocity gradients, potentially providing a more reliable representation of the landslide dynamics and impact force. Mechanical parameters are consistent with average soil characteristics, avoiding calibration analysis. The final landslide profile is compared with an experimental survey for model validation, showing good fit. Influence of uncertainties of geotechnical parameters on the landslide front velocity and impact force on the downstream wall is evaluated.

Numerical simulation of free-surface flow and convection heat transfer using a modified Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method

A novel Kernel Derivative-Free (KDF) Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) model is developed for simulation of free-surface flows and convection heat transfer. A high-order Laplacian operator is developed and then applied for the approximation of the diffusion terms (e.g., viscous term, thermal diffusion, and newly additional diffusion term in the continuity equation). The transient term in Navier–Stokes equation is discretized using the third-order TVD Runge-Kutta scheme, while a stiff equation of state is employed to predict pressure field. To increase numerical accuracy, a new high-order smoothing operator in the context of the MPS description (Moving Particle Semi-implicit) is also proposed and then applied for the treatment of the buoyancy force term in the momentum equation. Furthermore, a new high-order smoothing kernel is constructed and tested via simulation of the 1D Sod shock tube problem. A series of numerical benchmark cases such as: dam break, stretching of a circular water drop, rotating square patch of fluid and natural convection heat transfer in a square enclosure are used to verify and evaluate the feasibility of the proposed models. It is found that all simulation results are in excellent agreement with the available experimental and numerical data. Capability and performance of KDF-WCSPH method in handling particulate flows with thermal convection are further demonstrated through analysis of entropy generation due to natural convection heat transfer in the three different well-known geometries including: Differentially Heated Cavity, L-shaped enclosure and horizontal annuli. Comparison with the past Finite-Volume results demonstrates that the present model can maintain stability and accuracy, which makes it a very useful tool for simulation of thermo-hydraulic problems.

Development of computationally efficient augmented Lagrangian SPH for incompressible flows and its quantitative comparison with WCSPH simulating flow past a circular cylinder

SummaryIn Lagrangian particle‐based methods such as smoothed particle hydrodynamics (SPH), computing totally divergence‐free velocity field in a flow domain with the smallest error possible is the most critical issue, which might be achieved through solving pressure Poisson equation implicitly with higher particle resolutions. However, implicit solutions are computationally expensive and may be particularly challenging in the solution of multiphase flows with highly nonlinear deformations as well as fluid‐structure interaction problems. Augmented Lagrangian SPH (ALSPH) method is a new alternative algorithm as a prevalent pressure solver where the divergence‐free velocity field is achieved by iterative calculation of velocity and pressure fields. This study investigates the performance of the ALSPH technique by solving a challenging flow problem such as two‐dimensional flow around a cylinder within the Reynolds number range of 50 to 500 in terms of improved robustness, accuracy, and computational efficiency. The same flow conditions are also simulated using the conventional weakly compressible SPH (WCSPH) method. The results of ALSPH and WCSPH solutions are not only compared in terms of numerical validation/verification studies, but also rigorous investigations are performed for all related physical flow characteristics, namely, hydrodynamic coefficients, frequency domain analyses, and velocity divergence fields.

An improved non-reflecting outlet boundary condition for weakly-compressible SPH

Implementation of an outlet boundary condition is challenging in the context of the weakly-compressible Smoothed Particle Hydrodynamics method. We perform a systematic numerical study of several of the available techniques for the outlet boundary condition. We propose a new hybrid approach that combines a characteristics-based method with a simpler frozen-particle (do-nothing) technique to accurately satisfy the outlet boundary condition in the context of wind-tunnel-like simulations. In addition, we suggest some improvements to the do-nothing approach. We introduce a new suite of test problems that make it possible to compare these techniques carefully. We then simulate the flow past a backward-facing step and circular cylinder. The proposed method allows us to obtain accurate results with an order of magnitude less particles than those presented in recent research. We provide a completely open source implementation and a reproducible manuscript.

Modelling of wave generation in a numerical tank by SPH method

There have been many mathematical and physical modelling strategies to represent a numerical wave tank that can generate the desired wave spectrums. Presently, one of the recent methodologies that have certain intrinsic capabilities for the investigation of free-surface hydrodynamic problems, namely, Smoothed-Particle-Hydrodynamics (SPH) technique, has been utilized for the modelling of a numerical wave tank. The Navier–Stokes and continuity equations are utilized for governing the fluid motion through Weakly Compressible SPH (WCSPH) approach which couples pressure and density by an equation of state. As one of the major numerical treatments, kernel gradient normalization is included into the present SPH method together with the numerical treatments, namely, well-known density smoothing algorithm, hybrid velocity variance-based free surface (VFS), and artificial particle displacement (APD) algorithms. The generation of regular and irregular waves is performed by a moving boundary at the inlet where natural damping is targeted by utilizing a dissipative beach at the end of numerical wave tank. A wide range of test cases in terms of wave-lengths and steepness ratios have been investigated for the regular wave simulations. Although the wave-maker is forced linearly to oscillate sinusoidally at the inlet of the tank, due to the relatively high wave steepness ratios applied, the non-linear character of the free-surface has been clearly observed with the performed Fast Fourier Transform analyses. Wave energy densities of the SPH results have also been compared with the linear theory expectations per unit wave-length. To scrutinize the conditions for the wave-breaking inception, three additional wave steepness values have been simulated at a single wave-length value. As a further examination of the proposed SPH scheme, JONSWAP irregular wave spectrum has been utilized with both flap and piston type moving boundaries. In the light of performed simulations, the proposed SPH numerical scheme can provide robust and consistent results while generating regular and irregular wave systems in deep water conditions. Furthermore, it is observed that it has the capability of capturing the non-linear characteristics of generated waves with high sensitivity, including the wave-breaking phenomenon.

Lagrangian two-phase flow modeling of scour in front of vertical breakwater

ABSTRACT A Lagrangian particle-based two-phase flow model is developed to simulate the scouring process induced by standing wave in front of the trunk section of a vertical breakwater. Given the two-dimensional nature of the scouring problem at the trunk of vertical wall, the fluid phase is simulated with two-dimensional Navier–Stokes equations based on weakly compressible smoothed particle hydrodynamics (WCSPH) formulation in conjunction with sub-particle scale (SPS) turbulence closure model. The sediment phase is simulated using the Discrete Element Method (DEM). The effects of interparticle and particle-wall collisions are computed by activating a spring-dashpot system. The WCSPH fluid-phase and DEM sediment-phase are coupled through a weakly one-way coupling procedure using wave orbital velocity. The numerical model is successfully validated against experimental data. The maximum scour depth predicted by WCSPH-DEM model is closely approximate the experimental data. This study, for the first time, demonstrated an extra recirculating sediment transport mechanism in front of the vertical breakwater, similar to steady streaming recirculating cells in the fluid phase, which has a direct impact on the formation of scour hole and maximum scour depth at the breakwater trunk. The scenario modeling conducted in this study show that by increasing the steady streaming velocity, the deposition rate and the depth of scour hole were increased.

Smoothed Particle Hydrodynamics multiphase modelling of an experimental microfluidic device for conformal coating of pancreatic islets

The paper discusses a Smoothed Particle Hydrodynamics (SPH) model for the analysis of the multiphase flow occurring in an experimental microfluidic device for conformal coating of pancreatic islets with a biocompatible and permeable polymer. The proposed numerical model, based on a weakly-compressible SPH approach, accurately mimics the encapsulation process while assuring phase conservation, thus overcoming potential limitations of grid-based models. The proposed SPH model is a triphasic multi-phase model that allows one: (i) to reproduce the physics of islet conformal coating, including the effects of surface tension at the interface of the involved fluids and of the islet diameter; and (ii) to evaluate how modulation of process parameters influences the fluid dynamics within the microfluidic device and the resulting coating characteristics. This model can represent a valuable, time- and cost-effective tool for the definition of optimized encapsulation conditions through in silico screening of novel combinations of conformal coating parameters, including polymeric coating blends, size range of insulin-secreting cell clusters, utilized chemical reagents, device geometry and scale.

Numerical analysis of wave-induced current within the inhomogeneous coral reef using a refined SPH model

The effects of reef permeability on the spatial distributions of wave-induced current inside and outside the inhomogeneous coral reef body are investigated using an improved weakly compressible smoothed particle hydrodynamic (WCSPH) mixture model. The governing equations are formulated based on the two-phase mixture theory without considering the solid phase motion in terms of the intrinsic velocity and fluid density. The developed WCSPH mixture model is firstly validated by comparing the predicted results with the corresponding available data for Darcy seepage flow in a U-tube with permeable soil, wave damping over a permeable seabed and wave transformation over a permeable reef. The validated model is then applied to study the spatial distributions of wave-induced current inside and outside the permeable reef body with different porosity and porous layer thickness. Finally, a parametric study is carried out to investigate the effects of different porosity distribution types on wave-induced currents.

Dual-criteria time stepping for weakly compressible smoothed particle hydrodynamics

Implementing particle-interaction configuration, which consists of determining particle-neighbor lists and computing corresponding kernel weights and gradients, and time integration are performance intensive essentials of smoothed particle hydrodynamic (SPH) method. In this paper, a dual-criteria time-stepping method is proposed to improve the computational efficiency of the weakly-compressible SPH (WCSPH) method for modeling incompressible flows. The key idea is to introduce an advection time-step criterion, which is based on flow speed, for recreating the particle-interaction configuration. Within an advection time-step, several steps of pressure relaxation, i.e. the time integration of the particle density, position and velocity due to the action of pressure gradient, according to the acoustic time-step criterion based on the artificial speed of sound, can be carried out without updating the particle-interaction configuration and with much larger time steps compared with the conventional counterpart. The method has shown optimized computational performance through CPU cost analysis. Good accuracy is also obtained for the presented benchmarks implying promising potential of the proposed method for simulating incompressible flows and fluid-structure interactions.

Numerical simulation of self-consolidating engineered cementitious composite flow with the V-funnel and U-box

A 3D numerical model is developed in this paper to simulate the flow of self-consolidating engineered cementitious composites (SC-ECC) through the V-funnel test and U-box test. The synthetic fibres utilized in SC-ECC are considered as flexible fibres and modelled as separated particles, virtually connected by a drag force between two adjacent fibre particles. The fibre particles and mortar particles possess similar continuum properties in the domain of SC-ECC. The constitutive equations of the flow of SC-ECC are solved using the mesh-free, weakly compressible smoothed particle hydrodynamics (WCSPH). The V-funnel model focuses on the flow rate characteristic and the correlation of the dispersion of synthetic fibres with the plastic viscosity of fresh mixtures. The U-box simulation is to confirm the self-consolidating capability and the passing ability of SC-ECC flow through reinforcing bars. The simulation results of the discharge time in the V-funnel model and the self-levelling index in the U-box model agree well with experimental results from the literature, which provide convincing evidence for the correctness and effectiveness of the developed model. The proposed model thus is capable of providing insight into the flow behaviour of SC-ECC in terms of filling, passing abilities and the dispersion/orientation of flexible synthetic fibres.

A smoothed particle hydrodynamics (SPH) formulation of a two-phase mixture model and its application to turbulent sediment transport

A Smoothed Particle Hydrodynamics (SPH) formulation and implementation of the classical two-phase mixture model are reported, with a particular focus on the turbulent sediment transport and the sediment disturbances generated by moving equipment operating near or on the seabed. In the mixture model, the fluid-particle system is considered to be an equivalent medium whose evolution is described by a set of equations for the mixture continuity and momentum conservation, with the particle volume fraction being tracked by a transport equation. The governing equations are adapted to a Lagrangian, weakly-compressible SPH framework, the turbulence is modeled by a Reynolds-averaged Navier-Stokes approach, and adaptive boundary conditions for shear stress and turbulent quantities are implemented to account for laminar or turbulent local flow conditions. The complex rheological behavior of clay sediment/water mixtures is modeled using a volume fraction, shear rate-dependent viscosity which accounts for the existence of a yield stress. Hence, the proposed work encompasses several challenging modeling aspects: turbulence, non-Newtonian fluid behavior, sediment transport, and fluid-structure interactions. It is then illustrated on diverse cases of interest: a fluid-particle mixture column release, its subsequent turbulent transport and return to a hydrostatic equilibrium, the settling of particle clouds and two cases of particle-driven gravity currents, and their comparisons with available results. Finally, SPH simulation results for the disturbance of a bed of clay sediment/water mixture induced by a moving plate are reported and compared with experiments performed in our laboratory. The proposed SPH two-phase mixture model agrees well with the existing results considered in this study.