Smoothed Particle Hydrodynamics Particles Research Articles

A fully Lagrangian computational model for the integration of mixing and biochemical reactions in anaerobic digestion

The impact of mixing on biochemical reactions is of high importance in anaerobic digestion (AD). In this paper, a novel 2D fully Lagrangian computational model for the integration of mixing and biochemical reactions in AD is developed and presented. The mixing-induced fluid flow is modeled by smoothed particle hydrodynamics (SPH). The computational domain is discretized by SPH particles, each of which carries the information of biologically active compounds and follows the flow field. In this natural way, advection is reproduced, which is the main advantage of SPH for this type of problems. A mathematical model that governs the biochemical reactions is integrated in time for each particle, which allows to spatially resolve the biological concentrations. Mass transfer interactions between particles are reproduced by the diffusion equation to directly link mixing to biochemical reactions. The total biogas production is obtained by integrating over all the particles. Both SPH and biochemical models are verified against existing data in the literature and the integrated model is then applied to a real world anaerobic digester. The application of a novel fully Lagrangian method to AD is a stepping stone to future possible developments. However, in the simulation of such problems, SPH is still uncompetitive if compared to other mainstream methods and industrial application of the model depends on the computational efficiency of future SPH solvers.

Adaptive resolution for multiphase smoothed particle hydrodynamics

The smoothed particle hydrodynamics (SPH) method has been increasingly used to study fluid problems in recent years; but its computational cost can be high if high resolution is required. In this study, an adaptive resolution method based on SPH is developed for multiphase flow simulation. The numerical SPH particles are refined or coarsened as needed, depending on the distance to the interface. In developing the criteria, reference particle spacing is defined for each particle, and it changes dynamically with the location of the interface. A variable smoothing length is used together with adaptive resolution. An improved algorithm for calculating the variable smoothing length is further developed to reduce numerical errors. The proposed adaptive resolution method is validated by five examples involving liquid drops impact on dry or wet surfaces, water entry of a cylinder and dam break flow, with the consideration of ambient gas. Different resolution levels are used in the simulations. Numerical validations have proven that the present adaptive resolution method can accurately capture the dynamics of liquid–gas interface with low computational costs. The present adaptive resolution method can be incorporated into other particle-based methods for efficient fluid dynamics simulation.

Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications

Computer modeling of complex fluid flows usually presents great challenges for conventional grid-based numerical methods. Smoothed particle hydrodynamics (SPH) is a meshfree Lagrangian particle method and has special advantages in modeling complex fluid flows, especially those with large fluid deformations, fluid-structure interactions, and multi-scale physics. In this paper, we review the recent developments of SPH in methodology and applications for modeling complex fluid flows. Specifically, in methodology, some important issues including modified SPH particle approximation schemes for improving discretization accuracy, different particle regularization techniques, and various boundary treatment algorithms for solid boundary, free surface, or multiphase interface are described. More importantly, the SPH method with ideas from the dissipative particle dynamics for complex fluids in macro- or meso-scales is discussed. In applications, different complex fluid flows, including biological flows, microfluidics and droplet dynamics, non-Newtonian fluid flows, free surface flows, multiphase flows, and flows with fluid-structure interaction, are reviewed. Some concluding remarks in SPH modeling of complex fluid flows are provided.

A comparison of state-based peridynamics and solid mesh to SPH conversion techniques to reproduce fragmentation of a ceramic tile subject to ballistic impact

This paper presents a comparison of two present meshfree approaches for modelling brittle material in case of ballistic impact, where extensive cracking and fragmentation is present. These phenomena are very unfeasible to simulate with a standard Lagrangian technique thus alternative methods have been considered in the last years. A comparison between two methods is the main aim of the present article. Smoothed Particle Hydrodynamics (SPH) is an almost consolidated method that exploit the description of a continuum by means of discrete elements whose properties are “smoothed” by a Kernel Function. In this paper a procedure that exploits the transition from finite elements (FE) to SPH particles, following the onset of an erosion criterion is used. This approach and its results are then compared to the recent state-based Peridynamics. Peridynamics method is based on integral equation and allow a direct application to discontinuities and fractures. The results from both methods are critically compared with experimental data and show that the damage morphology is reproduced similarly by both approaches; however less computation efforts are required when peridynamics are used.

A differential variational approach for handling fluid–solid interaction problems via smoothed particle hydrodynamics

The fluid–solid interaction (FSI) problem is customarily solved by starting with the fluid dynamics component. One chooses an established computational fluid dynamics (CFD) method and subsequently embeds the solid phase dynamics within the CFD solution leading to either a monolithic or a staggered/co-simulated solution. The approach discussed here takes the opposite tack. We start with a differential variational framework to handle the solid phase; i.e., the multi-body dynamics problem in the presence of contact, friction, and bilateral kinematic constraints. The dynamics of the fluid phase, which is captured via smoothed particle hydrodynamics (SPH), is subsequently embedded into this framework in which the incompressibility attribute of the flow is enforced via kinematic constraint equations that involve SPH particles. The resulting monolithic FSI solution methodology relies on a half-implicit symplectic time integration method that uses a matrix-free iterative approach to solve a cone constrained quadratic optimization problem at each time step. This problem yields the contact forces, friction forces, boundary condition Lagrange multipliers, fluid–solid coupling terms, and bilateral constraint Lagrange multipliers. The solution of the optimization problem represents the computationally taxing component of the method. Large integration time steps, tight enforcement of incompressibility, a unified approach for handling the fluid and solid phases, and linear scaling are listed as the attractive attributes of the proposed method. The numerical experiments reported include three validation studies (incompressibility, dam break, and sloshing), a scaling analysis, and a tracked vehicle fording simulation.

Accuracy analysis of SPH for flow in a model extruder with a kneading element

The Smoothed Particle Hydrodynamics (SPH) method is used to determine the flow through a model screw extruder at low Reynolds number with an emphasis on resolving the flow in narrow gaps, which are known to produce high shear rates and generate large temperatures. Firstly we demonstrate the validity of the SPH methodology by comparison on simple flows with known analytic solutions. We find excellent agreement and this also allows us to estimate the SPH particle size that is required to obtain accurate solutions for these and more complex flows. SPH simulations on a model single screw extruder with a kneading element are then compared with FEM solutions. Once again excellent agreement is achieved. Finally we demonstrate the SPH method on a model twin screw extruder, which is shown to be robust and qualitatively valid. In general these results show that SPH will be an important computational tool to investigate flows in similar devices.

High-resolution Hydrodynamic Simulation of Tidal Detonation of a Helium White Dwarf by an Intermediate Mass Black Hole

Abstract We demonstrate tidal detonation during a tidal disruption event (TDE) of a helium (He) white dwarf (WD) with 0.45 M ⊙ by an intermediate mass black hole using extremely high-resolution simulations. Tanikawa et al. have shown tidal detonation in results of previous studies from unphysical heating due to low-resolution simulations, and such unphysical heating occurs in three-dimensional (3D) smoothed particle hydrodynamics (SPH) simulations even with 10 million SPH particles. In order to avoid such unphysical heating, we perform 3D SPH simulations up to 300 million SPH particles, and 1D mesh simulations using flow structure in the 3D SPH simulations for 1D initial conditions. The 1D mesh simulations have higher resolutions than the 3D SPH simulations. We show that tidal detonation occurs and confirm that this result is perfectly converged with different space resolution in both 3D SPH and 1D mesh simulations. We find that detonation waves independently arise in leading parts of the WD, and yield large amounts of 56Ni. Although detonation waves are not generated in trailing parts of the WD, the trailing parts would receive detonation waves generated in the leading parts and would leave large amounts of Si group elements. Eventually, this He WD TDE would synthesize 56Ni of 0.30 M ⊙ and Si group elements of 0.08 M ⊙, and could be observed as a luminous thermonuclear transient comparable to SNe Ia.

A multiphase ISPH method for simulation of droplet coalescence and electro-coalescence

In this paper, a numerical algorithm is introduced for simulation of droplet coalescence and electro-coalescence within the framework of the Smoothed Particle Hydrodynamics (SPH) method. The algorithm is developed based on the film drainage model which is used for simulation of coalescence in mesh-dependent methods. The film drainage model allows the SPH particles which are entrapped between two colliding droplets to be discharged. The algorithm is validated with available numerical and experimental results. Then, the algorithm is employed to model two-dimensional coalescence problems for wide ranges of Weber number (0 < We < 30) and impact parameter (0 < β < 0.8). Moreover, the method is extended for the simulation of the electro-coalescence of 2D stationary droplets. Employing the leaky dielectric model, it is observed that both prolate and oblate deformed pair of droplets approach each-other, leading to the permanent coalescence.

Smoothed particle hydrodynamics method for simulating waterfall flow

The existence of waterfall in many nations, such as Indonesia has a potential to develop and to fulfill the electricity demand in the nation. By utilizing mechanical flow energy of the waterfall, it would be able to generate electricity. The study of mechanical energy could be done by simulating waterfall flow using 2-D smoothed particle hydrodynamics (SPH) method. The SPH method is suitable to simulate the flow of the waterfall, because it has an advantage which could form particles movement that mimic the characteristics of fluid. In this paper, the SPH method is used to solve Navier-Stokes and continuity equation which are the main cores of fluid motion. The governing equations of fluid flow are used to obtain the acceleration, velocity, density, and position of the SPH particles as well as the completion of Leapfrog time-stepping method. With these equations, simulating a waterfall flow would be more attractive and able to complete the analysis of mechanical energy as desired. The mechanical energy that generated from the waterfall flow is calculated and analyzed based on the mass, height, and velocity of each SPH particle.

Influence of galactic arm scale dynamics on the molecular composition of the cold and dense ISM

Aim. We study the effect of large scale dynamics on the molecular composition of the dense interstellar medium during the transition between diffuse to dense clouds. Methods. We followed the formation of dense clouds (on sub-parsec scales) through the dynamics of the interstellar medium at galactic scales. We used results from smoothed particle hydrodynamics (SPH) simulations from which we extracted physical parameters that are used as inputs for our full gas-grain chemical model. In these simulations, the evolution of the interstellar matter is followed for ~50 Myr. The warm low-density interstellar medium gas flows into spiral arms where orbit crowding produces the shock formation of dense clouds, which are held together temporarily by the external pressure. Results. We show that depending on the physical history of each SPH particle, the molecular composition of the modeled dense clouds presents a high dispersion in the computed abundances even if the local physical properties are similar. We find that carbon chains are the most affected species and show that these differences are directly connected to differences in (1) the electronic fraction, (2) the C/O ratio, and (3) the local physical conditions. We argue that differences in the dynamical evolution of the gas that formed dense clouds could account for the molecular diversity observed between and within these clouds. Conclusions. This study shows the importance of past physical conditions in establishing the chemical composition of the dense medium.

Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid

As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.

Smoothed particle hydrodynamics method for evaporating multiphase flows.

The smoothed particle hydrodynamics (SPH) method has been increasingly used for simulating fluid flows; however, its ability to simulate evaporating flow requires significant improvements. This paper proposes an SPH method for evaporating multiphase flows. The present SPH method can simulate the heat and mass transfers across the liquid-gas interfaces. The conservation equations of mass, momentum, and energy were reformulated based on SPH, then were used to govern the fluid flow and heat transfer in both the liquid and gas phases. The continuity equation of the vapor species was employed to simulate the vapor mass fraction in the gas phase. The vapor mass fraction at the interface was predicted by the Clausius-Clapeyron correlation. An evaporationratewas derived to predict the mass transfer from the liquid phase to the gas phase at the interface. Because of the mass transfer across the liquid-gas interface, the mass of an SPH particle was allowed to change. Alternative particle splitting and merging techniques were developed to avoid large mass difference between SPH particles of the same phase. The proposed method was tested by simulating three problems, including the Stefan problem, evaporation of a static drop, and evaporation of a drop impacting a hot surface. For the Stefan problem, the SPH results of the evaporation rate at the interface agreed well with the analytical solution. For drop evaporation, the SPH result was compared with the result predicted by a level-set method from the literature. In the case of drop impact on a hot surface, the evolution of the shape of the drop, temperature, and vapor mass fraction were predicted.

From continuum mechanics to SPH particle systems and back: Systematic derivation and convergence

AbstractIn this paper, we derive from the principle of least action the equation of motion for a continuous medium with regularized density field in the context of measures. The eventual equation of motion depends on the order in which regularization and the principle of least action are applied. We obtain two different equations, whose discrete counterparts coincide with the scheme used traditionally in the Smoothed Particle Hydrodynamics (SPH) numerical method [27], and with the equation treated by Di Lisio et al. in [9], respectively. Additionally, we prove the convergence in the Wasserstein distance of the corresponding measure‐valued evolutions, moreover providing the order of convergence of the SPH method. The convergence holds for a general class of force fields, including external and internal conservative forces, friction and non‐local interactions. The proof of convergence is illustrated numerically by means of one and two‐dimensional examples.

Application of smoothed particle hydrodynamics for modeling the wave-moored floating breakwater interaction

The application of a Smoothed Particle Hydrodynamics (SPH) model to simulate the nonlinear interaction between waves and a moored floating breakwater is presented. The main aim is to predict and validate the response of the moored floating structure under the action of periodic waves. The Euler equations together with an artificial viscosity are used as the governing equations to describe the flow field. The motion of the moored floating body is described using the Newton’s second law of motion. The interactions between the waves and structures are modeled by setting a series of SPH particles on the boundary of the structure. The hydrodynamic forces acting on the floating body are evaluated by summing up the interacting forces on the boundary particles from the neighboring fluid particles. The water surface elevations, the movements of the floating body and the moored forces are all calculated and compared with the available experimental data. Good agreements are obtained for the dynamic response and hydrodynamic performance of the floating body. The numerical results of different immersion depths of the floating body are compared with that of the corresponding fixed body. The effects of the relative length and the density of the structure on the performance of the floating body are analyzed.

SPH with dynamical smoothing length adjustment based on the local flow kinematics

Due to the Lagrangian nature of Smoothed Particle Hydrodynamics (SPH), the adaptive resolution remains a challenging task. In this work, we first analyse the influence of the simulation parameters and the smoothing length on solution accuracy, in particular in high strain regions. Based on this analysis we develop a novel approach to dynamically adjust the kernel range for each SPH particle separately, accounting for the local flow kinematics. We use the Okubo–Weiss parameter that distinguishes the strain and vorticity dominated regions in the flow domain. The proposed development is relatively simple and implies only a moderate computational overhead. We validate the modified SPH algorithm for a selection of two-dimensional test cases: the Taylor–Green flow, the vortex spin-down, the lid-driven cavity and the dam-break flow against a sharp-edged obstacle. The simulation results show good agreement with the reference data and improvement of the long-term accuracy for unsteady flows. For the lid-driven cavity case, the proposed dynamical adjustment remedies the problem of tensile instability (particle clustering).

A consistent multi-resolution smoothed particle hydrodynamics method

We seek to accelerate and increase the size of simulations for fluid–structure interactions (FSI) by using multiple resolutions in the spatial discretization of the equations governing the time evolution of systems displaying two-way fluid–solid coupling. To this end, we propose a multi-resolution smoothed particle hydrodynamics (SPH) approach in which subdomains of different resolutions are directly coupled without any overlap region. The second-order consistent discretization of spatial differential operators is employed to ensure the accuracy of the proposed method. As SPH particles advect with the flow, a dynamic SPH particle refinement/coarsening is employed via splitting/merging to maintain a predefined multi-resolution configuration. Particle regularity is enforced via a particle-shifting technique to ensure accuracy and stability of the Lagrangian particle-based method embraced. The convergence, accuracy, and efficiency attributes of the new method are assessed by simulating four different flows. In this process, the numerical results are compared to the analytical, finite element, and consistent SPH single-resolution solutions. We anticipate that the proposed multi-resolution method will enlarge the class of SPH-tractable FSI applications.

Does Explosive Nuclear Burning Occur in Tidal Disruption Events of White Dwarfs by Intermediate-mass Black Holes?

Abstract We investigate nucleosynthesis in tidal disruption events (TDEs) of white dwarfs (WDs) by intermediate-mass black holes. We consider various types of WDs with different masses and compositions by means of three-dimensional (3D) smoothed particle hydrodynamics (SPH) simulations. We model these WDs with different numbers of SPH particles, N, from a few 104 to a few 107 in order to check mass resolution convergence, where SPH simulations with N &gt; 107 (or a space resolution of several 106 cm) have unprecedentedly high resolution in this kind of simulation. We find that nuclear reactions become less active with increasing N and that these nuclear reactions are excited by spurious heating due to low resolution. Moreover, we find no shock wave generation. In order to investigate the reason for the absence of a shock wave, we additionally perform one-dimensional (1D) SPH and mesh-based simulations with a space resolution ranging from 104 to 107 cm, using a characteristic flow structure extracted from the 3D SPH simulations. We find shock waves in these 1D high-resolution simulations, one of which triggers a detonation wave. However, we must be careful of the fact that, if the shock wave emerged in an outer region, it could not trigger the detonation wave due to low density. Note that the 1D initial conditions lack accuracy to precisely determine where a shock wave emerges. We need to perform 3D simulations with ≲106 cm space resolution in order to conclude that WD TDEs become optical transients powered by radioactive nuclei.

Parametric study on smoothed particle hydrodynamics for accurate determination of drag coefficient for a circular cylinder

Simulations of two-dimensional (2D) flow past a circular cylinder with the smoothed particle hydrodynamics (SPH) method were conducted in order to accurately determine the drag coefficient. The fluid was modeled as a viscous liquid with weak compressibility. Boundary conditions, such as a no-slip solid wall, inflow and outflow, and periodic boundaries, were employed to resemble the physical problem. A sensitivity analysis, which has been rarely addressed in previous studies, was conducted on several SPH parameters. Hence, the effects of distinct parameters, such as the kernel choices and the domain dimensions, were investigated with the goal of obtaining highly accurate results. A range of Reynolds numbers (1–500) was simulated, and the results were compared with existing experimental data. It was observed that the domain dimensions and the resolution of SPH particles, in comparison to the obstacle size, affected the obtained drag coefficient significantly. Other parameters, such as the background pressure, influenced the transient condition, but did not influence the steady state at which the drag coefficient was determined.

The Comparison of Viscous Force Approximations of Smoothed Particle Hydrodynamics in Poiseuille Flow Simulation

Poiseuille flows at two Reynolds numbers (Re) 2.5 × 10−2 and 5.0 are simulated by two different smoothed particle hydrodynamics (SPH) schemes on regular and irregular initial particles' distributions. In the first scheme, the viscous stress is calculated directly by the basic SPH particle approximation, while in the second scheme, the viscous stress is calculated by the combination of SPH particle approximation and finite difference method (FDM). The main aims of this paper are (a) investigating the influences of two different schemes on simulations and reducing the numerical instability in simulating Poiseuille flows discovered by other researchers and (b) investigating whether the similar instability exists in other cases and comparing results with the two viscous stress approximations. For Re = 2.5 × 10−2, the simulation with the first scheme becomes instable after the flow approaches to steady-state. However, this instability could be reduced by the second scheme. For Re = 5.0, no instability for two schemes is found.

An adaptive fully-Lagrangian meshless method for incompressible laminar flow airfoil studies

Laminar incompressible flow around a NACA0012 airfoil placed in a free-stream at various incidences has been revisited with the use of a fully-Lagrangian meshless method based on a Smoothed Particle Hydrodynamics (SPH) formulation. Spatial adaptivity has been incorporated in the scheme via splitting and merging of SPH particles employing zonal criteria. In addition, a novel algorithm has been proposed here so that particle merging may be achieved, ensuring the robustness, accuracy and efficiency of the computational simulations. The results obtained have been benchmarked against available data from mesh-based methods. Good agreement has been found both in steady and unsteady flow regimes. Overall, the present work demonstrated the effectiveness and competitiveness of this meshfree approach for detailed studies in aerodynamics.