SPH Models Research Articles

Discussion on “comparative study on volume conservation among various SPH models for flows of different levels of violence, coastal engineering, volume 191, August 2024, 104 521” by Wang et al

The paper by Wang et al. (2024) targets an interesting topic in the context of particle methods, namely, volume conservation. This important feature is studied by focusing on the time variation of mean water level under three different scenarios corresponding to hydrostatics, standing wave and dam break, and through consideration of a few variants of the Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) fluid model. In this discussion, the discussers briefly discuss some issues that could have been further considered in the paper by Wang et al. (2024) to ensure rigorousness and comprehensiveness of the conducted comparative analysis.

Comparative study on volume conservation among various SPH models for flows of different levels of violence

The weakly-compressible smoothed particle hydrodynamics (WCSPH) models offer distinct advantages in simulating free-surface flow. Within the rapidly evolving WCSPH field, Classical WCSPH model, based on the artificial viscous term, and its derived models, which additionally introduce numerical diffusive terms into the continuity equations - including the δ-SPH, δ-SPHC, δ-SPHC+, δ-LES-SPH, and δ-SPHF models have gained prominence recently. The numerical diffusive term is found to alter the particle distributions in the free-surface region, leading to a change in the mean water level that reflects the volume conservation, which might result in inaccuracies in some simulations. This study evaluates the volume conservations of the aforementioned WCSPH models for flows at quasi-hydrostatic states evolved from varying levels of flow violence under prolonged simulations, through a series of numerical tests involving hydrostatic, standing-wave, and dam-break cases. For the hydrostatic and standing-wave cases, the performance of different types of WCSPH models remains consistent overall. The Classical WCSPH and δ-LES-SPH models exhibit minimal changes in volume, with almost no decrease in the mean water level occurring. The δ-SPH, δ-SPHC, δ-SPHC + models demonstrate decreases in the mean water level converging to around 0.2 times the SPH particle diameter (Δx), indicating favorable volume conservation. Conversely, the δ-SPHF model consistently exhibits a decrease in the mean water level exceeding 1 Δx at t = 2000s in a linear fashion, resulting in a noticeable reduction in volume. Under the dam-break case, most of the mean water levels simulated by different models experience a small increase, which is close to the decrease observed under the hydrostatic and standing-wave cases with corresponding models. Only the δ-SPHF model continues to show a continuous decreasing tendency. In summary, considering volume conservation, the δ-LES-SPH model demonstrates the best performance (excluding the Classical WCSPH model as it cannot simulate violent flow), followed by the δ-SPHC, δ-SPHC+, δ-SPH and δ-SPHF models.

Coupling of stabilized total Lagrangian and weakly compressible SPH models for challenging fluid–elastic structure interaction problems

Coupling of stabilized total Lagrangian and weakly compressible SPH models for challenging fluid–elastic structure interaction problems

Inclusion of an acoustic damper term in weakly-compressible SPH models

The proposed work describes a novel viscous term specifically conceived to reduce the amount of acoustic pressure waves in weakly-compressible SPH models. The above-mentioned term only acts on the acoustic component of the pressure field, which is generated as a consequence of liquid impacts and of the assumption that the fluid is weakly-compressible, whereas it leaves the incompressible-like component unchanged. In comparison to the existing regularizing terms in the SPH literature, this allows for noise-free simulations which are similar to simulations of incompressible flows, and, at the same time, it maintains the advantages of explicit schemes (i.e. scalability and easiness of parallelization). The proposed acoustic damper term converges to zero when the particle resolution increases, recovering the consistency with the Navier-Stokes equations. Numerical results demonstrate that this term is effective for flow simulations with different weakly-compressible SPH models.

Depth-averaged vs. Full 3-D SPH Models: A Comparison of Accuracy and Computational Speed for Simulating Dam Break Flash Flood

Depth-averaged vs. Full 3-D SPH Models: A Comparison of Accuracy and Computational Speed for Simulating Dam Break Flash Flood

A three-dimensional fluid-structure interaction model based on SPH and lattice-spring method for simulating complex hydroelastic problems

The present work revolves around the development of a 3D particle-based Fluid-Structure Interaction (FSI) solver to simulate hydroelastic problems that involve free surface. The three-dimensional Volume-Compensated Particle Method (VCPM) for modelling deformable solid bodies is developed within the open-source SPH software package DualSPHysics. Complex 3D FSI problems are readily simulated within a reasonable time frame thanks to the parallel scalability of DualSPHysics on both CPU and GPU. The Sequential Staggered (SS) scheme paired with a multiple time-stepping procedure is implemented in DualSPHysics for coupling the SPH and VCPM models. It is found that the SPH-VCPM method is computationally more efficient than the previously reported SPH-TLSPH method. Extensive validations have been performed based on some very recent 3D experimental setups that involve violent free surface and complex structural dynamics. Findings from this research highlight the capability of the 3D SPH-VCPM model to reproduce some of the physical observations that were not captured by previous 2D studies. Some preliminary 3D FSI results involving solid fracture are also demonstrated.

New benchmark problems for validation and verification of incompressible multi-fluid flows based on the improved Volume-Of-Fluid (VOF) method

The present work describes the application of the improved Volume-Of-Fluid (VOF) method for the accurate capturing of phase interfaces in the problems of three-fluid bubble rising, water/oil droplets impacting onto wetted beds, three-fluid Rayleigh-Taylor Instability and merging of two rising bubbles, aiming to establish powerful benchmarking tools for validation of existing numerical models and code verification problems. To this end, an enhance version of the VOF model is exploited where a novel third-order TVD convection scheme is utilized for the discretization of convection terms in the Navier-Stokes and transport equations while the combination of the implicit non-iterative PISO and classical SIMPLER algorithms (PISOR) is applied for the treatment of the pressure-velocity coupling and acceleration of the iteration process in the Poisson equation. A series of canonical test cases including dam break over a dry bed, single and double rising bubbles, two-phase Rayleigh-Taylor Instability are considered to verify the performance and accuracy of the numerical method. The obtained results vividly demonstrate the superiority and versatility of the improved VOF model over the classical Eulerian and Lagrangian methods in handling multiphase flows with relevant breaking and fragmentation. Moreover, it is found that, the standard version of Lagrangian SPH models can not accurately address the problem of interface smearing, and thereby characterizing by noisy pressure distribution.

An SPH-based mass transfer model for simulating hydraulic characteristics and mass transfer process of dammed rivers

Aerated flow characterized by complex mass transfer processes with multiple hydraulic properties is a common enviro-hydraulics phenomenon, which have a variety of profound effects on aquatic ecosystems and the environment. Accurate prediction of the mass transfer process between air and water is crucial to manage the water ecosystem. In this research, an improved two-phase mass transfer smoothed particle hydrodynamics (ITMT-SPH) model is developed with considering the inherent hydrodynamic equations and transport equations to investigate multiple key factors that have ecological implications such as DO (dissolved oxygen) concentration and TDG (total dissolved gas) level. The established model can eliminate the effects of phase separation and non-physical voids for conventional SPH models, which performs better than conventional grid-based methods in terms of prediction accuracy of hydraulic calculation. In addition, to improve the prediction accuracy of mass transfer calculation, experimental and observed field data from a physical model and a practical project are used to calibrate the source parameter of transport equations. Then, a physical model of Songta Hydropower Station (1:80) is established to simulate DO concentration. At the same time, the practical project of Tongjiezi Hydropower Station is used to explore dynamics of TDG level. Simulation results show that ITMT-SPH can simulate ecological indicators of the aerated flow well. The maximum relative error of DO deficit recovery rate between simulation and experiment is 7.8% downstream of dam of Songta physical model. The predicted result of TDG level downstream of Second Dam is 130–148% for Tongjiezi Project, which is close to the monitoring result (138%). This work provides an important theoretical and technical support for the application of ITMT-SPH model to accurately simulate ecological indicators in the ecosystem management.

A study on the thermopower and resistivity properties of Ti doped manganites Gd0.7Sr0.3Mn1-xTixO3 (x = 0,0.1 and 0.15)

Thermoelectric power (TEP) along with temperature dependent resistivity of Ti doped Gd-Sr manganite (Gd0.7Sr0.3Mn1-xTixO3 (x = 0, 0.1 and 0.15) denoted by G, G0.1 and G0.15 respectively) are studied systematically. Significant Seebeck coefficients (S) are exhibited by all the three samples which is a most desirable quality of a good thermoelectric material. In the case of sample G, highest attained value of S is −35.57mVK−1 at 91 K. For G0.1 and G0.15 highest attained values are −31.60 mVK−1 at 114 K and –33.76 mVK−1 at 133 K respectively. This reveals that Ti doping shifts the highest value of S to higher temperatures. Diffusion and magnon drag contribute to TEP at lower temperatures. Temperature dependence of thermopower at comparatively higher temperature region gives an insight of combined SPH and VRH models. Temperature dependent electrical resistivity is successfully analyzed within the interesting framework of variable range hopping of small polarons.

An accurate SPH Volume Adaptive Scheme for modeling strongly-compressible multiphase flows. Part 1: Numerical scheme and validations with basic 1D and 2D benchmarks

In the present work, the single-phase and weakly-compressible δ-SPH model is further extended to simulate multiphase and strongly-compressible flows. This is motivated by the fact that traditional SPH models can meet some difficulties when modeling strongly-compressible flows with large volume variations (e.g. expansion and collapse of cavitation bubbles). Due to the strong compressibility of the fluid, the energy equation should be considered in the governing equations. In that case, the pressure is solved based on both density and internal energy. To stabilize the pressure field, density and energy diffusive terms should be applied. Large variations of particle volumes in the compressible phase would result in large variations of particle spacing. Therefore, particle smoothing lengths are adjusted in time to maintain appropriate neighboring particles. To ensure good properties of accuracy and conservation when particles with different smoothing lengths interact, corrected SPH operators are utilized to discretize the governing equations. Moreover, in order to limit the particle volume variations and maintain a homogeneous volume distribution in the entire flow field, especially near the interface between different phases of different compressibility, a new volume adaptive scheme is proposed to control particle volumes. The volumes which are over-expanded or over-compressed will be split or merged with others, maintaining a small particle volume variation in the flow. Finally, the proposed SPH model is validated with several challenging benchmarks including expansion and collapse of underwater-explosion bubbles or cavitation bubbles. All the SPH results are compared with other numerical solutions with good agreements.

Design of concrete walls and slabs for wind-borne missile loadings

Exterior walls and roofs in safety-related nuclear facilities in the United States, including nuclear power plants, must be designed to resist the loadings imposed by missiles (steel pipes, steel spheres, automobiles) borne by hurricanes and tornadoes. For confinement or containment, these walls and roofs are constructed from reinforced and/or prestressed concrete. The minimum required thicknesses of a reinforced panel to prevent scabbing and perforation for an impacting steel pipe are typically established using empirical formulae calibrated for rigid missiles and high velocities. To enable improved design of concrete panels to prevent scabbing and perforation by wind-borne steel pipes, numerical simulations were performed to: (1) investigate the effects of panel thickness, pipe mass and diameter, pipe velocity, and concrete uniaxial compressive and tensile strength on impact resistance, and (2) establish minimum panel thicknesses to prevent scabbing and perforation for the pipes and impact velocities specified in standards of practice. The numerical simulations used axisymmetric SPH models validated using data from tests at Sandia National Laboratory in the 1970s of four reinforced concrete panels impacted by Schedule 40 pipes. The values of panel thickness and concrete compressive strength considered in the parametric study are typical of those in existing nuclear power plant structures in the United States. The Schedule 40 pipe is the missile used for simulations because it is referenced in the United States Nuclear Regulatory Commission (USNRC) Standard Review Plan and the Department of Energy (DOE) Natural Phenomena Hazards Analysis and Design Criteria for DOE Facilities that point to Regulatory Guide (RG) 1.76, RG 1.221, and ANS-2.3. The impact velocities bound the maximum velocities recommended in the USNRC and ANS documents for design against the impact of Schedule 40 pipes. A considerable number of design parameters have a meaningful effect on the impact resistance of reinforced concrete panels but the most important, aside from panel thickness and impact velocity, is tensile strength of concrete. Results of the parametric study enable the writing of guidance on the minimum thickness of reinforced concrete panels to resist 152 mm (6 in), 203 mm (8 in) and 254 mm (10 in) diameter Schedule 40 pipes at impact velocities identified in RG 1.76, RG 1.221 and ANS-2.3. Panel thickness ranging from 305 mm (12 in) to 914 mm (36 in) are required to prevent perforation and scabbing caused by the impact of these Schedule 40 pipes. The required panel thickness decreases with increasing tensile strength.

Objective Symmetrically Physical Strain Tensors, Conjugate Stress Tensors, and Hill’s Linear Isotropic Hyperelastic Material Models

We introduce a new family of strain tensors—a family of symmetrically physical (SP) strain tensors—which is also a subfamily of the well-known Hill family of strain tensors. For the further analysis, five scale functions are chosen which generate strain tensors belonging to the families of strain tensors previously introduced by other authors (i.e., the Doyle–Ericksen, Curnier–Rakotomanana, Curnier–Zysset, Itskov, and Darijani–Naghdabadi families) and to the new family of SP strain tensors. In particular, these five scale functions include the scale function generating the Lagrangian and Eulerian Hencky strain tensors. We introduce the family of SPH models of isotropic hyperelastic materials (with Hill’s linear relations) which are generated by SP strain tensors and work-conjugate stress tensors based on Hill’s natural generalization of Hooke’s law. Five SPH models of isotropic hyperelastic materials are generated on the basis of chosen SP strain tensors and work-conjugate stress tensors. These models are tested by solving two problems with homogeneous strain and stress tensors fields: the simple elongation and simple shear problems. Analysis of these solutions shows that the solutions of both problems for the Hencky isotropic hyperelastic material model (one of the five generated SPH models of isotropic hyperelastic materials) are qualitatively different from the solutions for the remaining four material models. That is, the solutions using the Hencky isotropic hyperelastic material model are of yielding nature typical of inelastic deformation of metals whereas the solutions for the other four material models reproduce strain diagrams typical of rubber.

Multi-resolution Delta-plus-SPH with tensile instability control: Towards high Reynolds number flows

It is well known that the use of SPH models in simulating flow at high Reynolds numbers is limited because of the tensile instability inception in the fluid region characterized by high vorticity and negative pressure. In order to overcome this issue, the δ+-SPH scheme is modified by implementing a Tensile Instability Control (TIC). The latter consists of switching the momentum equation to a non-conservative formulation in the unstable flow regions. The loss of conservation properties is shown to induce small errors, provided that the particle distribution is regular. The latter condition can be ensured thanks to the implementation of a Particle Shifting Technique (PST). The novel variant of the δ+-SPH is proved to be effective in preventing the onset of tensile instability. Several challenging benchmark tests involving flows past bodies at large Reynolds numbers have been used. Within this a simulation characterized by a deforming foil that resembles a fish-like swimming body is used as a practical application of the δ+-SPH model in biological fluid mechanics.

Coupling SPH and thermochemical models of planets: Methodology and example of a Mars-sized body

Giant impacts have been suggested to explain various characteristics of terrestrial planets and their moons. However, so far in most models only the immediate effects of the collisions have been considered, while the long-term interior evolution of the impacted planets was not studied. Here we present a new approach, combining 3-D shock physics collision calculations with 3-D thermochemical interior evolution models.We apply the combined methods to a demonstration example of a giant impact on a Mars-sized body, using typical collisional parameters from previous studies. While the material parameters (equation of state, rheology model) used in the impact simulations can have some effect on the long-term evolution, we find that the impact angle is the most crucial parameter for the resulting spatial distribution of the newly formed crust. The results indicate that a dichotomous crustal pattern can form after a head-on collision, while this is not the case when considering a more likely grazing collision. Our results underline that end-to-end 3-D calculations of the entire process are required to study in the future the effects of large-scale impacts on the evolution of planetary interiors.

The [formula omitted]-SPH model: Simple procedures for a further improvement of the SPH scheme

The present work is dedicated to the improvement of the δ-SPH scheme. This is an enhanced weakly-compressible SPH model widely used in recent years thanks to its benefits to the standard SPH scheme, to its low CPU costs and to its ease of implementation. Nonetheless, the δ-SPH still presents some drawbacks as other SPH models. For example, in some critical conditions it does not prevent the tensile instability and the consequent numerical fragmentation. Furthermore, even if the use of a diffusive term in the SPH continuity equation is able to reduce numerical high frequencies on the pressure field, the velocity gradients are generally noisy because of the irregularities of the particle spatial configurations, which, in specific flow conditions, can induce also extra numerical-dissipation. For these reasons a particle shifting technique is used to improve the model and a special treatment has been developed for particles that are close to the free-surface region. The introduction of the particle-shifting procedure is generalized in the context of multi-resolutions for which a novel algorithm is formulated to handle the particle re-positioning in the different resolution levels. The proposed algorithms can be straightforwardly implemented in an SPH model without requiring cumbersome code modifications. The δ+-SPH is validated on seven different benchmarks giving a wide panorama on the improvements of this new SPH model.

Smoothed particle hydrodynamics numerical model for modeling an oscillating water chamber

This paper presents the application and the validation of the SPH numerical model SPHyCE, based on a standard Smoothed Particle Hydrodynamics formulation, for modeling an onshore oscillating water chamber, comparing results of amplification factor and phase lag with those obtained by a mesh-based RANS model. Firstly, an analysis of the results for different resolutions (i.e. particle dimension) showed the independence of results with refinement. Secondly, the amplification factor of mean free surface elevation inside the oscillating water chamber and the phase lag between time series of free surface elevation outside and inside the water chamber were analysed. A good agreement was achieved between the mesh free SPHyCE model and the mesh-based RANS model. SPHyCE model was finally applied to analyse the hydrodynamic fluid flow inside and outside the water chamber and to quantify the forces on the vertical wall and the amplification factor for different incident wave heights for a rough sea state with complex wave breaking, impact loads and overtopping, contributing to the future applications of SPH models for development and studies of OWC devices.

Direct collapse to supermassive black hole seeds: comparing the AMR and SPH approaches.

We provide detailed comparison between the adaptive mesh refinement (AMR) code enzo-2.4 and the smoothed particle hydrodynamics (SPH)/N-body code gadget-3 in the context of isolated or cosmological direct baryonic collapse within dark matter (DM) haloes to form supermassive black holes. Gas flow is examined by following evolution of basic parameters of accretion flows. Both codes show an overall agreement in the general features of the collapse; however, many subtle differences exist. For isolated models, the codes increase their spatial and mass resolutions at different pace, which leads to substantially earlier collapse in SPH than in AMR cases due to higher gravitational resolution in gadget-3. In cosmological runs, the AMR develops a slightly higher baryonic resolution than SPH during halo growth via cold accretion permeated by mergers. Still, both codes agree in the build-up of DM and baryonic structures. However, with the onset of collapse, this difference in mass and spatial resolution is amplified, so evolution of SPH models begins to lag behind. Such a delay can have effect on formation/destruction rate of H2 due to UV background, and on basic properties of host haloes. Finally, isolated non-cosmological models in spinning haloes, with spin parameter λ ∼ 0.01-0.07, show delayed collapse for greater λ, but pace of this increase is faster for AMR. Within our simulation set-up, gadget-3 requires significantly larger computational resources than enzo-2.4 during collapse, and needs similar resources, during the pre-collapse, cosmological structure formation phase. Yet it benefits from substantially higher gravitational force and hydrodynamic resolutions, except at the end of collapse.

3D Simulation of a Dust-Driven Wind In a Binary System

We implemented 3D SPH models of stellar winds including a self-consistent treatment of dust formation, radiative cooling, and radiation pressure on dust grains.

Numerical study of PPE source term errors in the incompressible SPH models

AbstractIn a recent work by Gui et al. , an incompressible SPH model was presented that employs a mixed pressure Poisson equation (PPE) source term combining both the density‐invariant and velocity divergence‐free formulations. The present work intends to apply the model to a wider range of fluid impact situations in order to quantify the numerical errors associated with different formulations of the PPE source term in incompressible SPH (ISPH) models. The good agreement achieved between the model predictions and the documented data is taken as a further demonstration that the mixed source term formulation can accurately predict the fluid impact pressures and forces, both in the magnitude and in the spatial and temporal patterns. Furthermore, an in‐depth numerical analysis using either the pure density‐invariant or velocity divergence‐free formulation has revealed that the pure density‐invariant formulation can lead to relatively large divergence errors while the velocity divergence‐free formulation may cause relatively large density errors. As compared with these two approaches, the mixed source term formulation performs much better having the minimum total errors in all test cases. Although some recent studies found that the weakly compressible SPH models perform somewhat better than the incompressible SPH models in certain fluid impact problems, we have shown that this could be largely caused by the particular formulation of PPE source term in the previous ISPH models and a better formulation of the source term can significantly improve the accuracy of ISPH models. Copyright © 2014 John Wiley & Sons, Ltd.

Modified moving particle method for modeling wave interaction with multi layered porous structures

Modified Moving Particle method in Porous media (MMPP) is introduced in this study for simulating a flow interaction with porous structures. By making use of the sub-particle scale (SPS) turbulence model, a unified set of equations are introduced for the entire computational domain and a proper boundary treatment is suggested at the interfaces between fluid and the porous media. Similar to the Incompressible Smoothed Particle Hydrodynamic (ISPH) method, a robust two-step semi-implicit scheme is utilized to satisfy the incompressibility criterion. By means of the introduced model, different flow regimes through multi-layered porous structures with arbitrary shapes can be simulated and there is no need to implement calibration factors.The developed MMPP model is then validated via simulating the experiments of Liu et al. (1999) i.e. linear and turbulent flows through porous dams and the experiments of Sakakiyama and Liu (2001) i.e. wave overtopping on a caisson breakwater protected by multi layered porous materials. Good agreements between numerical and laboratory data present the ability of the introduced model in simulating various flow regimes through multi-layered porous structures. It is concluded that the turbulent flow is an important issue particularly at the interface between the free fluid and porous media and consequently, the accuracy of the previous Lagrangian models that were based on neglecting the turbulence effect can be improved significantly by means of the present model. In addition, to satisfy the continuity criteria in the SPH models, it is necessary to modify density of particles in accordance with their porosity.