Meshless Lagrangian Method Research Articles

Principles of creating numerical models for studying the impact of impulse loads on underground structures

Summary. The current situation in Ukraine has led to new geotechnical challenges, the solution of which is aimed at protecting critical infrastructure facilities from the effects of explosive shock waves. Protective structures that are buried in the soil environment are built to protect critical infrastructure facilities. A necessary condition to ensure their safe operation is the assessment of the stress-strain state of the system “soil environment-shelter building”. It is important to choose an adequate phenomenological model of the behavior of the materials of the protective structure and the soil environment, which describes the work of materials under the impulse impacts. The paper analyses four methods of constructing numerical models for calculating the impact of impulse loads, namely: Lagrange mesh. Euler's mesh. Arbitrary Lagrangian-Eulerian (ALE). Smooth Particle Hydrodynamics (SPH). Each of the methods has its advantages and disadvantages. The Lagrangian mesh enables to easily track the boundary between materials of different structures, both before and after the calculation, and it does not require much computational time. However, this method is not practical in cases of significant model deformations with rapid changes in time. The Euler and Arbitrary Lagrange-Euler methods allow to model the problems with a large distortion of the model, such as an underground or underwater explosion. Their disadvantage is the size of the computational domain and the considerable labour intensity for the model setup. Smooth Particle Hydrodynamics is a meshless Lagrangian method. The advantage of this method is the ability to work with large model deformations. The disadvantage is labour intensity and calculation time. All of these methods of building a numerical model are available in the LS-Dyna software package. During the analysis of calculations in LS-Dyna, we found that it is advisable to use the Lagrange mesh to create a model of a structure made of reinforced concrete or steel due to their high stiffness. The Euler and ALE methods are preferable for soil, they enable a strong change in the geometry of the model under the influence of the blast. Different methods are combined to achieve adequate model performance and to obtain correct results that will closely match the actual behavior of structures, facilities and materials under impulse loads.

Lagrangian Split-Step Method for Viscoelastic Flows.

This research addresses and resolves current challenges in meshless Lagrangian methods for simulating viscoelastic materials. A split-step scheme, or pressure Poisson reformulation of the Navier-Stokes equations, is introduced for incompressible viscoelastic flows in a Lagrangian context. The Lagrangian differencing dynamics (LDD) method, which is a thoroughly validated Lagrangian method for Newtonian and non-Newtonian incompressible flows, is extended to solve the introduced split-step scheme to simulate viscoelastic flows based on the Oldroyd-B constitutive model. To validate and evaluate the new method's capabilities, the following benchmarks were used: lid-driven cavity flow, droplet impact response, 4:1 planar sudden contraction, and die swelling. These findings highlight the LDD method's effectiveness in accurately simulating viscoelastic flows and capturing large deformations and memory effects. Even though the extra stress was directly modeled without any regularization approach, the method produced stable simulations for high Weissenberg numbers. The stability and performance of the the Lagrangian numerics for complex temporal evolution of material properties and stress responses encourage its use for industrial problems dealing with polymers.

A physically consistent AI-based SPH emulator for computational fluid dynamics

Abstract The integration of artificial intelligence (AI) into computational fluid dynamics (CFD) has significantly expanded the scope of fluid modeling, allowing enhanced analysis capabilities and improved simulation performance. While Eulerian methods already benefit extensively from AI, notably in reliable weather prediction, the application of AI to Lagrangian methods remains less consolidated. Smoothed particle hydrodynamics (SPH) is a Lagrangian mesh-less numerical method for CFD with well-established advantages for the simulation of highly dynamic free-surface flows. Here, we explore an application of AI to SPH simulations, utilizing an artificial neural network (ANN) to estimate hydrodynamic forces between particle pairs, learning from SPH-simulated results. A model of this nature, which emulates the mathematical representation of physics, is termed an emulator. We examine the physical significance of the emulator, presenting its applications in benchmark tests, assessing its faithfulness to traditional SPH simulations, and highlighting its ability to generalize and simulate test cases with varying levels of complexity beyond its training data.

A fully explicit incompressible smoothed particle hydrodynamics approach for modeling transient heat transfer and thermo-capillary flows

This work presents a Lagrangian meshless method for modeling transient heat transfer and thermo-capillary effects at the interface of two-phase incompressible fluids. To simulate the thermo-capillary effect, we add the Marangoni force to the continuum surface force (CSF) model, by considering the forces caused by the surface tension gradient which acts tangentially to the interface position. In the current study, we extend our previously proposed model which uses a fully explicit incompressible smoothed particle hydrodynamics (EISPH) approach along with corrected SPH and VKF kernel function, to obtain stable and accurate results in non-isothermal single and multi-phase problems.The model is validated for several test cases, including transient heat conduction, natural convection heat transfer, and thermo-capillary droplet migration, against conventional numerical methods. The validated model is used to study the effects of several dimensionless parameters on thermo-capillary droplet migration. The results show that the proposed EISPH method can model accurately complex heat transfer problems such as thermo-capillary induced motion.

Investigation of Sloshing in Different Tank Shapes using Smoothed Particle Hydrodynamics

Sloshing is the violent motion of a resonant fluid in a moving tank; when the fluid moves and interacts with the tank, the dynamic pressure from such an interaction can cause large fluid deformations with tank walls. In this study, a 3D numerical simulation of sloshing was carried out with five variations of the tank model, i.e., prismatic, rectangular, tube, spherical, and the new model tank with a filling ratio of 25% and 50%. Forced oscillation motion in a roll used frequencies 1.04 Hz and 1.34 Hz. The amplitude of movement was 8.66°. One pressure sensor was used to measure dynamic pressure in the mid of the tank. Because sloshing deals with large deformation and discontinuities, the particle method was suitable for the application. This study used smoothed particle hydrodynamics based on weakly compressible SPH (WCSPH). SPH is a Lagrangian meshless method known as mesh-free computational fluid dynamics. Open-source SPH solver version 5.0 was used to reproduce sloshing in different tank shapes; in addition, advanced visualization was performed using the VisualSPHysics add-on in Blender version 2.92. The sloshing visualization is more realistic and attractive than conventional SPH post-processing. The results of this study indicate that different tank shapes influence reducing the value of dynamic pressure and hydrodynamic force. It is found that a practical tank shape is a tube tank and a new model tank with a reduced dynamic pressure value of 9% and 11% and a reduced hydrodynamic force value of 36% and 48%.

Numerical Simulation of the Effect of Tank Shape on Sloshing Using Smoothed Particle Hydrodynamics

Sloshing is the violent motion of a resonant fluid in a moving tank. When the fluid moves and interacts with the tank, the dynamic pressure from such an interaction can cause large deformations of the tank walls and structure. In this study, a 3D numerical simulation was carried out with five variations of the LNG ship tank model: prismatic, rectangular, tube, spherical, and the new model with a filling ratio of 25%. Forced oscillation motion in a roll with f = 1.04 Hz and amplitude of movement 8.66°. Smoothed Particle Hydrodynamics is a Lagrangian meshless (non-grid) method known as mesh-free computational fluid dynamics. This method is very appropriate for the sloshing phenomenon because the sloshing phenomenon is closely related to free surface motion. Advanced visualization was performed using Blender version 2.92, and the sloshing simulation visualization is more realistic and attractive than conventional SPH post-processing. The results of this study indicate that different tank shapes influence reducing the dynamic pressure value. It is found that an effective tank shape is a tube tank and a new model tank with a reduced dynamic pressure value of 9% and 11%.

Об использовании открытых сторонних библиотек при программной реализации вихревых методов вычислительной гидродинамики

The most general structure of a computational algorithm that implements meshless Lagrangian methods of computational fluid dynamics is discussed. Not only the main ones are touched upon, but also “auxiliary”, but therefore no less important procedures, which implementation is often practically ignored. The latter can lead to a significant imbalance and decrease in the efficiency of codes in which the “basic” computational operations are significantly optimized. The author's in-house codes VM2D and VM3D are discussed, the development of which at the first (“exploratory”) stage proceeded mainly along the path of choosing and implementing the necessary mathematical models, and the achievement of acceptable efficiency was ensured by an “extensive” way – involving significant computing resources (in particular, graphical accelerators). An attempt was made to make a conclusion about the expediency of using existing third-party libraries to perform computational geometry operations, solve problems on graphs, etc..

A fully explicit incompressible Smoothed Particle Hydrodynamics method for multiphase flow problems

Multiphase flow is a challenging area of computational fluid dynamics (CFD) due to their potential large topological change and close coupling between the interface and fluid flow solvers. As such, Lagrangian meshless methods are very well suited for solving such problems. In this paper, we present a new fully explicit incompressible Smoothed Particle Hydrodynamics approach (EISPH) for solving multiphase flow problems. Assuming that the change in pressure between consecutive time-steps is small, due to small time steps in explicit solvers, an approximation of the pressure for following time-steps is derived. To verify the proposed method, several test cases including both single-phase and multi-phase flows are solved and compared with either analytical solutions or available literature. Additionally, we introduce a novel kernel function, which improves accuracy and stability of the solutions, and the comparison with a well-established quintic spline kernel function is discussed. For the presented benchmark problems, results show very good agreements in velocity and pressure fields and the interface-capturing with those in the literature. To the best knowledge of the authors, the EISPH method is presented for the first time for multiphase flow simulations.

Lagrangian differencing dynamics for incompressible flows

A Lagrangian meshless method is introduced for numerical simulation of flows of incompressible fluids with free surface. Poisson Pressure Equation (PPE) formulation of Navier-Stokes equations is discretised in Lagrangian context using recently introduced spatial operators based on finite differences. The advection adjusts to moving or deforming boundaries, and volume-conservation is enforced by solving a set of geometrical constraints. A technique for detecting the edge or boundary of a point cloud is introduced, which is based on the Laplacian properties for detecting jumps. Since accurate and fast discrete versions of the operator are not straightforward to implement in meshless context, the technique exploits favourable properties of a discrete Laplacian that handles highly irregular arrangements of points. A geometrical scan-sphere test is optionally performed to verify that points are on the point–cloud boundary. The boundary–detection technique is validated on significantly deformed point clouds by artificial numerical experiments, and by simulating unsteady incompressible flows. The method was validated by simulating lid-driven cavity flow, dam-break and water-entry problems, and comparing the kinematics of flow and hydrodynamic loading during the impact. The method reproduced complex free surface shapes, violent fluid-structure interaction, and pressure fields with second-order accuracy.

Efficient response of an onshore Oscillating Water Column Wave Energy Converter using a one-phase SPH model coupled with a multiphysics library

In this paper the numerical modelling of an Oscillating Water Column (OWC) Wave Energy Converter (WEC) is studied using DualSPHysics, a software that applies the Smoothed Particle Hydrodynamics (SPH) method. SPH is a Lagrangian meshless method used in a growing range of applications within the field of Computational Fluid Dynamics (CFD). The power take-off (PTO) system of the OWC WEC is numerically modelled by adding a force on a plate floating on top of the free surface inside the OWC chamber. That force is implemented in the multiphysics library Project Chrono, which avoids the need of simulating the air phase that is computationally expensive in the SPH methods. Validation is carried out with experimental data received from the Korea Research Institute of Ship and Ocean Engineering (KRISO) and Ocean Energy Systems (OES) of the International Energy Agency (IEA) Task 10. The numerical and experimental water surface elevation at the centre of the OWC WEC chamber and the airflow speed through the orifice are compared for different wave conditions and different PTO systems (different orifice diameters at the top part of the chamber of the OWC WEC). Results show that DualSPHysics is a valid tool to model an OWC WEC with and without PTO system, even though no air phase is included.

Boundary condition enforcement for renormalised weakly compressible meshless Lagrangian methods

This paper introduces a boundary condition scheme for weakly compressible (WC) renormalised first-order accurate meshless Lagrangian methods (MLM) by considering both solid and free surface conditions.A hybrid meshless Lagrangian method-finite difference (MLM-FD) scheme on prescribed boundary nodes is proposed to enforce Neumann boundary conditions. This is used to enforce symmetry boundary conditions and the implied Neumann pressure boundary conditions on solid boundaries in a manner consistent with the Navier-Stokes equation leading to the accurate recovery of surface pressures. The free surface boundary conditions allow all differential operators to be approximated by the same renormalised scheme while also efficiently determining free surface particles.The boundary conditions schemes are implemented for two renormalised MLMs. A WC smoothed particle hydrodynamics (SPH) solver is compared to a WC generalised finite difference (GFD) solver. Applications in both 2D and 3D are explored. A substantial performance benefit was found when comparing the WCGFD solver to the WCSPH solver with the WCGFD solver realising a maximum speedup in the range of three times over WCSPH in both 2D and 3D configurations. The solvers were implemented in C++ and used the NVIDIA CUDA 10.1 toolkit for the parallelisation of the solvers.

A cross-platform, high-performance SPH toolkit for image-based flow simulations on the pore scale of porous media

Efficient numerical simulations of fluid flow on the pore scale allow for the numerical estimation of effective material properties of porous media like effective permeability or tortuosity, among others. In contrast to time-consuming and often expensive laboratory tests, pore scale-resolved numerical simulations further enable the computational quantification of anisotropy of inherent material properties and the estimation of representative sample domains. Numerically calculated quantities are valuable in several fields, such as carbon dioxide sequestration, geothermal energy production and groundwater contamination remediation. Our specific pore scale-resolved simulation method directly based on images obtained from Micro X-Ray Computed Tomography (μXRCT) is based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) approach. SPH is a meshless Lagrangian method, highly suitable for modeling complex geometries and flow at moderate Reynolds numbers. Low Reynolds number flow, also denoted as creeping flow, is a typical scenario present in the above mentioned applications. However, SPH is computationally demanding, especially in simulations of large domains. To overcome these difficulties, we have designed a specific SPH module for the highly optimized HOOMD-blue Molecular Dynamics software. Our implementation supports single-phase flow, and targets both CPU and GPU clusters. Due to the high computational demands, scalability is essential to make the software practically usable, and our tests indicate that our implementation can scale almost ideally. We study a wide variety of test cases, which are not only representative for XRCT-based geometries, but for pore scale-resolved flow simulations in general. Additionally, we present a large-scale simulation investigating an unconventional high porous volcanic rock sample (Reticulite). Program summaryProgram title:: HOOMD-Blue.sphCPC Library link to program files::https://doi.org/10.17632/zdnj8zsrf9.1Licensing provisions:: BSD 3-Clause licenseProgramming language:: C++, CUDA, PythonNature of problem:: Fluid flow simulation in XRCT imaged porous media for digital rock physics applicationsSolution method:: Smoothed Particle Hydrodynamics

Influence of the Drag Force on the Average Absorbed Power of Heaving Wave Energy Converters Using Smoothed Particle Hydrodynamics

In this paper, we investigated how the added mass, the hydrodynamic damping and the drag coefficient of a Wave Energy Converter (WEC) can be calculated using DualSPHysics. DualSPHysics is a software application that applies the Smoothed Particle Hydrodynamics (SPH) method, a Lagrangian meshless method used in a growing range of applications within the field of Computational Fluid Dynamics (CFD). Furthermore, the effect of the drag force on the WEC’s motion and average absorbed power is analyzed. Particularly under controlled conditions and in the resonance region, the drag force becomes significant and can greatly reduce the average absorbed power of a heaving point absorber. Once the drag coefficient has been determined, it is used in a modified equation of motion in the frequency domain, taking into account the effect of the drag force. Three different methods were compared for the calculation of the average absorbed power: linear potential flow theory, linear potential flow theory modified to take the drag force into account and DualSPHysics. This comparison showed the considerable effect of the drag force in the resonance region. Calculations of the drag coefficient were carried out for three point absorber WECs: one spherical WEC and two cylindrical WECs. Simulations in regular waves were performed for one cylindrical WEC with two different power take-off (PTO) systems: a linear damping and a Coulomb damping PTO system. The Coulomb damping PTO system was added in the numerical coupling between DualSPHysics and Project Chrono. Furthermore, we considered the optimal PTO system damping coefficient taking the effect of the drag force into account.

Quadric SFDI for Laplacian Discretisation in Lagrangian Meshless Methods

In the Lagrangian meshless (particle) methods, such as the smoothed particle hydrodynamics (SPH), moving particle semi-implicit (MPS) method and meshless local Petrov-Galerkin method based on Rankine source solution (MLPG_R), the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities (such as the viscous stresses). In some meshless applications, the Laplacians are also needed as stabilisation operators to enhance the pressure calculation. The particles in the Lagrangian methods move following the material velocity, yielding a disordered (random) particle distribution even though they may be distributed uniformly in the initial state. Different schemes have been developed for a direct estimation of second derivatives using finite difference, kernel integrations and weighted/moving least square method. Some of the schemes suffer from a poor convergent rate. Some have a better convergent rate but require inversions of high order matrices, yielding high computational costs. This paper presents a quadric semi-analytical finite-difference interpolation (QSFDI) scheme, which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices, i.e. 3 × 3 for 3D cases, compared with 6 × 6 or 10 × 10 in the schemes with the best convergent rate. Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations. The convergence, accuracy and robustness of the present schemes are compared with the existing schemes. It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures, particularly for estimating the Laplacian of given functions.

SPH simulation of surge waves generated by aerial and submarine landslides

Since the Indian Ocean Tsunami in 2004, there has been extensive research on tsunami modelling. Tsunami catastrophes were generally generated by earthquake fault plate or mass landslide. This article is focused on surge waves induced by mass landslides. Here we restrict to two dimensional study, in which a solid mass was sliding down over a sloping beach. Our approach is numerical simulation using the Smoothed Particle Hydrodynamics (SPH) method. The SPH method is a Lagrangian meshless method, commonly used to describe complex events. Here, the solid mass was modeled as a solid box with triangular-cross section. Its movement follows analytical solution derived by Watts in [1]. The SPH method was used to simulate surge waves induced by two types of landslides; aerial and submarine. Our results were validated using the experimental data of Heinrich [2]. It was shown that the resulting waves induced by aerial and submarine landslides as well as the solid box movement agree quite well with the experimental data. The Root Mean Square Error (RMSE) of free surface deformation in aerial simulation recorded at time t = 0.6, 1.0, 1.5 are 0.02053, 0.02342, 0.02221, respectively and in submarine simulation recorded at time t = 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 are 0.02908, 0.04085, 0.03772, 0.03843, 0.03753, 0.02582, respectively. Whereas motion of the solid box in submarine simulation has better accuracy than in aerial simulation with RMSE 0.00799 and 0.03831, respectively.

A fully Lagrangian method for fluid–structure interaction problems with deformable floating structure

A fully Lagrangian meshless method was developed to solve the nonlinear fluid–structure interaction (FSI) problem. The improved moving particle semi-implicit (MPS) method was applied to simulate the incompressible fluid flow, and the bonded-particle model (BPM) was introduced in the discrete element method (DEM) to predict the structure deformation. The coupled MPS–DEM method was established based on the refined interface force calculation and time steps matching. In addition, a new dimensionless parameter, the deformation coefficient (DC), was proposed to quantitatively evaluate the deformation and displacement changes for the deformable structure. The oscillation of the DC would show the position fluctuation on the structure due to the deformation, and it makes the stability analysis of the deformable structure more comprehensive and reasonable. The proposed MPS–DEM(BPM) method was developed to study the motion of the moored deformable structure under solidary wave, and the effect of the Young’s modulus on the stability of the deformable structure was discussed.

A comprehensive SPH model for three-dimensional multiphase interface simulation

Smoothed particle hydrodynamics is a typical Lagrangian meshless method, which has unique advantages in modelling multiphase phenomena with interface deformation and fragmentation. Current study proposes a comprehensive multiphase SPH model, which takes the advantages of some numerical techniques such as numerical interfacial force and damping technique. An improved boundary model is also introduced to deal with the solid walls. Additionally, the multiphase phenomena are investigated by solving an enhanced continuous surface force (CSF) model. In order to verify the proposed model, the droplet in shear flow is firstly considered and the results are consistent with the analytical solutions. Furthermore, the oscillations of square droplets are simulated under different particle resolutions, density and viscosity ratios. Finally, two and three dimensional bubble rising at high density ratios (up to 1000) are tested.

Dynamic analysis of large-scale amplitude liquid sloshingin the spacecraft

With the development of space technology, functionalities and life span of the spacecraft are increasing, leading to requirement of a greater proportion of fuels. Liquid sloshing in fuel tanks has more unavoidable effect on the spacecraft. During the attitude and orbital maneuvering of the spacecraft, large-scale amplitude liquid sloshing can be excited with liquid merging and splitting. Generally, theoretical, experimental and numerical methods can be used to predict the dynamics of liquid sloshing. However, most theoretical formulas, like the equivalent mechanical model methods, are only valid for liquid sloshing with small amplitude in simple geometrical tanks. Meanwhile, experimental results are difficult to obtain under a low gravity environment and the accurate measurement of nonlinear liquid sloshing is also a challenge. In most actual simulations, numerical simulation are required. In this paper, based on the smoothed particle hydrodynamics (SPH) method which is a Lagrangian mesh-less method, the linear and angular momentum theorem of the particles system are adopted to calculate the force and moment exerted by liquid against the spacecraft accurately, which avoids the accuracy loss of the pressure field. Moreover, aimed at the low computational efficiency of the common computational fluid dynamics (CFD) method, the impact of particle initial spacing on the accuracy of sloshing force and moment calculated is discussed and enough accuracy of global loads can be guaranteed with fewer particles, which greatly improves the computational efficiency. The time-efficiency of the SPH solver is adequate for embedding into a whole-spacecraft simulation system. Finally, in order to verify the validity of the method, results from SPH method are compared with those obtained by a traditional CFD solver for a 3D liquid sloshing case.

A Numerical Landslide-Tsunami Hazard Assessment Technique Applied on Hypothetical Scenarios at Es Vedrà, Offshore Ibiza

This study presents a numerical landslide-tsunami hazard assessment technique for applications in reservoirs, lakes, fjords, and the sea. This technique is illustrated with hypothetical scenarios at Es Vedrà, offshore Ibiza, although currently no evidence suggests that this island may become unstable. The two selected scenarios include two particularly vulnerable locations, namely: (i) Cala d’Hort on Ibiza (3 km away from Es Vedrà) and (ii) Marina de Formentera (23 km away from Es Vedrà). The violent wave generation process is modelled with the meshless Lagrangian method smoothed particle hydrodynamics. Further offshore, the simulations are continued with the less computational expensive code SWASH (Simulating WAves till SHore), which is based on the non-hydrostatic non-linear shallow water equations that are capable of considering bottom friction and frequency dispersion. The up to 133-m high tsunamis decay relatively fast with distance from Es Vedrà; the wave height 5 m offshore Cala d’Hort is 14.2 m, reaching a maximum run-up height of over 21.5 m, whilst the offshore wave height (2.7 m) and maximum inundation depth at Marina de Formentera (1.2 m) are significantly smaller. This study illustrates that landslide-tsunami hazard assessment can nowadays readily be conducted under consideration of site-specific details such as the bathymetry and topography, and intends to support future investigations of real landslide-tsunami cases.

Enhancement of stabilization of MPS to arbitrary geometries with a generic wall boundary condition

As a Lagrangian meshless method, moving particle semi-implicit (MPS) method has been proven useful in the analysis of the free-surface flow, especially accompanied by the large deformation and fragmentation of fluids. The improvement of pressure distribution in three dimensions is an important aspect to verify the effectiveness of MPS. The accurate representation of 3-D geometries especially complex geometries is the premise of obtaining convincing pressure distribution. However, most of MPS applications cannot accurately represent complex wall geometries, which highly affects the reliability of MPS. For this reason, the triangle meshes are used to accurately represent the complex wall geometries in this research. The polygon wall boundary condition (PW) is adopted to enforce the wall boundary condition to the triangle meshes. The pressure of the wall boundaries is derived from the Neumann boundary condition to improve the velocity distribution of fluid particles near the wall boundaries. A first-order gradient model is presented to improve the accuracy and stability of the PW. Our approach can enhance the numerical stabilization to arbitrary geometries. We simulate several 3-D examples such as the classic hydrostatic simulation and the complex 3-D geometries with sharp angles and curved surfaces to demonstrate the general applicability of our new model.