Simulation Of Free Surface Flows Research Articles

Simulation of viscoelastic free-surface flows with the Particle Finite Element Method

AbstractViscoelastic fluids are central in numerous applications from polymer manufacturing to the pharmaceutical industry and biological research. However, since analytical solutions are generally not available or too complex, it is common practice to study free-surface viscoelastic flows through numerical simulation techniques. This work proposes the use of the so-called particle finite element method (PFEM), a Lagrangian approach combining standard FEM techniques with a remeshing strategy. The PFEM is able to efficiently handle mesh distortion and to accurately track the free-surface evolution. Therefore, it is exploited in this work to deal with large displacements problems in the context of nonlinear viscoelasticity. An implementation of the Oldroyd-B constitutive model in the PFEM framework is here presented including details regarding how to deal with the transfer of the internal variables during remeshing events. Additionally, an innovative approach to impose unilateral Dirichlet boundary conditions ensuring optimal mass conservation is presented. The implementation is verified with two free-surface highly viscous benchmark flows: the impacting drop and the jet buckling problems. The results show perfect agreement with those obtained with other numerical techniques. The proposed framework opens the way for using PFEM in various applications, ranging from polymer extrusion to more sophisticated scenarios involving viscoelastic and viscoelasto-plastic constitutive laws.

A semi-Lagrangian Splitting framework for the simulation of non-hydrostatic free-surface flows

Incorporation of the free-surface dynamics plays an important role in the numerical modelling of non-hydrostatic flows. In the present work a novel semi-Lagrangian splitting (SLS) scheme for the free-surface Euler system is proposed.Using the operator splitting technique, the three main components emerge: the multilayer Shallow Water Equations (mSWE) (enforcing the free-surface kinematics), the Vertical Remeshing Operator (VRO) (that blends the Eulerian and Lagrangian techniques) and the Pressure Correction Operator (PCO) (that is a classic elliptic equation used in projection-type pressure coupling schemes). The first two are solved by two separate Finite Volume schemes, while the latter is resolved in a Finite Difference manner.In order to assess the SLS’s performance, numerical simulations of periodic waves and solitons propagating over variable bathymetry are performed. The last case concerns the propagation of waves on top of a shear current, showcasing the use of the SLS on rotational flows. The results are compared with experiments and analytic relations and the method is proven to be robust and efficient.

Volume conservation issue within SPH models for long-time simulations of violent free-surface flows

Smoothed Particle Hydrodynamics (SPH) simulations of violent sloshing flows characterized by a strong fragmentation of free-surface can be affected by volume conservation errors. These errors can accumulate in time and preclude the possibility of using such models for long-time simulations. In the present work, different techniques to measure directly the particles’ volumes by their positions are displayed. Thanks to these algorithms, we discussed how volume errors develop when introducing stabilization terms in the standard SPH schemes. Further, we show that the control of these errors can be achieved through two different (non-alternative) stabilization terms: (i) enforcement of dynamic boundary conditions on thin fluid jets and drops; and (ii) a dynamical switch that can impose or not the time variation of the particle masses.To demonstrate the effectiveness of the numerical techniques, four different violent sloshing flows are investigated and compared with experimental data.

Improved MPS models for simulating free surface flows

Two improved Laplacian models are introduced in this study for more accurate simulation of free surface flows in the context of the moving particle semi-implicit (MPS) method, a well-known mesh-less approach. The Euler equations are the governing equations of these flows without considering viscous forces which are solved in the Lagrangian frame by the MPS and two-step projection methods for spatial and temporal discretization, respectively. Considering the similarity between the MPS and SPH (smoothed particle hydrodynamics) methods, one of the introduced Laplacian models is formulated by a corrective matrix firstly proposed in an improved SPH method [28]. The other modified Laplacian model is also derived from the divergence of a newly developed MPS gradient model proposed for solving elasticity problems [33]. The higher accuracy of these methods compared to the classic SPH, MPS and even three modified SPH and MPS Laplacian models [7, 34, 44] is verified by solving 2D Poisson equations. Moreover, the excellent performance of the Laplacian models and the improved gradient model in obtaining smooth pressure field is validated by solving three benchmark free surface flows. Furthermore, the problem of wave damping in the original MPS computations can be resolved by using the applied models.

An efficient correction method in Riemann SPH for the simulation of general free surface flows

In this paper, a new efficient weighted correction method for weakly-compressible smoothed particle hydrodynamics is proposed and successfully implemented in the simulation of violent free-surface flow exhibiting breaking and impact events for the first time. It is well known that the original kernel gradient correction (KGC) encounters numerical instability resulting from matrix inversion. The present method remedies this issue by introducing a weighted average of the KGC matrix and the identity matrix, other than directly applying the KGC matrix, to achieve numerical stability meanwhile decrease numerical dissipation. To ensure momentum conservation, the correction is implemented in a particle-average pattern by rewriting the pressure term of the Riemann solution. Furthermore, the proposed weighted KGC scheme is incorporated into the dual-criteria time-stepping framework developed by Zhang et al. (2020) to achieve optimized computational efficiency. A set of numerical examples in both two- and three-dimensions are investigated to demonstrate that the present method can significantly reduce numerical dissipation meanwhile exhibit a smooth pressure field for general free-surface flows.

A 2D Hydraulic Simulation Model Including Dynamic Piping and Overtopping Dambreach

Numerical simulation of unsteady free surface flows using depth averaged equations that consider the presence of initial discontinuities has been often reported for situations dealing with dam break flow. The usual approach is to assume a sudden removal of the gate at the dam location. Additionally, in order to prevent any kind of dam risk in earthen dams, it is very interesting to include the possibility of a progressive dam breach leading to dam overtopping or dam piping so that predictive hydraulic models benefit the global analysis of the water flow. On the other hand, when considering a realistic large domain with complex topography, a fine spatial discretization is mandatory. Hence, the number of grid cells is usually very large and, therefore, it is necessary to use parallelization techniques for the calculation, with the use of Graphic Processing Units (GPU) being one of the most efficient, due to the leveraging of thousands of processors within a single device. The aim of the present work is to describe an efficient GPU-based 2D shallow water flow solver (RiverFlow2D-GPU) supplied with the formulation of internal boundary conditions to represent dynamic dam failure processes. The results obtained indicate that it is able to develop a transient flow analysis taking into account several scenarios. The efficiency of the model is proven in two complex domains, leading to >76× faster simulations compared with the traditional CPU computation.

Numerical Simulation of Three-Dimensional Free Surface Flows Using the K-BKZ-PSM Integral Constitutive Equation.

This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically the K-BKZ-PSM (Kaye-Bernstein, Kearsley, Zapas-Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach along with the deformation fields method to solve the integral constitutive equation and the marker particle method (known as marker-and-cell) to accurately capture the evolution of the fluid's free surface. The newly developed numerical method has proven its effectiveness in handling complex fluid flow scenarios, including confined flows and extrudate swell simulations of Boger fluids. Furthermore, a new semi-analytical solution for velocity and stress fields is derived, considering fully developed flows of a K-BKZ-PSM fluid in a pipe.

Large-eddy simulation of free-surface turbulent flow in a non-prismatic channel

Abstract Hydraulic engineering applications require a good knowledge of turbulent behaviour in non-prismatic channels. This paper aims to predict turbulent behaviour using large-eddy simulation (LES). The model channel has a warped transition. We perform two-phase LES of free-surface flow and validate the results using experimental data and benchmark solution. We discuss rigorous strategies for model set-up, parameter selection and parametric value assignment, including parameters in spectrum synthesiser (SS) and vortex method (VM) for inlet turbulence. The predicted flow displays complex structures due to eddy motions translated from upstream and locally generated by asymmetrical separation in the transition. The history of the flow dynamics may affect the flow development. The predicted velocity, energy spectrum, root-mean-square error, hit-rate and factor-of-two compare well with measurements and benchmark solution. Mapping mean-velocity distribution from experimental data, combined with SS, gives satisfactory inlet condition; alternatively, a 1/7th power-law for the mean-velocity, combined with VM, is acceptable. This paper uses the Okubo–Weiss parameter to delineate instantaneous coherent structures. The LES methods are reliable, efficient and cost-effective. As compared to the simulation of prismatic channels, the flow dynamics in non-prismatic channels exhibit flow separation and turbulence interactions, which increase the flow-complexity, while offering results with crucial practical applications.

Development of Advective Dynamic Stabilization scheme for ISPH simulations of free-surface fluid flows

This study presents an enhanced version of a numerical stabilizing scheme, namely, the Dynamic Stabilization scheme (DS) by Tsuruta et al. (2013), referred to as the Advective DS scheme (ADS) for further enhancement of the numerical stability and accuracy in ISPH simulations of free-surface fluid flows. To ensure general stability of calculations, particle methods may benefit from particle regularization schemes including artificial repulsive force schemes to keep particles equally distanced. DS explicitly provides a stabilizing force based on the overlapped state of a target particle and its neighboring particle, resulting in a momentum-conservative repulsive force and stable simulations. However, DS may also result in numerical noises and numerical dissipation. Such numerical noises stem from the excess stabilizing forces because of consideration of the particle positions only. The approaching velocities of particles, corresponding to the divergence-free condition, are ignored. To precisely consider the dynamic states of particles in derivation of stabilizing forces, in ADS, the approaching velocities are additionally considered and the stabilizing forces are derived in a variationally consistent form based on time rate of particle overlapping state, to precisely recover the exact deteriorated particle regularity state. The enhanced performance of the proposed ADS scheme is shown through some benchmark tests including a Taylor-Green vortex, a dam break as a violent free-surface flow, an oscillating drop and a rotating square patch. The enhanced performance of ADS in terms of reproduced pressure and velocity fields, energy conservation and convergence are well demonstrated.

Coupling SPH with a mesh-based Eulerian approach for simulation of incompressible free-surface flows

This paper presents a coupling algorithm for the simulation of incompressible free-surface flows over the near and far fields by solving the Navier-Stokes equations. The coupling combines the Smoothed Particle Hydrodynamics (SPH) with the Finite Difference (FD) method implemented on structured Eulerian grids. Based on the domain decomposition, the SPH is applied to the near-field core region for modeling with high-fidelity the severe free-surface deformation and even fragmentation of flow, while the FD method is used to resolve the remaining far-field region with relatively high efficiency. The primary purpose of the hybrid approach is to mitigate the computational load of SPH applications through combination with a mesh-based Eulerian method while maintaining high accuracy for both the near-field and far-field simulations. Two-way coupling between the FD and SPH models is achieved by the overlapping region between the computational subdomains, in which the Eulerian solutions and the Lagrangian solutions are coupled with each other through interpolation in the overlapping region for the fluid transfer and free-surface movement between the near-field and far-field regions. The proposed algorithm is validated by several test cases, showing favorable accuracy, convergence, and applicability in the simulation of wave interactions with complex bathymetry and structures.

Large-eddy simulation of free-surface turbulent channel flow over square bars

The results of large-eddy simulations of free-surface turbulent channel flow over spanwise-aligned square bars are used to investigate the effects of bed roughness and water surface deformations on the root-mean-squared velocity fluctuations, dispersive shear stress, double-averaged Reynolds shear stress, wake kinetic energy and double-averaged turbulent kinetic energy. Two bar spacings, corresponding to transitional and k-type roughness, at similar Reynolds and Froude numbers are considered. The main peak of all statistical quantities occurs at the bar crest height. The effects of a standing wave at the water surface in flow over k-type roughness is marked by a local peak under the water surface for all statistical quantities considered here except wall-normal and spanwise velocity fluctuations. Quadrant analysis shows that sweeps and ejections are the strongest events contributing to both dispersive and double-averaged Reynolds shear stress but their contributions are different for the two bar spacings. Examining the budgets of dispersive and double-averaged Reynolds shear stress reveals that the dominant terms of these stresses are pressure–strain correlation and pressure transport and the contribution of wake production is similar for both of these stresses but with opposite sign. In addition to the main role of the bars in consuming or producing wake kinetic energy through production and transport and convection, the standing wave at the water surface in flow over k-type roughness induces large convection in the bulk flow too. The dominant terms in the double-averaged turbulent kinetic energy budget are similarly production, transport and convection. Large shear production renders large temporal fluctuations than spatial fluctuations of flow variables. The interaction of bars, bed and water surface is seen in the convection term in flow over k-type roughness.

A numerical investigation on three-dimensional swirling instability in viscous sloshing flows

Resonant three-dimensional nonlinear sloshing in a square-base basin is analysed numerically to investigate swirling instability. The aim of this research is based on understanding how viscosity influences this instability. Four different fluids at increasing Reynolds number were considered in a tank forced to oscillate in a horizontal motion. The present study investigates the tight relation between the energy dissipation and this instability, showing that water tends to dissipate more energy during its rotating motion than the other three liquids characterised by higher viscosity. This aspect is strictly linked to the occurrence of free-surface fragmentation and liquid impacts. The numerical solutions are provided using an enhanced version of the Smoothed Particle Hydrodynamics (SPH) model called δ-LES-SPH model which proved to be suitable for the simulation of violent free-surface flows.

Numerical simulation of temperature-driven free surface flows, with application to laser melting and polishing

We present a multi-physics model for the approximation of the coupled system formed by the heat equation and the Navier-Stokes equations with solidification and free surfaces. The computational domain is the union of two overlapping regions: a larger domain to account for thermal effects, and a smaller region to account for the fluid flow. Temperature-dependent surface effects are accounted for via surface tension and Marangoni forces. The volume-of-fluid approach is used to track the free surfaces between the metal (liquid or solidified) and the ambient air. The numerical method incorporates all the physical phenomena within an operator splitting strategy. The discretization relies on a two-grid approach that uses an unstructured finite element mesh for diffusion phenomena and a structured Cartesian grid for advection phenomena. The model is validated through numerical experiments, the main application being laser melting and polishing.

Free-surface flow simulations with floating objects using lattice Boltzmann method

ABSTRACTIn tsunami inundations or slope disasters of heavy rain, a lot of floating debris or driftwood logs are included in the flows. The damage to structures from solid body impacts is more severe than the damage from the water pressure. In order to study free-surface flows that include floating debris, developing a high-accurate simulation code of free-surface flows with high performance for large-scale computations is desired. We propose the single-phase free-surface flow model based on the cumulant lattice Boltzmann method coupled with a particle-based rigid body simulation. The discrete element method calculates the contact interaction between solids. An octree-based AMR (Adaptive Mesh Refinement) method is introduced to improve computational accuracy and time-to-solution. High-resolution grids are assigned near the free surfaces and solid boundaries. We conducted two kinds of tsunami flow experiments in the 15 and 70 m water tanks at Hachinohe Institute of Technology and Kobe University to validate the accuracy of the proposed model. The simulation results have shown good agreement with the experiments for the drifting speed, the number of trapped wood pieces, and the stacked angles.

Smoothed Particle Hydrodynamics-Based Study of 3D Confined Microflows

In this study, we investigate the performance of the smoothed particle hydrodynamics (SPH) method regarding the computation of confined flows in microchannels. Modeling and numerical simulation with SPH involve the representation of flowing matter as distinct mass points, leading to particle discretization of the Navier–Stokes equations. The computational methodology exhibits similarities with other well-established particle methods, such as molecular dynamics (MD), dissipative particle dynamics (DPD), and smooth dissipative particle dynamics (SDPD). SPH has been extensively tested in the simulation of free-surface flows. However, studies on the performance of the method in internal flow computations are limited. In this work, we study flows in microchannels of variable cross-sections with a weakly compressible SPH formulation. After preliminary studies of flows in straight constant cross-section ducts, we focus on channels with sudden expansion and/or contraction. Flow models based on periodic or various inlet/outlet boundary conditions and their implementations are discussed in the context of 2D and 3D simulations. Numerical experiments are conducted to evaluate the accuracy of the method in terms of flowrate, velocity profiles, and wall shear stress. The relation between f and Re for constant cross-section channels is computed with excellent accuracy. SPH captured the flow characteristics and achieved very good accuracy. Compressibility effects due to the weakly compressible smoothed particle hydrodynamics (WCSPH) formulation are negligible for the flows considered. Several typical difficulties and pitfalls in the application of the SPH method in closed conduits are highlighted as well as some of the immediate needs for the method’s improvement.

A nodal position finite element model for fluid-structure interaction analysis of floating bodies with mooring

A numerical model based on the Nodal Position Finite Element Method (NPFEM) is proposed in this work for fluid-structure interaction (FSI) analysis of moored bodies subject to multiphase free surface flows. The semi-implicit CBS (Characteristic-Based Split) method is utilized here for discretization of the flow fundamental equations in the context of the Finite Element Method, where linear tetrahedral elements are adopted. Turbulence is analyzed using Large Eddy Simulation (LES) with the dynamic sub-grid scale model and the Level Set method is utilized for simulation of multiphase free surface flows. The structural system is modeled using a three-dimensional rigid body approach for the floating object, while the mooring is discretized using a geometrically nonlinear cable formulation based on the NPFEM. A partitioned coupling scheme is adopted for fluid-structure interaction analysis taking into account the fluid-structure and cable-structure couplings, where the flow equations are kinematically described employing an Arbitrary Lagrangean-Eulerian (ALE) formulation with a numerical scheme for mesh motion. The algorithms constituting the numerical model are verified first considering classical applications on fluid dynamics and FSI, in addition to applications involving the dynamic analysis of cables. Finally, problems involving floating bodies with and without mooring are simulated to demonstrate the applicability and accuracy of the proposed numerical model.

An Improved Neural Particle Method for Complex Free Surface Flow Simulation Using Physics-Informed Neural Networks

The research on free surface flow is of great interest in fluid mechanics, with the primary task being the tracking and description of the motion of free surfaces. The development of numerical simulation techniques has led to the application of new methods in the study of free surface flow problems. One such method is the Neural Particle Method (NPM), a meshless approach for solving incompressible free surface flow. This method is built on a Physics-Informed Neural Network (PINN), which allows for training and solving based solely on initial and boundary conditions. Although the NPM is effective in dealing with free surface flow problems, it faces challenges in simulating more complex scenarios due to the lack of additional surface recognition algorithms. In this paper, we propose an improved Neural Particle Method (INPM) to better simulate complex free surface flow. Our approach involves incorporating alpha-shape technology to track and recognize the fluid boundary, with boundary conditions updated constantly during operation. We demonstrate the effectiveness of our proposed method through three numerical examples with different boundary conditions. The result shows that: (1) the addition of a surface recognition module allows for the accurate tracking and recognition of the fluid boundary, enabling more precise imposition of boundary conditions in complex situations; (2) INPM can accurately identify the surface and calculate even when particles are unevenly distributed. Compared with traditional meshless methods, INPM offers a better solution for dealing with complex free surface flow problems that involve random particle distribution. Our proposed method can improve the accuracy and stability of numerical simulations for free surface flow problems.

Smoothed particle hydrodynamics method for free surface flow based on MPI parallel computing

In the field of computational fluid dynamics (CFD), smoothed particle hydrodynamics (SPH) is very suitable for simulating problems with large deformation, free surface flow and other types of flow scenarios. However, traditional smoothed particle hydrodynamics methods suffer from the problem of high computation complexity, which constrains their application in scenarios with accuracy requirements. DualSPHysics is an excellent smoothed particle hydrodynamics software proposed in academia. Based on this tool, this paper presents a largescale parallel smoothed particle hydrodynamics framework: parallelDualSPHysics, which can solve the simulation of large-scale free surface flow. First, an efficient domain decomposition algorithm is proposed. And the data structure of DualSPHysics in a parallel framework is reshaped. Secondly, we proposed a strategy of overlapping computation and communication to the parallel particle interaction and particle update module, which greatly improves the parallel efficiency of the smoothed particle hydrodynamics method. Finally, we also added the pre-processing and post-processing modules to enable parallelDualSPHysics to run in modern high performance computers. In addition, a thorough evaluation shows that the 3 to 120 million particles tested can still maintain more than 90% computing efficiency, which demonstrates that the parallel strategy can achieve superior parallel efficiency.

Efficient lattice Boltzmann simulation of free-surface granular flows with μ(I)-rheology

This paper presents a lattice Boltzmann framework for accurate and efficient simulation of free-surface granular flows. The granular assembly is treated as a viscoplastic fluid, whose apparent viscosity varies locally with the shear rate and pressure according to a regularized μ(I)-rheology. A single-phase free-surface model is employed to track the evolution of the particle-air interface. The lattice Boltzmann implementation is first validated by simulating a steady-state granular flow on a rough inclined plane and a good agreement with the analytical solution is achieved. The validated model is then applied to simulate a transient granular column collapse problem. Compared to a companion discrete element simulation, the lattice Boltzmann model with the μ(I)-rheology is able to capture the overall dynamic behaviors of granular column collapse. However, a different behavior is observed when a similar Bingham viscoplastic model with a fixed yield stress is applied, highlighting the pressure dependent nature of granular flows. The proposed lattice Boltzmann formulation is highly efficient compared to the conventional computational fluid dynamics, and has the potential to conduct three-dimensional continuum simulation of large-scale geophysical flows with microscopic granular physics.

Enhanced resolution of the continuity equation in explicit weakly compressible SPH simulations of incompressible free‐surface fluid flows

This paper is dedicated to improved resolution of the continuity equation and thus more precise satisfaction of incompressibility conditions in explicit weakly compressible SPH (Smoothed Particle Hydrodynamics) simulations of incompressible free-surface fluid flows. In the explicit weakly compressible SPH methods, including δ-SPH with a widely adopted particle shifting scheme (or the so-called δ-plus-SPH), two incompressibility conditions corresponding to the invariant density condition and divergence-free velocity condition are not well resolved. To achieve enhanced resolution of the continuity equation as well as satisfaction of both incompressibility conditions, this paper presents two novel schemes, namely, Velocity-divergence Error Mitigating (VEM) and Volume Conservation Shifting (VCS) schemes. The VEM scheme corresponds to an additional term in the momentum equation that mitigates the velocity divergence error at every computational time step. The VEM term is derived by linking the instantaneous velocity divergence error to the undesired density time variations and accordingly to an error mitigating pressure pVEM obtained through an Equation of State (EOS). The corresponding pressure gradient term or acceleration leads to attenuation of numerical noise in the velocity divergence field. The VCS acts as a distinct particle shifting scheme to enforce local and thus global volume conservation. This distinct shifting is obtained through calculation of the gradient of a corresponding pressure, namely, pVCS, obtained through efficient solution of a Poisson Pressure Equation (PPE) derived from the concept of projection-based particle methods. By adopting both proposed schemes, the explicit SPH method is shown to provide enhanced satisfaction of both incompressibility conditions, i.e., divergence-free velocity and invariant density conditions, in simulation of incompressible free-surface fluid flows.