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Fully resolved simulations of viscoelastic suspensions by an efficient immersed boundary-lattice Boltzmann method

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Particuology 2023年第4期75卷 26-49页

作者： Shenxu Qin Maoqiang Jiang Kuang Ma Jin Su Zhaohui Liu State Key Laboratory of Coal Combustion School of Energy and Power EngineeringHuazhong University of Science and TechnologyWuhan430074China School of Science Xian Polytechnic UniversityXi'an710048China

An efficient immersed boundary-lattice Boltzmann method(IB-LBM)is proposed for fully resolved simulations of suspended solid particles in viscoelastic flows.Stress LBM based on Giesekus and Oldroyd-B constitutive equation are used to model the viscoelastic stress tensor.A boundary thickening-based direct forcing IB method is adopted to solve the particle-fluid interactions with high accuracy for non-slip boundary conditions.A universal law is proposed to determine the diffusivity constant in a viscoelastic LBM model to balance the numerical accuracy and stability over a wide range of computa-tional parameters.An asynchronous calculation strategy is adopted to further improve the computing efficiency.The method was firstly applicated to the simulation of sedimentation of a single particle and a pair of particles after good validations in cases of the flow past a fixed cylinder and particle migration in a Couette flow against FEM and FVM methods.The determination of the asynchronous calculation strategy and the effect of viscoelastic stress distribution on the settling behaviors of one and two particles are revealed.Subsequently,504 particles settling in a closed cavity was simulated and the phenomenon that the viscoelastic stress stabilizing the Rayleigh-Taylor instabilities was observed.At last,simulations of a dense flow involving 11001 particles,the largest number of particles to date,were performed to investigate the instability behavior induced by elastic effect under hydrodynamic interactions in a viscoelastic fluid.The elasticity-induced ordering of the particle structures and fluid bubble structures in this dense flow is revealed for the first time.These simulations demonstrate the capability and prospects of the present method for aid in understanding the complex behaviors of viscoelastic particle suspensions.

关键词： Fullyresolved simulation Lattice Boltzmann method immersed boundary method Viscoelastic suspension Particle sedimentation

ADirect-Forcing immersed boundary Projection method for Thermal Fluid-Solid Interaction Problems

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Advances in Applied Mathematics and Mechanics 2023年第1期15卷 1-29页

作者： Cheng-Shu You Po-Wen Hsieh Suh-Yuh Yang Department of Applied Mathematics Feng Chia UniversityXitun DistrictTaichung City 40724Taiwan Department of Applied Mathematics National Chung Hsing UniversitySouth DistrictTaichung City 40227Taiwan Department of Mathematics National Central UniversityJhongli DistrictTaoyuan City 32001Taiwan

In this paper,we develop a direct-forcing immersed boundary projection method for simulating the dynamics in thermal fluid-solid interaction problems.The underlying idea of the method is that we treat the solid as made of fluid and introduce two virtual forcing terms.First,a virtual fluid force distributed only on the solid region is appended to the momentum equation to make the region behave like a real solid body and satisfy the prescribed velocity.Second,a virtual heat source located inside the solid region near the boundary is added to the energy transport equation to impose the thermal boundary condition on the solid boundary.We take the implicit second-order backward differentiation to discretize the time variable and employ the Choi-Moin projection scheme to split the coupled system.As for spatial discretization,second-order centered differences over a staggered Cartesian grid are used on the entire domain.The advantages of this method are its conceptual simplicity and ease of implementation.Numerical experiments are performed to demonstrate the high performance of the proposed method.Convergence tests show that the spatial convergence rates of all unknowns seem to be super-linear in the 1-norm and 2-norm while less than linear in the maximum norm.

关键词： Fluid-solid interaction heat transfer direct-forcing method immersed boundary method projection scheme

Lattice Boltzmann Simulations of Two Linear Microswimmers Using the immersed boundary method

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Communications in Computational Physics 2023年第1期33卷 310-329页

作者： D.Geyer S.Ziegler A.Sukhov M.Hubert A.-S.Smith O.Aouane P.Malgaretti J.Harting Helmholtz Institute Erlangen-Nurnberg for Renewable Energy(IEK-11) Forschungszentrum JulichCauerstrase 191058 ErlangenGermany PULS Group Department of PhysicsInterdisciplinary Center for Nanostructured FilmsFriedrich-Alexander-Universitat Erlangen-NurnbergCauerstrase 391058 ErlangenGermany Department of Chemical and Biological Engineering and Department of Physics Friedrich-Alexander-Universitat Erlangen-N¨urnbergFurther Strase 24890429 NurnbergGermany

The performance of a single or the collection of microswimmers strongly depends on the hydrodynamic coupling among their constituents and themselves.We present a numerical study for a single and a pair of microswimmers based on lattice Boltzmann method(LBM)simulations.Our numerical algorithm consists of two separable parts.Lagrange polynomials provide a discretization of the microswimmers and the lattice Boltzmann method captures the dynamics of the surrounding fluid.The two components couple via an immersed boundary method.We present data for a single swimmer system and our data also show the onset of collective effects and,in particular,an overall velocity increment of clusters of swimmers.

关键词： immersed boundary method lattice Boltzmann method finite element method microswimmer collective motion

Effective Force Stabilising Technique for the immersed boundary method

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Communications in Computational Physics 2023年第1期33卷 349-366页

作者： Arnab Ghosh Alessandro Gabbana Herman Wijshoff Federico Toschi Department of Applied Physics and Science Education Eindhoven University of TechnologyPO Box 5135600 MB EindhovenThe Netherlands Department of Mechanical Engineering Eindhoven University of TechnologyP.O.Box 5135600 MB EindhovenThe Netherlands Canon Production Printing Netherlands B.V. P.O.Box 1015900 MA VenloThe Netherlands

The immersed boundary method has emerged as an efficient approach for the simulation of finite-sized solid particles in complex fluid flows.However,one of the well known shortcomings of the method is the limited support for the simulation of light particles,i.***.particles with a density lower than that of the surrounding fluid,both in terms of accuracy and numerical stability.Although a broad literature exists,with several authors reporting different approaches for improving the stability of the method,most of these attempts introduce extra complexities and are very costly from a computational point of view.In this work,we introduce an effective force stabilizing technique,allowing to extend the stability range of the method by filtering spurious oscillations arising when dealing with light-particles,pushing down the particle-to-fluid density ratio as low as 0.04.We thoroughly validate the method comparing with both experimental and numerical data available in literature.

关键词： immersed boundary method lattice Boltzmann method light particle force stabilization added mass effect

Numerical Simulation of Low Reynolds Number Fluid-Structure Interaction with immersed boundary method

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Chinese Journal of Aeronautics 2009年第5期22卷 480-485页

作者： Ming Pingjian Zhang Wenping School of Power and Energy Engineering Harbin Engineering University Harbin 150001 China

This article introduces a numerical scheme on the basis of semi-implicit method for pressure-linked equations （SIMPLE） algorithm to simulate incompressible unsteady flows with fluid-structure interaction. The Navier-Stokes equation is discretized spatially with collocated finite volume method and Eulerian implicit method in time domain. The hybrid method that combines immersed boundary method （IBM） and volume of fluid （VOF） method is used to deal with rigid body motion in fluid domain. The details of movement of immersed boundary （IB） and calculation of VOF are also described. This method can be easily applied to any existing finite-volume-based computational fluid dynamics （CFD） solver without complex operation, with which fluid flow interaction of arbitrarily complex geometry can be realized on a fixed mesh. The method is verified by low Reynolds number flows passing both stationary and oscillating cylinders. The drag and lift coefficients acquired by the study well accord with other published results, which indicate the reasonability of the proposed method.

关键词： fluid-structure interaction immersed boundary method volume of fluid vortex shedding incompressible flow

Adaptive mesh refinement immersed boundary method for simulations of laminar flows past a moving thin elastic structure

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Journal of Hydrodynamics 2020年第1期32卷 148-160页

作者： Mohammed Suleman Aldlemy Mohammad Rasidi Rasani AKAriffin TMYSTuan Ya Centre for Integrated Design for Advanced Mechanical Systems Faculty of Engineering and Built EnvironmentUniversiti Kebangsaan Malaysia43600 BangiSelangorMalaysia Department of Mechanical Engineering College of Mechanical Engineering TechnologyBenghaziLibya Department of Mechanical Engineering Faculty of EngineeringUniversiti Teknologi Petronas31750 TronohPerakMalaysia

One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions,especially for flows past a stationary thin elastic structure where large deformations occur.High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body.Hence,in this work,an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses.In this algorithm,adaptive mesh refinement(AMR)is integrated with immersed boundary finite element method(IBFEM)with two-stage pressure-velocity corrections.Despite successive interpolation of the flow field by IBM,the governing equations were solved using a fixed structured mesh,which significantly reduces the computational time associated with mesh reconstruction.The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface.AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface.The AMR-IBFEM algorithm is first verified by comparing the drag coefficient,lift coefficient,and Strouhal number for a benchmark case(laminar flow past a circular cylinder at Re=100)and the results showed good agreement with those of other researchers.The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction.The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian(ALE)algorithm for elastic thin boundaries.It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy(error of-0.02%)with only-1%of the computational time for simulations with full mesh refinem

关键词： immersed boundary method finite element method adaptive mesh refinement two-stage velocity-pressure correction thin deformable structures

Combined immersed boundary method and multiple-relaxation-time lattice Boltzmann flux solver for numerical simulations of incompressible flows

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Applied Mathematics and Mechanics(English Edition) 2017年第12期38卷 1679-1696页

作者： Xiaodi WU Fu CHEN Huaping LIU Department of Energy Science and Engineering Harbin Institute of TechnologyHarbin 150001China

A method combining the immersed boundary technique and a multi- relaxation-time （MRT） lattice Boltzmann flux solver （LBFS） is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations （LBEs）. The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.

关键词： immersed boundary method lattice Boltzmann equation （LBE） multiple relaxation time incompressible flow

Numerical Investigation on Vortex-Induced Rotations of A Triangular Cylinder Using An immersed boundary method

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China Ocean Engineering 2019年第6期33卷 723-733页

作者： WANG Hua-kun YAN Yu-hao CHEN Can-ming JI Chun-ning ZHAI Qiu Jiangsu Key Laboratory of Coast Ocean Resources Development and Environment Security College of HarbourCoastal and Offshore EngineeringHohai UniversityNanjing 210098China State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin UniversityTianjin 300072China Key Laboratory of Water Science and Water Engineering of Ministry of Water Resources Nanjing Hydraulic Research InstituteNanjing 210029China

A numerical study of vortex-induced rotations(VIRs) of an equivalent triangular cylinder, which is free to rotate in the azimuthal direction in a uniform flow, is presented. Based on an immersed boundary method, the numerical model is established, and is verified through the benchmark problem of flow past a freely rotating rectangular body.The computation is performed for a fixed reduced mass of m~*=2.0 and the structural stiffness and damping ratio are set to zero. The effects of Reynolds number(Re=25-180) on the characteristics of VIR are studied. It is found that the dynamic response of the triangular cylinder exhibits four distinct modes with increasing Re: a rest position,periodic rotational oscillation, random rotation and autorotation. For the rotational oscillation mode, the cylinder undergoes a periodic vibration around an equilibrium position with one side facing the incoming flow. Since the rotation effect, the outset of vortex shedding from cylinder shifts to a much lower Reynolds number. Further increase in Re leads to 2 P and P+S vortex shedding modes besides the typical 2 S pattern. Our simulation results also elucidate that the free rotation significantly changes the drag and lift forces. Inspired by these facts, the effect of free rotation on flow-induced vibration of a triangular cylinder in the in-line and transverse directions is investigated. The results show that when the translational vibration is coupled with rotation, the triangular cylinder presents a galloping response instead of vortex-induced vibration(VIV).

关键词： vortex-induced rotation triangular cylinder dynamic response vortex shedding mode immersed boundary method

New immersed boundary method on the Adaptive Cartesian Grid Applied to the Local Discontinuous Galerkin method

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Chinese Journal of Mechanical Engineering 2018年第2期31卷 176-185页

作者： Xu-Jiu Zhang Yong-Sheng Zhu Ke Yan You-Yun Zhang Key Laboratory of Education Ministry for Modern Design&Rotor-Bearing System Xi'an Jiaotong University

Currently, many studies on the local discontinuous Galerkin method focus on the Cartesian grid with low computational e ciency and poor adaptability to complex shapes. A new immersed boundary method is presented, and this method employs the adaptive Cartesian grid to improve the adaptability to complex shapes and the immersed boundary to increase computational e ciency. The new immersed boundary method employs different boundary cells(the physical cell and ghost cell) to impose the boundary condition and the reconstruction algorithm of the ghost cell is the key for this method. The classical model elliptic equation is used to test the method. This method is tested and analyzed from the viewpoints of boundary cell type, error distribution and accuracy. The numerical result shows that the presented method has low error and a good rate of the convergence and works well in complex geometries. The method has good prospect for practical application research of the numerical calculation research.

关键词： immersed boundary method Adaptive Cartesian grid Local discontinuous Galerkin method Reconstruction Heat transfer equation