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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 *** 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 ***,in this work,an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin *** this algorithm,adaptive mesh refinement(AMR)is integrated with immersed boundary finite element method(IBFEM)with two-stage pressure-velocity *** 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 *** 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 *** is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid *** 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 *** algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream *** results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian(ALE)algorithm for elastic thin *** 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 computati

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

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High-order compact finite volume methods on unstructured grids with adaptive mesh refinement for solving inviscid and viscous flows

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Chinese Journal of Aeronautics 2018年第9期31卷 1829-1841页

作者： Jianhua PAN Qian WANG Yusi ZHANG Yuxin REN School of Aerospace Engineering Tsinghua University

In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The highorder variational reconstruction technique in terms of compact stencil is improved to reduce local condition numbers. To further improve the efficiency of computation, the adaptive mesh refinement technique is implemented in the framework of high-order finite volume methods. mesh refinement and coarsening criteria are chosen to be the indicators for certain flow structures. One important challenge of the adaptive mesh refinement technique on unstructured grids is the dynamic load balancing in parallel computation. To solve this problem, the open-source library p4 est based on the forest of octrees is adopted. Several two-and three-dimensional test cases are computed to verify the accuracy and robustness of the proposed numerical schemes.

关键词： adaptive mesh refinement Compact stencil High-order finite volume scheme Unstructured grids Variational reconstruction

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A Numerical Model for Simulating Two-Phase Flow with adaptive mesh refinement

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Computer Modeling in Engineering & Sciences 2021年第7期128卷 43-64页

作者： Yunxing Zhang Shan Ma Kangping Liao Wenyang Duan Harbin Engineering University Harbin150001China

In this study,a numerical model for simulating two-phase flow is *** Cartesian grid with adaptive mesh refinement(AMR)is adopted to reduce the computational *** explicit projection method is used for the time integration and the Finite Difference Method(FDM)is applied on a staggered grid for the discretization of spatial *** Volume of Fluid(VOF)method with Piecewise-Linear Interface Calculation(PLIC)is extended to the AMR grid to capture the gas-water interface accurately.A coarse-fine interface treatment method is developed to preserve the flux conservation at the *** two-dimensional(2D)and three-dimensional(3D)benchmark cases are carried out for the validation of the model.2D and 3D shear flow tests are conducted to validate the extension of the VOF method to the AMR grid.A 2D linear sloshing case is considered in which the model is proved to have 2nd-order accuracy in *** efficiency of applying the AMR grid is discussed with a nonlinear sloshing ***,2D solitary wave past stage and 2D/3D dam break are simulated to demonstrate that the model is able to simulate violent interface problems.

关键词： Two-phase flow adaptive mesh refinement VOF coarse-fine interface treatment

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An adaptive mesh refinement Strategy for Immersed Boundary/Interface Methods

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Communications in Computational Physics 2012年第7期12卷 515-527页

作者： Zhilin Li Peng Song Center for Research in Scientific Computation&Department of Mathematics North Carolina State UniversityRaleighNC 27695USA Nanjing Normal University China Operations Research Program North Carolina StateUniversityRaleighNC 27695USA

An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular *** interface is represented by the zero level set of a Lipschitz functionϕ(x,y).Our adaptive mesh refinement is done within a small tube of|ϕ(x,y)|δwith finer Cartesian *** discrete linear system of equations is solved by a multigrid *** AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically,therefore,reduce the size of the linear system of the *** examples presented show the efficiency of the grid refinement strategy.

关键词： adaptive mesh refinement immersed boundary method immersed interface method elliptic interface problem Cartesian grid method level set representation singular sources

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A three-dimensional robust volume-of-fluid solver based on the adaptive mesh refinement

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Theoretical & Applied Mechanics Letters 2021年第6期11卷 370-374页

作者： Xin Zhao Department of Mechanics Beijing Institute of TechnologyBeijing 100081China

The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement *** projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stokes *** octree structure mesh is employed to solve the flow velocities and the *** developed solver is applied to simulate the deformation of the cubic droplet driven by the surface tension without the effect of the *** numerical results well predict the shape evolution of the droplet.

关键词： adaptive mesh refinement Volume of fluid method Surface tension Interfacial flow Projection method

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Simulation of violent free surface flow by AMR method

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Journal of Hydrodynamics 2018年第3期30卷 384-389页

作者： Changhong Hu Cheng Liu Research Institute for Applied Mechanics Kyushu University Fukuoka Japa

A novel CFD approach based on adaptive mesh refinement（AMR） technique is being developed for numerical simulation of violent free surface flows. CIP method is applied to the flow solver and tangent of hyperbola for interface capturing with slope weighting（THINC/SW） scheme is implemented as the free surface capturing scheme. The PETSc library is adopted to solve the linear system. The linear solver is redesigned and modified to satisfy the requirement of the AMR mesh topology. In this paper, our CFD method is outlined and newly obtained results on numerical simulation of violent free surface flows are presented.

关键词： adaptive mesh refinement CIP method parallel computation violent free surface flow

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Simulation of shock-induced instability using an essentially conservative adaptive CE/SE method

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Chinese Physics B 2014年第2期23卷 29-33页

作者：付峥刘凯欣罗宁 LTCS and Department of Mechanics & Aerospace Engineering College of EngineeringPeking University Center for Applied Physics and Technology Peking University State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology

An essentially conservative adaptive space time conservation element and solution element （CE/SE） method is pro- posed for the effective simulation of shock-induced instability with low computational cost. Its implementation is based on redefined conservation elements （CEs） and solution elements （SEs）, optimized interpolations and a Courant number insensitive CE/SE scheme. This approach is used in two applications, the Woodward double Mach reflection and a two- component Richtmyer-meshkov instability experiment. This scheme reveals the essential features of the investigated cases, captures small unstable structures, and yields a solution that is consistent with the results from experiments or other high order methods.

关键词： CE/SE method shock-induced instability adaptive mesh refinement

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Simple and robust h-adaptive shock-capturing method for flux reconstruction framework

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Chinese Journal of Aeronautics 2023年第7期36卷 348-365页

作者： Lintao HUANG Zhenhua JIANG Shuai LOU Xin ZHANG Chao YAN School of Aeronautic Science and Engineering Beihang UniversityBeijing 100191China Research Office No.12 Beijing Institute of Astronautical Systems EngineeringBeijing 100076China

In this paper,a simple and robust shock-capturing method is developed for the Flux Reconstruction(FR)framework by combining the adaptive mesh refinement(AMR)technique with the positivity-preserving *** adaptive technique avoids the use of redundant meshes in smooth regions,while the positivity-preserving property makes the solver capable of providing numerical solutions with physical *** compatibility of these two significant features relies on a novel limiter designed for mesh *** ensures the positivity of solutions on all newly created ***,the proposed method is completely positivity-preserving and thus highly *** performs well in solving challenging problems on highly refined meshes and allows the transition of cells at different levels to be completed within a very short *** performance of the proposed method is examined in various numerical *** solving Euler equations,the technique of Local Artificial Diffusivity(LAD)is additionally coupled to damp *** importantly,when solving Navier-Stokes equations,the proposed method requires no auxiliaries and can provide satisfying numerical solutions *** implementation of the method becomes rather simple.

关键词： adaptive mesh refinement Flux reconstruction Positivity-preserving scheme Robustness Shock-capturing

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An adaptive Nonhydrostatic Atmospheric Dynamical Core Using a Multi-Moment Constrained Finite Volume Method

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Advances in Atmospheric Sciences 2022年第3期39卷 487-501页

作者： Pei HUANG Chungang CHEN Xingliang LI Xueshun SHEN Feng XIAO State Key Laboratory for Strength and Vibration of Mechanical Structures Xi’an Jiaotong UniversityXi’an 710049China Center of Numerical Weather Prediction China Meteorological AdministrationBeijing 100081China Department of Mechanical Engineering Tokyo Institute of TechnologyTokyo 226-8502Japan

An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several pointwise values within each computational cell as the predicted variables to build high-order schemes based on single-cell reconstruction. Two types of moments, such as the volume-integrated average(VIA) and point value(PV), are defined as constraint conditions to derive the updating formulations of the unknowns, and the constraint condition on VIA guarantees the rigorous conservation of the proposed model. In this study, the MCV scheme is implemented on a height-based, terrainfollowing grid with variable resolution to solve the nonhydrostatic governing equations of atmospheric dynamics. The AMR grid of Berger-Oliger consists of several groups of blocks with different resolutions, where the MCV model developed on a fixed structured mesh can be used directly. Numerical formulations are designed to implement the coarsefine interpolation and the flux correction for properly exchanging the solution information among different blocks. Widely used benchmark tests are carried out to evaluate the proposed model. The numerical experiments on uniform and AMR grids indicate that the adaptive model has promising potential for improving computational efficiency without losing accuracy.

关键词： adaptive mesh refinement multi-moment constrained finite-volume method nonhydrostatic model dynamical core high-order methods

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A NUMERICAL METHOD FOR THE SIMULATION OF FREE SURFACE FLOWS OF VISCOPLASTIC FLUID IN 3D

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Journal of Computational Mathematics 2011年第6期29卷 605-622页

作者： Kirill D. Nikitin Maxim A. Olshanskii Kirill M. Terekhov Yuri V. Vassilevski Institute of Numerical Mathematics Russian Academy of Sciences Moscow Russia Department of Mechanics and Mathematics Moscow State University Moscow Russia

In this paper we study a numerical method for the simulation of free surface flows of viscoplastic （Herschel-Bulkley） fluids. The approach is based on the level set method for capturing the free surface evolution and on locally refined and dynamically adapted octree cartesian staggered grids for the discretization of fluid and level set equations. A regu- larized model is applied to handle the non-differentiability of the constitutive relations. We consider an extension of the stable approximation of the Newtonian flow equations on staggered grid to approximate the viscoplastic model and level-set equations if the free boundary evolves and the mesh is dynamically refined or coarsened. The numerical method is first validated for a Newtonian case. In this case, the convergence of numerical solutions is observed towards experimental data when the mesh is refined. Further we compute several 3D viscoplastic Herschel-Bulkley fluid flows over incline planes for the dam-break problem. The qualitative comparison of numerical solutions is done versus experimental investigations. Another numerical example is given by computing the freely oscillating viscoplastic droplet, where the motion of fluid is driven by the surface tension forces. Altogether the considered techniques and algorithms （the level-set method, compact discretizations on dynamically adapted octree cartesian grids, regularization, and the surface tension forces approximation） result in efficient approach to modeling viscoplastic free-surface flows in possibly complex 3D geometries.

关键词： Free surface flows Viscoplastic fluid adaptive mesh refinement Oetree meshes.

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