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摘 要：結合格子Boltzmann方法和隐式扩散浸入边界方法，实现流体-固体耦合运动的求解。预测的速度和压力场可以通过格子Boltzmann方法快速求解，而流固耦合界面力由满足流固界面的无滑移边界条件隐式获得，固体边界节点与流场节点间的信息交换通过高阶导数光滑函数实现。该方法的主要优点是易于实施，效率高，并且减少了非物理振荡和非物理流线穿透。为了确定该数值方法的有效性，通过圆柱绕流和翼型绕流基准算例证实了该方法的可靠性;模拟不同雷诺数下被动旋转转子与流体的相互作用，进一步验证了该方法的鲁棒性。
关键词：格子Boltzmann方法; 隐式扩散浸入边界法; 高阶光滑函数;流体固体相互作用
中图分类号：O35
文献标志码：A
参考文献：
[1]PESKIN C S. Flow patterns around heart valves： a numerical method[J]. Journal of Computational Physics， 1972， 10（2）： 252-271.
[2]CENICEROS H D， FISHER J E， ROMA A M. Efficient solutions to robust， semi-implicit discretizations of the immersed boundary method[J]. Journal of Computational Physics， 2009， 228 （19）： 7137-7158.
[3]FADLUN E A， VERZICCO R， ORLANDI P， et al. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations[J]. Journal of Computational Physics， 2000， 161 （1）： 35-60.
[4]UHLMANN M. An immersed boundary method with direct forcing for the simulation of particulate flows[J]. Journal of Computational Physics， 2005， 209 （2）： 448-476.
[5]KEMPE T， FROHLICH J. An improved immersed boundary method with direct forcing for the simulation of particle laden flows[J]. Journal of Computational Physics， 2012， 231 （9）： 3663-3684.
[6]WANG S， ZHANG X. An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows[J]. Journal of Computational Physics， 2011， 230 （9） ： 3479-3499.
[7]LIU Q， VASILYEV O V. A Brinkman penalization method for compressible flows in complex geometries[J]. Journal of Computational Physics， 2007， 227 （2） ： 946-966.
[8]CHENY Y， BOTELLA O. The LS-STAG method： a new immersed boundary/level-set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties [J]. Journal of Computational Physics， 2010， 229 （4） ： 1043-1076.
[9]SCHNEIDERS L， GNTHER C， MEINKE M， et al. An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows[J]. Journal of Computational Physics， 2016， 311： 62-86.
[10]SHU C， LIU N， CHEW Y T. A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder[J]. Journal of Computational Physics， 2007， 226： 1607-1622.
[11]WU J， SHU C. Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications[J]. Journal of Computational Physics， 2009， 228： 1963-1979. [12]WU J， QIU Y L， SHU C， et al. An adaptive immersed boundary-lattice Boltzmann method for simulating a flapping foil in ground effect[J]. Computer and Fluids， 2015， 106： 171-184.
[13]TIAN F B， LUO H， ZHU L， et al. An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments[J]. Journal of Computational Physics， 2011， 230 （19）：7266-7283.
[14]ZHANG H， TAN Y， SHU S， et al. Numerical investigation on the role of discrete element method in combined LBM-IBM-DEM modeling[J]. Computer and Fluids， 2014， 94： 37-48.
[15]ZHANG H， YUAN H Z， YU A B，et al. Particulate immersed boundary method for complex fluid-particle interaction problems with heat transfer[J]. Computers and Mathematics with Applications， 2016， 71： 391-407.
[16]HUANG R， WU H. An immersed boundary-thermal lattice Boltzmann method for solid-liquid phase change[J]. Journal of Computational Physics， 2014， 277： 305-319.
[17]PESKIN C S. The immersed boundary method[J]. Acta Numer， 2002， 11： 479-517.
[18]ROMA A M， PESKIN C S， BERGER M J. An adaptive version of the immersed boundary method[J]. Journal of Computational Physics， 1999， 153 （2）： 509-534.
[19]YANG X， XING Z， LI Z， et al. A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations[J]. Journal of Computational Physics， 2009， 228 （20）： 7821-7836.
[20]BAO Y， KAYE J. PESKIN C S. A gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance[J]. Journal of Computational Physics， 2016， 316 ： 139-144.
[21]SUN Y， SHU C， WANG Y， et al. An immersed boundary-gas kinetic flux solver for simulation of incompressible flows[J]. Computer and Fluids， 2017， 142： 45-56 .
[22]SHUKLA R K， TATINENI M， ZHONG X. Very high-order compact finite difference schemes on non-uniform grids for incompressible Navier-Stokes equations[J]. Journal of Computational Physics， 2007， 224： 1064-1094.
[23]IMAMURA T， SUZUKI K， NAKAMURA T， et al. Flow simulation around an airfoil using lattice Boltzmann method on generalized coordinates[J]. AIAA Journal， 2015， 43（9）： 1968-1973.
（責任编辑：于慧梅）
Abstract：
The lattice Boltzmann method and the implicit diffused interface immersed boundary method are combined to solve the fluid-solid coupling motion.The predicted velocity and pressure fields can be solved quickly by lattice Boltzmann method. The fluid-structure interface forces are obtained implicitly by the no-slip boundary condition satisfying the fluid-structure interface. The information exchange between solid boundary nodes and flow field nodes is realized by the high-order derivative smooth function.The main advantage of this present method is that it is not only simple in concept and easy for implementation， but also it is of high efficiency and reduces the non-physical oscillations. In order to identify the effectiveness and validity of this numerical method， to flow around a stationary circular cylinder and airfoil NACA0012 are simulated firstly. It clarified that this method is reliable and the no-slip boundary is satisfied very well. Then， the interaction between the passively rotating rotor and the fluid under different Reynolds numbers is simulated to further verify the robustness of the proposed method.
Key words：
lattice Boltzmann method; implicit diffused interface immersed boundary method; high-order smooth functions; fluid-solid interaction
王文全，男，1977年生，四川南充人，博士，教授，博士生导师，霍英东青年基金获得者，云南省中青年学术与技术带头人，云南省万人计划产业技术领军人才，云南省引进高层次人才（二层次），四川大学“双百人才工程A计划”。长期潜心于多场耦合基础理论以及可再生能源利用方面的研究。已出版学术专著2部，发表学术论文120余篇。申请国内发明专利17项，已授权9项。获云南省自然科学一等奖2项，云南省自然科学二等奖2项。主持/参与完成国家自然科学基金重大研究计划项目、国家自然科学基金重点项目、云南省重大科技专项等纵向科技项目19项以及其它横向项目多项。
关键词：格子Boltzmann方法; 隐式扩散浸入边界法; 高阶光滑函数;流体固体相互作用
中图分类号：O35
文献标志码：A
参考文献：
[1]PESKIN C S. Flow patterns around heart valves： a numerical method[J]. Journal of Computational Physics， 1972， 10（2）： 252-271.
[2]CENICEROS H D， FISHER J E， ROMA A M. Efficient solutions to robust， semi-implicit discretizations of the immersed boundary method[J]. Journal of Computational Physics， 2009， 228 （19）： 7137-7158.
[3]FADLUN E A， VERZICCO R， ORLANDI P， et al. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations[J]. Journal of Computational Physics， 2000， 161 （1）： 35-60.
[4]UHLMANN M. An immersed boundary method with direct forcing for the simulation of particulate flows[J]. Journal of Computational Physics， 2005， 209 （2）： 448-476.
[5]KEMPE T， FROHLICH J. An improved immersed boundary method with direct forcing for the simulation of particle laden flows[J]. Journal of Computational Physics， 2012， 231 （9）： 3663-3684.
[6]WANG S， ZHANG X. An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows[J]. Journal of Computational Physics， 2011， 230 （9） ： 3479-3499.
[7]LIU Q， VASILYEV O V. A Brinkman penalization method for compressible flows in complex geometries[J]. Journal of Computational Physics， 2007， 227 （2） ： 946-966.
[8]CHENY Y， BOTELLA O. The LS-STAG method： a new immersed boundary/level-set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties [J]. Journal of Computational Physics， 2010， 229 （4） ： 1043-1076.
[9]SCHNEIDERS L， GNTHER C， MEINKE M， et al. An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows[J]. Journal of Computational Physics， 2016， 311： 62-86.
[10]SHU C， LIU N， CHEW Y T. A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder[J]. Journal of Computational Physics， 2007， 226： 1607-1622.
[11]WU J， SHU C. Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications[J]. Journal of Computational Physics， 2009， 228： 1963-1979. [12]WU J， QIU Y L， SHU C， et al. An adaptive immersed boundary-lattice Boltzmann method for simulating a flapping foil in ground effect[J]. Computer and Fluids， 2015， 106： 171-184.
[13]TIAN F B， LUO H， ZHU L， et al. An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments[J]. Journal of Computational Physics， 2011， 230 （19）：7266-7283.
[14]ZHANG H， TAN Y， SHU S， et al. Numerical investigation on the role of discrete element method in combined LBM-IBM-DEM modeling[J]. Computer and Fluids， 2014， 94： 37-48.
[15]ZHANG H， YUAN H Z， YU A B，et al. Particulate immersed boundary method for complex fluid-particle interaction problems with heat transfer[J]. Computers and Mathematics with Applications， 2016， 71： 391-407.
[16]HUANG R， WU H. An immersed boundary-thermal lattice Boltzmann method for solid-liquid phase change[J]. Journal of Computational Physics， 2014， 277： 305-319.
[17]PESKIN C S. The immersed boundary method[J]. Acta Numer， 2002， 11： 479-517.
[18]ROMA A M， PESKIN C S， BERGER M J. An adaptive version of the immersed boundary method[J]. Journal of Computational Physics， 1999， 153 （2）： 509-534.
[19]YANG X， XING Z， LI Z， et al. A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations[J]. Journal of Computational Physics， 2009， 228 （20）： 7821-7836.
[20]BAO Y， KAYE J. PESKIN C S. A gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance[J]. Journal of Computational Physics， 2016， 316 ： 139-144.
[21]SUN Y， SHU C， WANG Y， et al. An immersed boundary-gas kinetic flux solver for simulation of incompressible flows[J]. Computer and Fluids， 2017， 142： 45-56 .
[22]SHUKLA R K， TATINENI M， ZHONG X. Very high-order compact finite difference schemes on non-uniform grids for incompressible Navier-Stokes equations[J]. Journal of Computational Physics， 2007， 224： 1064-1094.
[23]IMAMURA T， SUZUKI K， NAKAMURA T， et al. Flow simulation around an airfoil using lattice Boltzmann method on generalized coordinates[J]. AIAA Journal， 2015， 43（9）： 1968-1973.
（責任编辑：于慧梅）
Abstract：
The lattice Boltzmann method and the implicit diffused interface immersed boundary method are combined to solve the fluid-solid coupling motion.The predicted velocity and pressure fields can be solved quickly by lattice Boltzmann method. The fluid-structure interface forces are obtained implicitly by the no-slip boundary condition satisfying the fluid-structure interface. The information exchange between solid boundary nodes and flow field nodes is realized by the high-order derivative smooth function.The main advantage of this present method is that it is not only simple in concept and easy for implementation， but also it is of high efficiency and reduces the non-physical oscillations. In order to identify the effectiveness and validity of this numerical method， to flow around a stationary circular cylinder and airfoil NACA0012 are simulated firstly. It clarified that this method is reliable and the no-slip boundary is satisfied very well. Then， the interaction between the passively rotating rotor and the fluid under different Reynolds numbers is simulated to further verify the robustness of the proposed method.
Key words：
lattice Boltzmann method; implicit diffused interface immersed boundary method; high-order smooth functions; fluid-solid interaction
王文全，男，1977年生，四川南充人，博士，教授，博士生导师，霍英东青年基金获得者，云南省中青年学术与技术带头人，云南省万人计划产业技术领军人才，云南省引进高层次人才（二层次），四川大学“双百人才工程A计划”。长期潜心于多场耦合基础理论以及可再生能源利用方面的研究。已出版学术专著2部，发表学术论文120余篇。申请国内发明专利17项，已授权9项。获云南省自然科学一等奖2项，云南省自然科学二等奖2项。主持/参与完成国家自然科学基金重大研究计划项目、国家自然科学基金重点项目、云南省重大科技专项等纵向科技项目19项以及其它横向项目多项。