一種隱式擴散浸入邊界-格子Boltzmann方法及應(yīng)用

王文全 王金霖 駱佳玲

摘 要：結(jié)合格子Boltzmann方法和隱式擴散浸入邊界方法，實現(xiàn)流體-固體耦合運動的求解。預(yù)測的速度和壓力場可以通過格子Boltzmann方法快速求解，而流固耦合界面力由滿足流固界面的無滑移邊界條件隱式獲得，固體邊界節(jié)點與流場節(jié)點間的信息交換通過高階導(dǎo)數(shù)光滑函數(shù)實現(xiàn)。該方法的主要優(yōu)點是易于實施，效率高，并且減少了非物理振蕩和非物理流線穿透。為了確定該數(shù)值方法的有效性，通過圓柱繞流和翼型繞流基準算例證實了該方法的可靠性;模擬不同雷諾數(shù)下被動旋轉(zhuǎn)轉(zhuǎn)子與流體的相互作用，進一步驗證了該方法的魯棒性。

關(guān)鍵詞：格子Boltzmann方法; 隱式擴散浸入邊界法; 高階光滑函數(shù);流體固體相互作用

中圖分類號：O35

文獻標志碼：A

參考文獻：

[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.

（責任編輯：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，博士生導(dǎo)師，霍英東青年基金獲得者，云南省中青年學(xué)術(shù)與技術(shù)帶頭人，云南省萬人計劃產(chǎn)業(yè)技術(shù)領(lǐng)軍人才，云南省引進高層次人才（二層次），四川大學(xué)“雙百人才工程A計劃”。長期潛心于多場耦合基礎(chǔ)理論以及可再生能源利用方面的研究。已出版學(xué)術(shù)專著2部，發(fā)表學(xué)術(shù)論文120余篇。申請國內(nèi)發(fā)明專利17項，已授權(quán)9項。獲云南省自然科學(xué)一等獎2項，云南省自然科學(xué)二等獎2項。主持/參與完成國家自然科學(xué)基金重大研究計劃項目、國家自然科學(xué)基金重點項目、云南省重大科技專項等縱向科技項目19項以及其它橫向項目多項。