采用格子Boltzm ann方法(lattice Boltzm ann m ethod,LBM)中的被动标量模型,不考虑温度的影响,采用合适的密度分布函数和碰撞处理,并在一般坐标系下完成迁移过程的插值。固壁边界条件采用无滑移边界条件,模拟了雷诺数为60 000,攻角分别...采用格子Boltzm ann方法(lattice Boltzm ann m ethod,LBM)中的被动标量模型,不考虑温度的影响,采用合适的密度分布函数和碰撞处理,并在一般坐标系下完成迁移过程的插值。固壁边界条件采用无滑移边界条件,模拟了雷诺数为60 000,攻角分别为0度和8度状态下的NACA0012翼型绕流。其翼型表面流线图和压力云图分布结果均与D2Q9模型结果吻合较好,证明该方法能够很好的模拟低速翼型的绕流。并且,在方程中加入等离子体激励器简化的作用力模型,初步达到带攻角下流动分离的控制效果,证明了该方法在带有体积力项流动的数值模拟方面的优良特性。展开更多
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
文摘采用格子Boltzm ann方法(lattice Boltzm ann m ethod,LBM)中的被动标量模型,不考虑温度的影响,采用合适的密度分布函数和碰撞处理,并在一般坐标系下完成迁移过程的插值。固壁边界条件采用无滑移边界条件,模拟了雷诺数为60 000,攻角分别为0度和8度状态下的NACA0012翼型绕流。其翼型表面流线图和压力云图分布结果均与D2Q9模型结果吻合较好,证明该方法能够很好的模拟低速翼型的绕流。并且,在方程中加入等离子体激励器简化的作用力模型,初步达到带攻角下流动分离的控制效果,证明了该方法在带有体积力项流动的数值模拟方面的优良特性。
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
