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An implicit dual-time stepping spectral difference lattice Boltzmann method for simulation of viscous compressible flows on structured meshes

机译:用于结构网格上的粘性可压缩流模拟的隐式双时踩踏谱差格晶体Boltzmann方法

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摘要

In this work, the spectral difference lattice Boltzmann method (SDLBM) is extended and applied for accurately computing two-dimensional viscous compressible flows on structured meshes. Here, the compressible form of the discrete Boltzmann-BGK equation with the Watari model is considered and the numerical solution of the resulting LB equation is obtained by using the spectral difference method. The main benefit of the use of the LB method in simulating compressible flows is that a same formulation can be applied to compute the inviscid and viscous portions of the flowfield. Note that the LB formulation for simulating the viscous flows is the same as that used for the inviscid ones, however, the wall boundary conditions are changed in a manner to consider the no-slip conditions. Here, the SDLBM is also extended to use curved-edge cells for properly representing curved wall boundaries. In addition, to enhance the solution of the SDLBM the time integration is efficiently performed by implementing an implicit dual-time stepping method which does not require a matrix inversion. Both steady and unsteady flows are simulated. Different test cases including the Couette flow, the viscous shock-vortex interaction, the flow over a circular cylinder and the flow over a NACA-0012 airfoil are simulated to assess the accuracy and robustness of the solution procedure proposed based on the SDLBM in computing steady and unsteady viscous compressible flows. The present results obtained by applying the SDLBM exhibit good agreement compared to the analytical and available high-order accurate solutions of the LB and Navier-Stokes equations.
机译:在这项工作中,频谱差晶格Boltzmann方法(SDLBM)被延伸并施加用于精确计算结构化网格上的二维粘性可压缩流。这里,考虑具有Watari模型的离散Boltzmann-BGK方程的可压缩形式,并且通过使用光谱差法获得所得到的LB方程的数值解。使用LB方法在模拟可压缩流中的主要益处是可以应用相同的配方来计算流场的粘性和粘性部分。注意,用于模拟粘性流的LB配方与用于无粘性的流量相同,然而,以考虑无滑移条件的方式改变壁边界条件。这里,SDLBM也扩展以使用曲线边缘单元来正确表示弯曲壁边界。另外,为了增强SDLBM的解决方案,通过实现不需要矩阵反转的隐式双时踏步方法,有效地执行时间集成。模拟稳定和不稳定的流量。不同的测试用例包括弯曲流动,粘性冲击涡流相互作用,圆筒上的流量和NACA-0012翼型上的流量被模拟,以评估基于计算稳定的SDLBM提出的解决方案程序的精度和鲁棒性和不稳定的粘性可压缩流动。与LB和Navier-Stokes方程的分析和可用的高阶准确解决方案相比,通过应用SDLBM获得良好协议所获得的目前的结果。

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