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An investigation into curved and moving boundary treatments in the lattice Boltzmann method

机译：格子Boltzmann方法中弯曲和运动边界处理的研究

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Curved boundary treatments provide a means of improving the computational accuracy of the conventional stair-shaped approximation used in lattice Boltzmann (LB) simulations. Furthermore, curved boundary treatments can be extended to the modeling of moving boundary problems simply by adding a momentum term to the bounced distribution functions at the solid surface. This study commences by investigating three conventional interpolating treatments for curved boundaries in LB problems, namely the Filippova and Hanel (FH) model [O. Filippova, D. Hanel, Grid refinement for lattice-BGK models, J. Comput. Phys. 147 (1998) 219-228], Bouzidi's model [M. Bouzidi, M. Firdaouss, P. Lallemand, Momentum transfer of a Boltzmann-lattice fluid with boundaries, Phys. Fluids 13(11) (2001) 3452-3459], and Yu's model [D. Yu, R. Mei, W. Shyy, A Unified Boundary Treatment in Lattice Boltzmann Method, AIAA 2003-0953, New York, 2003]. Previous investigations have indicated that the interpolations would break the mass conservation at the boundaries, since the inaccuracy in evaluation of the momentum transfer at boundary leads to a net mass flux. Based on this reason, a concept of the interpolation-free treatment for modeling the curved and moving boundary conditions is proposed to overcome the drawback of these interpolation-based curved boundary treatments. In present study, two interpolation-free models are then proposed, namely on-site interpolation-free (OSIF) and composite interpolation-free (CPIF) models. These proposed models are initially applied to simulate the flow in the channels containing a stationary square block positioned at various locations along the longitudinal axis. The simulations results are then compared with those obtained using the three conventional interpolating treatments. The interpolation-free models are then applied to the case of moving boundary problems in which a square block and a cylindrical block, respectively, move with a constant speed along a channel containing stationary flows. To test the Galilean effect of the proposed CPIF model, a Couette flow past the stationary square/cylinder block with the moving top/bottom walls is simulated. Overall, the numerical results show that the proposed interpolation-free curved treatment models significantly improve the accuracy of the mass flux computation near the solid surface, and thus enhance the accuracy of the momentum interaction at the moving boundaries. (c) 2008 Elsevier Inc. All rights reserved.
机译：弯曲边界处理提供了一种提高格子Boltzmann（LB）模拟中使用的传统阶梯形近似计算精度的方法。此外，只需在实体表面的反弹分布函数中添加动量项，就可以将弯曲边界处理扩展到运动边界问题的建模。这项研究从调查LB问题中弯曲边界的三种常规插值处理开始，即Filippova和Hanel（FH）模型[O。 Filippova，D。Hanel，《晶格BGK模型的网格细化》，J。Comput。物理147（1998）219-228]，Bouzidi的模型[M. Bouzidi，M。Firdaouss，P。Lallemand，带边界的玻尔兹曼-格状流体的动量传递，物理。流体13（11）（2001）3452-3459]和Yu的模型[D. Yu，R。Mei，W。Shyy，《格子Boltzmann方法的统一边界处理》，AIAA 2003-0953，纽约，2003年。先前的研究表明，插值法会破坏边界处的质量守恒，因为边界处动量传递的评估结果不准确会导致净质量通量。基于这个原因，提出了一种用于建模弯曲和运动边界条件的无插值处理的概念，以克服这些基于插值的弯曲边界处理的缺点。在本研究中，然后提出了两种无插值模型，即现场无插值（OSIF）和无复合插值（CPIF）模型。这些建议的模型最初用于模拟通道中的流动，该通道中包含一个固定的方形块，该方形块位于沿纵轴的各个位置。然后将模拟结果与使用三种常规插值处理获得的结果进行比较。然后将无插值模型应用于移动边界问题的情况，在该问题中，正方形块和圆柱形块分别沿包含固定流的通道以恒定速度移动。为了测试所提出的CPIF模型的伽利略效应，模拟了经过顶部和底部活动壁的固定正方形/圆柱体的Couette流。总体而言，数值结果表明，所提出的无插值曲线处理模型显着提高了固体表面附近质量通量计算的准确性，从而提高了运动边界处动量相互作用的准确性。 （c）2008 Elsevier Inc.保留所有权利。

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