The objective of this study is to develop and apply an arbitrary Lagrangian-Eulerian unstructured finite-volume lattice-Boltzmann method (ALE-FVLBM) for solving two-dimensional compressible inviscid flows around moving bodies. The two-dimensional compressible form of the LB equation is considered and the resulting LB equation is formulated in the ALE framework on an unstructured body-fitted mesh to correctly model the body shape and properly incorporate the mesh movement due to the body motion. The spatial discretization of the resulting system of equations is performed by a second-order cell-centered finite-volume method on arbitrary quadrilateral meshes and an implicit dual-time stepping method is utilized for the time integration. To stabilize the numerical solution, appropriate numerical dissipation terms are added to the formulation. At first, the shock tube problem is computed to examine the accuracy of the solution obtained by applying the proposed FVLBM for this unsteady test case which includes shock, expansion wave, and contact discontinuity in the flow domain. Then, the stationary isentropic vortex is simulated on both the stationary and moving meshes to assess the implementation of the geometric conservation law in enhancing the solution accuracy of the ALE-FVLBM. The compressible inviscid flow in the transonic regime is then computed around the stationary NACA0012 airfoil in order to further study the sensitivity of the solution method to the user defined parameters. Now, the transonic inviscid flow is simulated over the pitching or plunging NACA0012 airfoil to investigate the accuracy and capability of the proposed solution method (ALE-FVLBM) for the computation of the compressible flows over moving bodies. Finally, the pitching or plunging NACA0012 airfoil near the ground in the transonic inviscid flow is simulated as a practical and challenging problem to study the ground effect on the aerodynamic characteristics of the airfoil. It is indicated that the solution methodology proposed based on the finite-volume LBM formulated in the arbitrary Lagrangian-Eulerian framework (ALE-FVLBM) is capable of accurately computing the compressible inviscid flows around the moving bodies with and without the ground effect.

中文翻译：

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拉格朗日-欧拉非结构化有限体积格-玻尔兹曼方法，用于计算运动物体上的二维可压缩无粘性流

这项研究的目的是开发和应用任意拉格朗日-欧拉非结构化有限体积格-玻尔兹曼方法（ALE-FVLBM）来解决运动物体周围的二维可压缩无粘性流。考虑LB方程的二维可压缩形式，并将所得LB方程在ALE框架中公式化为非结构化的人体拟合网格，以正确地建模身体形状并适当地合并由于身体运动引起的网格运动。所得方程组的空间离散化是通过在任意四边形网格上通过二阶单元中心有限体积方法进行的，并且隐式双时间步长方法用于时间积分。为了稳定数值解，将适当的数值耗散项添加到公式中。首先，计算激波管问题，以检验针对此不稳定的测试案例应用建议的FVLBM获得的解决方案的准确性，该测试案例包括冲击，膨胀波和流域中的接触不连续性。然后，在固定网格和移动网格上都模拟了静态等熵涡流，以评估几何守恒定律在提高ALE-FVLBM求解精度方面的实现。然后围绕固定的NACA0012翼型计算跨音速状态下的可压缩无粘性流，以进一步研究求解方法对用户定义的参数的敏感性。现在，在俯仰或俯冲NACA0012机翼上模拟跨音速无粘性流，以研究所提出的求解方法（ALE-FVLBM）的准确性和能力，以计算运动物体上的可压缩流。最后，模拟跨音速无粘性流中靠近地面的俯仰或俯冲NACA0012机翼是一个实际的，具有挑战性的问题，以研究地面对机翼气动特性的影响。结果表明，基于在任意拉格朗日-欧拉框架（ALE-FVLBM）中公式化的有限体积LBM提出的求解方法，能够精确计算有无地面效应的运动物体周围的可压缩无粘性流。为了研究地面对翼型气动特性的影响，模拟了跨音速无粘性流中靠近地面的俯仰或俯冲NACA0012翼型，这是一个实际且具有挑战性的问题。结果表明，基于在任意拉格朗日-欧拉框架（ALE-FVLBM）中公式化的有限体积LBM提出的求解方法，能够精确计算有无地面效应的运动物体周围的可压缩无粘性流。为了研究地面对翼型气动特性的影响，模拟了跨音速无粘性流中靠近地面的俯仰或俯冲NACA0012翼型，这是一个实际且具有挑战性的问题。结果表明，基于在任意拉格朗日-欧拉框架（ALE-FVLBM）中公式化的有限体积LBM提出的求解方法，能够精确计算有无地面效应的运动物体周围的可压缩无粘性流。