Abstract—

A new approach of the axisymmetric compressible lattice Boltzmann method (LBM) has been developed for the numerical simulation of supersonic inviscid flow using the finite volume method. The circular function idea has been used for capturing the compressibility effect in the supersonic flow field. In this study, the axisymmetric LBM equations based on the circular function have been derived for the first time and presented in detail and appropriate axisymmetric boundary conditions have been applied for the 2-dimensional, 13-velocity, 2-energy-level lattices. For validation of developed code, two supersonic axisymmetric flows have been simulated around the hemisphere nose and 60° blunt body. A comparison of the obtained results with some valid empirical data shows the accuracy of the developed numerical algorithm. Also, the results of 2D and axisymmetric simulations have been studied to evaluate the effects of the new derived axisymmetric formulation on flow macroscopic properties.

中文翻译：

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轴对称可压缩有限格格子玻尔兹曼方法的超音速无粘性流数值模拟新方法

摘要-

轴对称可压缩晶格玻尔兹曼方法（LBM）的一种新方法已经被开发出来，用于使用有限体积法对超音速无粘性流进行数值模拟。圆形函数的思想已被用于捕获超声速流场中的压缩效应。在这项研究中，首次推导了基于圆形函数的轴对称LBM方程，并对其进行了详细介绍，并将适当的轴对称边界条件应用于二维，13速度，2能级晶格。为了验证已开发的代码，在半球鼻子和60°钝体周围模拟了两个超声速轴对称流。将获得的结果与一些有效的经验数据进行比较，表明了所开发数值算法的准确性。还，