A new approach of combination of the LBM and adjoint method based on the circular function idea is developed for optimization of unsteady incompressible/compressible inviscid flow in 1D and 2D problems. The circular function distribution is used for capturing the compressibility effect in the flowfield and the continuous adjoint method allows designers to implement large number of design variables in actual optimization problems. The adjoint approach is successfully derived for the first time based on the compressible LBM with terminal conditions for estimation of the cost function gradient vector in 1D/2D flow inverse design problem. To validate the new derived flow solver with new lattice, firstly, accuracy of the flow simulation is shown for the inviscid compressible discontinuous flows with shock wave. Secondly, for validation of novel derived adjoint optimization algorithm, three optimization problems in form of the inverse design, including the smooth and shock wave inviscid compressible flowfields, are presented. Also, trend of optimization algorithm is studied in all cases. The results indicate that the presented numerical optimization approach gives desirable accuracy in 1D/2D inverse design of inviscid unsteady compressible flowfields.

针对一维和二维问题中的非定常不可压缩/可压缩无粘性流，提出了一种基于循环函数思想的结合LBM和伴随方法的新方法。圆形函数分布用于捕获流场中的可压缩性效果，连续伴随方法允许设计人员在实际的优化问题中实现大量设计变量。基于带有终端条件的可压缩LBM，首次成功地导出了伴随方法，以估算1D / 2D流逆设计问题中的成本函数梯度向量。为了用新的网格验证新的派生流动求解器，首先，显示了具有冲击波的无粘性可压缩不连续流动的流动模拟精度。其次，为了验证新颖的伴随优化算法，提出了逆设计形式的三个优化问题，包括光滑波和冲击波无粘性可压缩流场。此外，在所有情况下都研究了优化算法的趋势。结果表明，所提出的数值优化方法在无粘性非定常可压缩流场的一维/二维逆设计中具有令人满意的精度。