Computational fluid dynamics (CFD) encompasses a variety of numerical methods. Some depend on macroscopic model representatives, which are solved by finite volume, finite element or finite difference method, while others rely on a microscopic description. The lattice Boltzmann method (LBM) is considered a mesoscopic particle method, with its scale lying between macroscopic and microscopic. LBM works well when solving incompressible flow problems, but limitations arise when solving compressible flows, particularly at high Mach numbers. In the present research, this limitation will be overcome by using higher-order Taylor series expansion of the Maxwell equilibrium distribution function and Kataoka and Tsutahara (KT) models for compressible flows. The multiple relaxation times (MRT) approach associated with the collision term of the lattice Boltzmann equation (LBE) will be adopted to enhance the numerical stability of the code, while the large eddy simulation (LES) scale model will be implemented in LBM to simulate compressible jet flows at high subsonic speeds pertinent to jet noise problems. Three-dimensional simulation is performed using 19- and 15-lattice velocity with D3Q19 and D3Q15 models, respectively. In addition, compressible LBM is applied to simulate both heated and unheated jets to show the ability of the nonadiabatic fifth-order equilibrium distribution function in solving nonadiabatic compressible flows. The near-field flow physics and noise simulations are performed using a compressible lattice Boltzmann method. The results from the LMB simulation are used in the Kirchhoff surface integral approach to predict far-field jet noise. Finally, because of the ability of lattice Boltzmann in parallel computing and to improve the computation efficiency of LBM on the numerical simulations of turbulent flows, compute unified device architecture (CUDA) is used to implement LBM in the graphics processing unit (GPU), creating the hybrid code LBM-MRT-LES by utilizing the Kirchhoff integral method, a powerful tool for simulating aeroacoustics problems.