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<p dir="ltr">The kinetic-based lattice Boltzmann method (LBM) is a specialized computational fluid dynamics (CFD) technique that resolves intricate flow phenomena at the mesoscale level. The LBM is particularly suited for large-scale parallel computing on Graphic Processing Units (GPU) and simulating multi-phase flows. By incorporating a volume fraction parameter, LBM becomes a volumetric lattice Boltzmann method (VLBM), leading to advantages such as easy handling of complex geometries with/without movement. These capabilities render VLBM an effective tool for modeling various complex flows. In this study, we investigated the computational modeling of complex flows using VLBM, focusing particularly on pulsatile flows, the transition to turbulent flows, and pore-scale porous media flows. Furthermore, a new discrete dynamical system (DDS) is derived and validated for potential integration into large eddy simulations (LES) aimed at enhancing modeling for turbulent and pulsatile flows. Pulsatile flows are prevalent in nature, engineering, and the human body. Understanding these flows is crucial in research areas such as biomedical engineering and cardiovascular studies. However, the characteristics of oscillatory, variability in Reynolds number (Re), and shear stress bring difficulties in the numerical modeling of pulsatile flows. To analyze and understand the shear stress variability in pulsatile flows, we first developed a unique computational method using VLBM to quantify four-dimensional (4-D) wall stresses in image-based pulsatile flows. The method is validated against analytical solutions and experimental data, showing good agreement. Additionally, an application study is presented for the non-invasive quantification of 4-D hemodynamics in human carotid and vertebral arteries. Secondly, the transition to turbulent flows is studied as it plays an important role in the understanding of pulsatile flows since the flow can shift from laminar to transient and then to turbulent within a single flow cycle. We conducted direct numerical simulations (DNS) using VLBM in a three-dimensional (3-D) pipe and investigated the flow at Re ranging from 226 to 14066 in the Lagrangian description. Results demonstrate good agreement with analytical solutions for laminar flows and with open data for turbulent flows. Key observations include the disappearance of parabolic velocity profiles when Re>2300, the fluctuation of turbulent kinetic energy (TKE) between laminar and turbulent states within the range 2300</p>