A novel two-dimensional D2Q9 cumulant-based lattice Boltzmann method: simulation and validation across multiple flow phenomena

This study presents a novel two-dimensional (2D) cumulant lattice Boltzmann method (CuLBM), known as D2Q9 CuLBM, which has been implemented using compute unit device architecture (CUDA) C/C++ to leverage graphics processing unit (GPU) computing for enhanced efficiency and performance. The cumulant-based lattice Boltzmann approach is a recent advancement in computational fluid dynamics (CFD) methods designed to offer improved stability and accuracy, particularly for simulating complex fluid flows. This work comprehensively describes the D2Q9 CuLBM formulation, focusing on its application to several benchmark and complex fluid flow cases. The well known validation tests include lid-driven cavity (LDC) flow and backward-facing step (BFS) flow, both frequently used in CFD to assess the accuracy and stability of numerical methods. Additionally, the model is evaluated on periodic double shear layer flow, a challenging problem for flow stability, Green–Taylor vortex and Kida–Pelz vortex flows and extended to shear-dependent non-Newtonian fluids, specifically those obeying power-law and Bingham models in the lid driven cavity, Couette and Poiseuille flows. These non-Newtonian cases are critical for capturing flows with complex rheological properties, demonstrating the versatility and accuracy of the D2Q9 CuLBM approach in handling a broad spectrum of fluid dynamics problems.