High-Order Regularization and Velocity Stencil Effects in Lattice Boltzmann Simulations of Turbulent Flow

We investigate the combined effects of high-order regularization and velocity stencil selection in the lattice Boltzmann method (LBM), particularly in simulations of turbulent flows. The transition from the D3Q19 to the D3Q27 stencil results in approximately a 40% decrease in computational performance. However, this modification leads to significantly improved flow characterization, owing to the enhanced rotational invariance of D3Q27 under nonlinear momentum advection correction.

High-order regularization introduces a smaller computational overhead while effectively reducing simulation error. This is achieved through a refined regularization expansion based on a recursive formulation, where all higher-order moments are expressed as functions of second-order moments. This strategy avoids additional memory storage and supports computational scalability.

The synergy between these strategies is fundamental. The D3Q27 stencil ensures discrete Hermite orthogonality, which is essential for accurate high-order modeling. Combined with high-order regularization, it enhances both accuracy and stability. These developments are implemented within a CUDA-accelerated, moment-based framework that enables efficient and accurate simulations.

While the proposed modifications impose a moderate reduction in raw performance, they lead to significant improvements in numerical fidelity, making them well-suited for high-resolution LBM simulations of complex, turbulent flows.