The semi-Lagrangian Vortex method (VM) and the Lattice Boltzmann method (LBM) are used to investigate flows simulations in the incompressible regime. In this study, a proven version of each method is used and compared on different three dimensional benchmarks in terms of numerical accuracy, convergence, numerical diffusion and dissipation. The first comparisons are made on a convected vortex to study and compare the numerical dissipation of LBM and VM. Then the Taylor–Green vortex is investigated to compare the dissipation rate of the kinetic energy of each method. It is shown that both methods converge to the same solution but in a different way. The VM performs better than the LBM for the lowest resolution whereas LBM appears to be more accurate for the growing resolutions. These results are confirmed on 3D simulations with wall boundaries for the stiff test case of the wake behind a 3D cube at $Re=290$ and $Re=570$.

半拉格朗日涡旋法（VM）和格子Boltzmann方法（LBM）用于研究不可压缩状态下的流动模拟。在这项研究中，使用了每种方法的可靠版本，并在数值精度，收敛性，数值扩散和耗散方面在不同的三维基准上进行了比较。在对流涡旋上进行第一次比较，以研究和比较LBM和VM的数值耗散。然后研究泰勒-格林涡旋，比较每种方法的动能耗散率。结果表明，这两种方法都收敛于相同的解决方案，但方式不同。在最低分辨率下，VM的性能优于LBM，而在分辨率不断提高的情况下，LBM似乎更准确。$\mathrm{[R}Ë=290$ 和 $\mathrm{[R}Ë=570$。