Various numerical methods are generally suitable for solving flow equations, such as finite element, finite difference, and finite volume methods, which directly use the Navier-Stokes equations, as well as kinetic particle methods. Due to the variety of variants within these method classes, it is difficult to identify a universally optimal method. The order of convergence plays a significant role in all discretization methods, with most commercial codes offering spatial quadratic convergence for the velocity field and linear or quadratic approximations for the pressure field.
Besides the order of convergence, stability, numerical diffusion, and dispersion are crucial for solution quality. Numerical diffusion can lead to an artificially increased viscosity, while numerical dispersion can cause oscillations or phase errors in transient calculations.
Kinetic methods, such as the Lattice Boltzmann Method (LBM), discretize a simplified Boltzmann equation instead of the Navier-Stokes equations and are well-suited for weakly compressible flow problems in wind engineering. Integral equation methods, like the vortex particle method, are occasionally used for fluid-structure interactions in bridge construction.
Some fast particle methods are used for simple visualizations and 3D movie effects, but they are generally unsuitable for wind engineering due to a lack of physical accuracy.