A runtime based comparison of highly tuned lattice Boltzmann and finite difference solvers

The aim of this work is a fair and unbiased comparison of a lattice Boltzmann method (LBM) against a finite difference method (FDM) for the simulation of fluid flows. Rather than reporting metrics such as floating point operation rates or memory throughput, our work considers the engineering quest of reaching a desired solution quality with the least computational effort. The specific lattice Boltzmann and finite difference methods selected here are of a very basic nature to emphasize the influence of the fundamentally different approaches. To minimize the skew in the measurements, complex boundary condition schemes and further advanced techniques are avoided and instead both methods are fully explicit, weakly compressible approaches. Due to the highly optimized nature of both codes, different sets of restrictions are imposed by either method. Using the common set of features, two relatively simple test cases in terms of a duct flow and the flow in a lid driven cavity are considered and are tuned to perform optimally with both approaches. As a third test case, a transient flow around a square cylinder is used to demonstrate the applicability to engineering oriented settings and in a temporal domain. The performance of the two methods is found to be very similar with no full advantage for any of the approaches. Overall a tendency toward better performance of the LBM at larger target errors and for indirect benchmark quantities, such as lift and drag, is observed, while the FDM excels at smaller target errors and direct comparisons of velocity and pressure profiles to analytical solutions. Other factors such as the difficulty of setting consistent boundary conditions in the LBM or the effect of stabilization in the FDM are likely to be the most important criteria when searching for a very fast flow solver for practical applications.