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.

这项工作的目的是将格子Boltzmann方法（LBM）与有限差分方法（FDM）进行公平公正的比较，以模拟流体流动。我们的工作不是报告诸如浮点运算速率或内存吞吐量之类的指标，而是考虑以最少的计算量来达到所需解决方案质量的工程任务。这里选择的特定晶格玻尔兹曼法和有限差分法具有非常基本的性质，以强调根本不同方法的影响。为了最大程度地减少测量中的偏斜，避免了复杂的边界条件方案和进一步的先进技术，而是两种方法都是完全明确的，弱可压缩的方法。由于两个代码的高度优化特性，因此每种方法都施加了不同的限制集。使用一组通用的功能，考虑了两个相对简单的测试案例，分别针对管道流量和盖驱动腔中的流量，并通过两种方法进行了优化，以实现最佳性能。作为第三个测试用例，使用绕方形圆柱体的瞬变流来演示在面向工程的设置和时域中的适用性。发现这两种方法的性能非常相似，而对于任何一种方法都没有充分的优势。总的来说，在较大的目标误差和间接基准量（例如升力和阻力）下，LBM表现出更好的性能趋势，而FDM在较小的目标误差以及将速度和压力曲线与分析解决方案进行直接比较方面表现出色。