  We introduce a collection of benchmark problems in 2D and 3D (geometry
description and boundary conditions), including simple cases with known
analytic solution, classical experimental setups, and complex geometries with
fabricated solutions for evaluation of numerical schemes for incompressible
Navier-Stokes equations in laminar flow regime. We compare the performance of a
representative selection of most broadly used algorithms for Navier-Stokes
equations on this set of problems. Where applicable, we compare the most common
spatial discretization choices (unstructured triangle/tetrahedral meshes and
structured or semi-structured quadrilateral/hexahedral meshes).
  The study shows that while the type of spatial discretization used has a
minor impact on the accuracy of the solutions, the choice of time integration
method, spatial discretization order, and the choice of solving the coupled
equations or reducing them to simpler subproblems have very different
properties. Methods that are directly solving the original equations tend to be
more accurate than splitting approaches for the same number of degrees of
freedom, but numerical or computational difficulty arise when they are scaled
to larger problem sizes. Low-order splitting methods are less accurate, but
scale more easily to large problems, while higher-order splitting methods are
accurate but require dense time discretizations to be stable.
  We release the description of the experiments and an implementation of our
benchmark, which we believe will enable statistically significant comparisons
with the state of the art as new approaches for solving the incompressible
Navier-Stokes equations are introduced.
