Exact fully 3D Navier–Stokes solutions for benchmarking

Abstract Unsteady analytical solutions to the incompressible Navier–Stokes equations are presented. They are fully three‐dimensional vector solutions involving all three Cartesian velocity components, each of which depends non‐trivially on all three co‐ordinate directions. Although unlikely to be physically realized, they are well suited for benchmarking, testing and validation of three‐dimensional incompressible Navier–Stokes solvers. The use of such a solution for benchmarking purposes is described.