Numerical investigation using an exact solution of the effects of non-solenoidality of the viscous terms on the incompressible flow

We examine effects of the divergence of the viscous terms on the numerical results of an incompressible flow by using an exact solution of the governing equation. When the Poisson equation is solved using fractional steps, the divergence in the velocity field may have nonzero magnitude. It should be noted that the divergence of the viscous terms can be larger than that of the velocity field. We use an exact solution, which is commonly used for benchmarking, to examine the effects of the divergence of the viscous terms. The divergence of the viscous terms affects the equilibrium relations found in the exact solution. In the present numerical results, the divergence of the viscous terms reduces the rate of decay of the kinetic energy and the pressure, and it also causes some harmonic waves in the flow field. We examine these results quantitatively by using approximations to the numerical results. Skewness and kurtosis factors of the physical quantities are also affected by the divergence of the viscous terms. These results show that the divergence of the viscous terms significantly affects the flow field.