Wolf Dynamics - Multiphysics simulations, optimization, and data analytics

OPENFOAM VALIDATION CASES

Taylor-Green Vortex

The Taylor–Green vortex solution is a classical case used for testing and validation of spatial and temporal accuracy of CFD solvers.

In 2D, the Taylor-Green vortex has the following analytical solution,

In this case, we solve the governing equations in a square domain with a length equal to $$2 \pi$$. The arbitrary constant $$k$$ is equal to 1, and  $$\rho$$ and  $$\nu$$ are equal to 1.  The simulation was run until reaching a physical time (t) equal to 0.3 seconds.

 Comparison of numerical and analytical solutions for pressure field (p).  Left figure: error (p analytical - p numerical). Right figure: contours of pressure field (numerical and analytical). Physical time equal to 0.3 seconds.

 Comparison of numerical and analytical solutions for velocity field (U).  Left figure: error (U analytical - U numerical). Right figure: contours of velocity field (numerical and analytical). Physical time equal to 0.3 seconds.

 Left figure:  comparison of numerical and analytical solutions of pressure field. Right figure: comparison of numerical and analytical solutions of velocity field. The sampling was done in the left boundary (a vertical line). Physical time equal to 0.3 seconds.

The solution initialization was implemented using codeStream, and the analytical solution was computed within paraview. The solver used was pisoFoam (but pimpleFoam or icoFoam can be used as well), and different mesh resolution and discretization schemes were tested (space and time).

References:

Taylor, G. I. and Green, A. E., Mechanism of the Production of Small Eddies from Large Ones, Proc. R. Soc. Lond. A, 158, 499–521 (1937).

Kim, J. and Moin, P., Application of a fractional-step method to incompressible Navier–Stokes equations, J. Comput. Phys., 59, 308–323 (1985).

Chorin, A. J., Numerical solution of the Navier–Stokes equations, Math. Comp., 22, 745–762 (1968).

Download here the case file.