DNS solver for the Navier-Stokes equations using a spectral method

Homogenous isotropic forced turbulence.

3D-isotropic turbulence, N=512, Re=1600, T=60.

Particle distribution in a 3D-isotropic turbulence, N=512, Re=1600, Tmax = 46 seconds.

See [1] for initialization and [2] for a section on forcing the lowest wavenumbers (k<=kf=8) to maintain a constant turbulent kinetic energy. Parameters related to the initial condition are set such that the kinetic energy matches Taylor-Green initial conditions (a= [9.5,3.5], C=[10000,2600]).

Decaying Taylor Green Vortex.

3D-isotropic turbulence using Re=1600. Taylor Green Vortex. N=512. The planes presented are respectively the xy-, xz- and yz-plane with last accessible index in corresponding axis. The code ran on the Idun cluster using 128 cores for 24 hours.

Computed energy spectrum E(k) for the time range t in [0,42]. Right image shows enstrophy distribution with a peak dissipation at t=9 seconds.

3D-isotropic turbulence using Re=1.6M. Taylor Green Vortex. Left: N=64, Right: N=128.

2D "turbulence" generated from vorticity-streamfunction formulation.

Note: timescales on animations not fixed. See [3] for a presentation of the vorticity-streamfunction formulation and 2D advection diffusion equation and the initial condition to these PDE's.

Left animation: 2D- vorticity field. Re=1600, N=256. Smaller vortices give energy to larger vortices. Right animation: 2D Advection-Diffusion equation solved with an initial concentration distribution. Velocity distribution from the left vorticity field. Diffusion constant set to be 0.0008

References

[1] R. S. Rogallo, "Numerical experiments in homogeneous turbulence," NASA TM 81315 (1981)

[2] A. G. Lamorgese and D. A. Caughey and S. B. Pope, "Direct numerical simulation of homogeneous turbulence with hyperviscosity", Physics of Fluids, 17, 1, 015106, 2005, (https://doi.org/10.1063/1.1833415)

[3] D. Halvorsen, "Studies of Turbulent Diffusion through Direct Numerical Simulation", Specialization Project, NTNU 2019, (https://github.com/danielhalvorsen/Project_Turbulence_Modelling/blob/master/Texts/Project_NTNU_2019.pdf)