In this paper we study the enstrophy transfers in helical turbulence using direct numerical simulation. We observe that the helicity injection does not have significant effects on the inertial-range energy and helicity spectra (∼k −5/3) and fluxes (constants). We also calculate the separate contributions to enstrophy transfers via velocity-to-vorticity and vorticity-tovorticity channels. There are four different enstrophy fluxes associated with the former channel or vorticity stretching, and one flux associated with the latter channel or vorticity advection. In the inertial range, the fluxes due to vorticity stretching are larger than that due to advection. These transfers too are insensitive to helicity injection.
In this paper, we briefly discuss the challenges in porting hydrodynamic codes to futuristic exascale HPC systems. In particular, we sketch the computational complexities of finite difference (FD) method, pseudo-spectral method, and fast Fourier transform (FFT). The global data communication among the compute cores brings down the efficiency of pseudo-spectral codes and FFT. A FD solver involves relatively lower data communication. However, an incompressible FD flow solver has a pressure Poisson equation, whose computation in multigrid scheme is quite expensive. Hence, a comparative study between the two sets of solvers on exascale system would be valuable. In this paper, we report a comparative performance analysis between a FD code and a spectral code on a relatively smaller grid using 1024 compute cores of Shaheen II; here, the FD code yields comparable accuracy to the spectral code, but it is relatively slower. The above features need to be retested on much larger grids with many more processors.
In this paper we employ renormalized viscosity and thermal diffusivity to construct a subgridscale model for large eddy simulation (LES) of turbulent thermal convection. For LES, we add νren ∝ Π 1/3 u (π/∆) −1/3 to the kinematic viscosity; here Πu is the turbulent kinetic energy flux, and ∆ is the grid spacing. In our model, the turbulent Prandtl number is unity. We performed LES of turbulent thermal convection on a 128 3 grid and compare the results with direct numerical simulation (DNS) on a 512 3 grid. There is a good agreement between the LES and DNS results on the evolution of kinetic energy and entropy, spectra and fluxes of velocity and temperature fields, and the isosurfaces of temperature. We also show the capability of our LES to simulate thermal convection at very high Rayleigh numbers and exhibit some results for Ra = 10 18 . arXiv:1806.05916v1 [physics.flu-dyn]
The laws that govern natural systems can often be modelled mathematically using partial differential equations (PDEs). Usually the resultant PDEs are not solvable analytically, leaving numerical solutions as the only recourse to gain useful insights into such systems. As a result, it is important to efficiently calculate numerical solutions of PDEs to further our understanding of such systems. In this paper we briefly describe the design and validation of SARAS, a general-purpose PDE solver based on finite difference method (Anderson, 1995;Ferziger & Peric, 2001).
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