ISSN 2079-3537      

Scientific Visualization
Issue Year: 2014
Quarter: 2
Volume: 6
Number: 2
Pages: 1 - 20
Authors: I. Shirokov (Russian Federation), T. Elizarova (Russian Federation)
Address: I. Shirokov
Lomonosov Moscow State University, Moscow, Russian Federation
T. Elizarova
Keldysh Institute of Applied Mathematics RAS, Moscow, Russian Federation
Abstract: We report the results of numerical modeling and visualization for the classical Taylor–Green vortex decay problem basing on smoothed gas dynamic equation system – namely quasi- gas dynamic (QGD) equations for viscous compressible gas flow. QGD system can be obtained by temporal averaging of Navier-Stokes system and differs form it by strongly non-linear terms with the small coefficient that has the dimension of time. The QGD system determines the temporal evolution of the gas density, velocity, and pressure as functions of Eulerian coordinates and time. The temperature, pressure, and density are related by the ideal gas state equation. The Taylor–Green vortex decay is examined for nitrogen at normal temperature with Mach number equal to 0.1. Variations in the Reynolds number are produced by varying the flow density and pressure.
The QGD system is approximated by an explicit time-differencing scheme. All spatial derivatives are approximated by central differences to second-order accuracy, and the time derivatives are approximated with the first-order accuracy. The computation based on the explicit scheme corresponds to the temporal evolution of the gas dynamic flow. The boundary conditions are periodic in three directions, which means that a system of identical Taylor–Green vortices is contained in an unbounded domain. The periodic boundary conditions are implemented by introducing shadow cells adjacent to the physical boundary.
The computations were carried out on the multiprocessor computer system K-100 at the Keldysh Institute of Applied Mathematics of the Russian Academy of Science. The numerical algorithm was parallelized as based on a decomposition of the computational domain by planes x=const with the use of the MPI standard. Our code is portable across different platforms supporting the C language and the MPI standard.
It is shown that QGD equations provide a uniform adequate numerical simulation of both laminar and turbulent evolution of the vortex in a unified manner without varying the parameters of the algorithm. For high Reynolds numbers (Re=1600) numerical results show the transition to turbulence, with the creation of small scale structures accomplished by special evolution of the kinetic energy decay with Kolmogorov scaling of kinetic energy spectrum. For small Reynolds numbers (Re=280 and 100) vortex decay remains laminar. Comparison with reference data show, that for turbulent flow QGD method requires less grid points to achieve the same accuracy compared with different variants of high-order DNS methods. On identical spatial grids at Re=1600, the QGD algorithm was found to be more accurate than the LES method with the Smagorinsky subgrid-scale eddy viscosity model.
The evolution of the vortex flow obtained in the numerical simulation is visualized by depicting the z-component of the vorticity in a 3D domain. Data visualization demonstrates a development of the 3D flow structures and gives opportunity to compare them for laminar and turbulent flow regimes, including a laminar-turbulent transition.
Language: English

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