Abstract
A parallel algorithm is presented for the Direct Numerical Simulation of buoyancy- induced flows in open or partially confined periodic domains, containing immersed cylindrical bodies of arbitrary cross-section. The governing equations are discretized by means of the Finite Volume method on Cartesian grids. A semi-implicit scheme is employed for the diffusive terms, which are treated implicitly on the periodic plane and explicitly along the homogeneous direction, while all convective terms are explicit, via the second-order Adams-Bashfort scheme. The contemporary solution of velocity and pressure fields is achieved by means of a projection method. The numerical resolution of the set of linear equations resulting from discretization is carried out by means of efficient and highly parallel direct solvers. Verification and validation of the numerical procedure is reported in the paper, for the case of flow around an array of heated cylindrical rods arranged in a square lattice. Grid independence is assessed in laminar flow conditions, and DNS results in turbulent conditions are presented for two different grids and compared to available literature data, thus confirming the favorable qualities of the method.
Highlights
Introduction and scope Direct NumericalSimulation (DNS) is a powerful research tool for the analysis of turbulent flows
Grid independence is assessed in laminar flow conditions, and Direct NumericalSimulation (DNS) results in turbulent conditions are presented for two different grids and compared to available literature data, confirming the favorable qualities of the method
As soon as care is taken in the choice of spatial and temporal discretization schemes, and grids or modal expansion truncations are adequate, DNS allows for a full 3D representation of all the turbulent scales of a flow in a set of time steps, from which a large amount of information can be extracted on the nature of the simulated turbulent flow [1]
Summary
Doi:10.1088/1742-6596/655/1/012054 where ui indicates the i-th component of the velocity field and the repeated index notation is implied. As in the case of fully developed flow with imposed heat flux, the temperature profile in axial direction is linear, equation (4) can be set as ρgi = ρogi − ρogiβo T − T m(x) − ρogiβoa(x − xo). The time averaged streamwise gradient of the modified pressure is constant [10]. Time-discretizations of the conservation equations are performed according to a three-level scheme, which is semi-implicit (explicit in the homogeneous direction x) for the diffusive terms, and explicit Adams-Bashfort for the advective terms Such a practice is second order accurate in time. A fast direct resolution of the discrete momentum and energy equations at each time-step is made possible by means of Approximate Factorization, while the Poisson problem associated with the pressure-velocity coupling [12] is solved through a fast Poisson solver, based on Matrix Decomposition [13]
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