M. Soria

DIRECT NUMERICAL SIMULATION OF A THREE-DIMENSIONAL NATURAL-CONVECTION FLOW IN A DIFFERENTIALLY HEATED CAVITY OF ASPECT RATIO 4

The majority of the direct numerical simulations of turbulent and transition natural- convection flows in cavities assume two-dimensional behavior. To investigate the effect of the three-dimensional fluctuations, a complete direct numerical simulation has been carried out, in a cavity with aspect ratio 4, Raz = 6.4 × 108 , and Pr = 0.71, using a low-cost PC cluster. A description of the parallel algorithm and the methodology used to verify the code and the accuracy of the statistics obtained is presented. The main features of the two- and three-dimensional flows are described and compared. Several first- and second-order statistic distributions have been evaluated, including the Reynolds stress tensor. Significant differences are observed between the second-order statistics of the two- and three- dimensional simulations.

A DIRECT PARALLEL ALGORITHM FOR THE EFFICIENT SOLUTION OF THE PRESSURE-CORRECTION EQUATION OF INCOMPRESSIBLE FLOW PROBLEMS USING LOOSELY COUPLED COMPUTERS

The numerical simulation of time-accurated complex flows needs large computational resources. For the case of incompressible flows, the solution of the pressure-correction equation is typically the main bottleneck, especially on loosely coupled parallel computers such as PC clusters. An algorithm intended to solve this problem is presented. It is a variant of the Schur complement method that uses direct solvers for each subdomain and for the interface equation. The inverse of the interface matrix is evaluated and stored in parallel. Simulation of turbulent natural convection is used as a benchmark to show its potential and limitations.

Analysis of Different Numerical Schemes for the Resolution of Convection-Diffusion Equations using Finite-Volume Methods on Three-Dimensional Unstructured Grids. Part II: Numerical Analysis

ABSTRACT Based on the numerical criteria/schemes for the evaluation of both the diffusion and convection terms in the convection-diffusion equations presented in the companion article (Part I), a comprehensive numerical study is presented considering eight different test problems and more than 1,800 test cases. All the 3-D unstructured meshes generated are clearly defined through their most important parameters (number of grid nodes, departure from orthogonality, smoothness, grid expansion ratios, grid aspect ratios). Numerical criteria are analyzed individually and within the convection-diffusion equation using prescribed velocity fields. Most of the test cases are specified in such a way that analytical solutions can be obtained. Therefore, discretization errors can be evaluated exactly, considering the different numerical criteria and model parameters. The results presented show the possibilities and drawbacks of the numerical criteria tested in terms of accuracy, computational effort, and convergence characteristics.

A DIRECT SCHUR-FOURIER DECOMPOSITION FOR THE SOLUTION OF THE THREE-DIMENSIONAL POISSON EQUATION OF INCOMPRESSIBLE FLOW PROBLEMS USING LOOSELY COUPLED PARALLEL COMPUTERS

Parallel computers based on PC-class hardware (Beowulf clusters) provide a matchless computing power per cost unit. However, their network performance tends to be too low for standard parallel computational fluid dynamics (CFD) algorithms. A relevant example is the solution of the Poisson equations. The subject of this article is a direct Schur-Fourier decomposition (DSFD) algorithm that, for certain three-dimensional flows, produces an accurate solution of each Poisson equation with just one message, providing speed-ups of at least 24 in a low-cost PC cluster with a conventional network and 36 processors. Direct Numerical Simulation (DNS) of turbulent natural convection flow is used as a benchmark problem.

Effect of contaminant properties and temperature gradients on the efficiency of transient gaseous contaminant removal from an enclosure : a numerical study

Abstract This paper reports the results of a numerical study on the transient removal of a contaminant from a two-dimensional enclosure with one inlet and one outlet. The influence of buoyancy forces due to thermal and concentration gradients, contaminant diffusivity, inlet velocity and outlet disposition over the cleaning-time are studied. The governing equations of the laminar flow (continuity, momentum, energy and contaminant concentration) are solved by means of the SIMPLEC algorithm. Several simulations of the same test case have been made, using two numerical schemes : PLDS and SMART, in order to determinate which one provides better performances. For isothermal situations, the time required to remove the contaminant is studied parametrically as a function of the outlet position and the governing dimensionless numbers (Reynolds number, Schmidt number and solutal Rayleigh number) , while the effect of horizontal temperature differences is studied in several situations in which it plays an important role. Buoyancy forces are found to have a strong influence over the flows and, in consequence, over the cleaning times.

Parallel direct Poisson solver for DNS of complex turbulent flows using Unstructured Meshes

In this paper a parallel direct Poisson solver for DNS simulation of turbulent flows statistically homogeneous in one spatial direction is presented. It is based on a Fourier diagonalization and a Schur decomposition on the spanwise and streamwise directions respectively. Numerical experiments carried out in order to test the robustness and efficiency of the algorithm are presented. This solver is being used for a DNS of a turbulent flow around a circular cylinder at Re = 1 ×104, the size of the required mesh is about 104 M elements and the discrete Poisson equation derived is solved in less than one second of CPU time using 720 CPUs of Marenostrum supercomputer.

Parameter-Free Symmetry-Preserving Regularization Modelling of Turbulent Natural Convection Flows

Since direct numerical simulations of natural convection flows cannot be performed at high Ra-numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the nonlinearity. The regularization method basically alters the convective terms to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yields a novel class of regularizations that restrain the convective production of smaller and smaller scales of motion by means of vortex stretching in an unconditional stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. The regularization model is successfully tested for a 3D natural convection flow in air-filled (Pr = 0.71) differentially heated cavity of height aspect ratio 4 at Ra = 1010 and 1011. Moreover, a method to dynamically determine the regularization parameter (local filter length) is also proposed and tested.