Parallel multigrid finite volume computation of three-dimensional thermal convection

A massively parallel version of the configuration interaction (CI) section of the COLUMBUS multireference singles and doubles CI (MRCISD) program system is described. In an extension of our previous parallelization work, which was based on message passing, the global array (GA) toolkit has now been used. For each process, these tools permit asynchronous and efficient access to logical blocks of 1- and 2-dimensional (2-D) arrays physically distributed over the memory of all processors. The GAs are available on most of the major parallel computer systems enabling very convenient portability of our parallel program code. To demonstrate the features of the parallel COLUMBUS CI code, benchmark calculations on selected MRCI and SRCI test cases are reported for the CRAY T3D, Intel Paragon, and IBM SP2. Excellent scaling with the number of processors up to 256 processors (CRAY T3D) was observed. The CI section of a 19 million configuration MRCISD calculation was carried out within 20 min wall clock time on 256 processors of a CRAY T3D. Computations with 38 million configurations were performed recently; calculations up to about 100 million configurations seem possible within the near future. © 1997 by John Wiley & Sons, Inc.

A massively parallel version of the configuration interaction (CI) section of the COLUMBUS multireference singles and doubles CI (MRCISD) program system is described. In an extension of our previous parallelization work, which was based on message passing, the global array (GA) toolkit has now been used. For each process, these tools permit asynchronous and efficient access to logical blocks of 1- and 2-dimensional (2-D) arrays physically distributed over the memory of all processors. The GAs are available on most of the major parallel computer systems enabling very convenient portability of our parallel program code. To demonstrate the features of the parallel COLUMBUS CI code, benchmark calculations on selected MRCI and SRCI test cases are reported for the CRAY T3D, Intel Paragon, and IBM SP2. Excellent scaling with the number of processors up to 256 processors (CRAY T3D) was observed. The CI section of a 19 million configuration MRCISD calculation was carried out within 20 min wall clock time on 256 processors of a CRAY T3D. Computations with 38 million configurations were performed recently; calculations up to about 100 million configurations seem possible within the near future. © 1997 by John Wiley & Sons, Inc.

This paper describes an experimental investigation on unsteady thermal convection flow in a horizontal closed-duct combined with acoustic standing wave induced in the duct. As the amplitude of acoustic standing wave increases, steady circulating streaming caused by nonlinear effect of finite amplitude oscillatory flow appears within every 1/4 wavelength section. It is called acoustic streaming. On the other hand, the thermal convection flow is characterized by Rayleigh number. In the range of high Rayleigh number, the convection current changes to unsteady and turbulent. When a strong acoustic standing wave is combined to the unsteady or turbulent convection flow, the flow pattern of the convection quickly changes to steady circulating flow similar to the acoustic streaming. PIV technique is applied to quantitative analyses of the resultant flow depending on mode of standing wave, sound pressure, and Rayleigh number. The results show that the resultant flow becomes unstable according to increase of Rayleigh number and at lower mode of oscillation.

The parallel multigrid method is expected to play an important role in large-scale scientific computing on post-peta/exa-scale supercomputer systems, and it also includes serial and parallel communication processes which are generally expensive. In the present work, new format for sparse matrix storage based on sliced Ellpack-Itpack (ELL) format is proposed for optimization of serial communication in data transfer through memories, and hierarchical coarse grid aggregation (hCGA) is introduced for optimization of parallel communication by message passing. The proposed methods are implemented for pGW3D-FVM, a parallel code for 3D groundwater flow simulations using the multigrid method, and the robustness and performance of the code was evaluated on up to 4,096 nodes (65,536 cores) of the Fujistu FX10 supercomputer system at the University of Tokyo. The parallel multigrid solver using the sliced ELL format provided performance improvement in both weak scaling (25%–31%) and strong scaling (9%–22%) compared to the code using the original ELL format. Moreover, hCGA provided excellent performance improvement in both weak scaling (1.61 times) and strong scaling (6.27 times) for flat MPI parallel programming model.

Implementations of a Parallel 3D Thermal Convection Software Package

Steady, laminar, natural-convection flow in the presence of a magnetic field in a cavity heated from left and cooled from right is considered. In our formulation of the governing equations, mass, momentum, energy and induction equations are applied to the cavity. To solve the governing differential equations a finite volume code based on PATANKAR's SIMPLER method is utilized. Numerical predictions are obtained for a wide range of Rayleigh number (Ra) and Hartmann number (Ha) at the Prandtl number Pr = 0.733. When the magnetic field is relatively strengthened, the thermal field resembles that of a conductive distribution, and the fluid in much of the interior is nearly stagnant. Further, when the magnetic field is weak and the Rayleigh number is high, the convection is dominant and vertical temperature stratification is predominant in the core region. However, for sufficiently large Ha, the convection is suppressed and the temperature stratification in the core region diminishes. The numerical results show that the effect of the magnetic field is to decrease the rate of convective heat transfer and the average Nusselt number decreases as Hartmann number increases. The results are presented for Rayleigh number from 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> up to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> and are in form of streamlines, isotherms, and Nusselt number for various Rayleigh and Hartman numbers.

The solution of a sparse linear system of equations is the core of the problem in many mathematical models. In this paper a strategy is proposed to reduce the bandwidth of the system matrix, so that direct banded solvers can be used with high efficiency. A combinatorial optimization method is implemented on an IBM SP2 (8 nodes) and on a Cray T3D (64 nodes) to perform a global bandwidth minimization, superior to previous constructive approaches. Examples of applications of the strategy in microwave circuit design demonstrate the efficiency of the method and its parallel implementation, as well as its versatility.KeywordsFinite Element Method AnalysisParallel PlatformBandwidth ReductionSingle Program Multiple DataElectromagnetic CircuitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Two-dimensional flow instability induced by natural convection in a square enclosure with four inner cylinders. Part II: Effect of various positions of inner cylinders

Lattice-Boltzmann simulations of the thermally driven 2D square cavity at high Rayleigh numbers

MHD free convection within trapezoidal cavity with non-uniformly heated bottom wall

We present results from stereoscopic PIV measurements in a Rayleigh-Benard convection (RBC) cell filled with (compressed) air at Rayleigh numbers: Ra = 1.5×104, 2×104, 1×105, 2×105, 5×105, and Prandtl number Pr ' 0.7. The three largest Rayleigh numbers are obtained pressurising the whole set-up including cameras and objective lenses, up to 4.5 bars. The main goal of this study is to reproduce DNS data that are acquired at the same Rayleigh numbers to study far-tail events of the out-of-plane vorticity component (ωz). The measurements are performed in a RBC cell with aspect ratio Γ = W/H = 10, where W is the width and H = 3 cm is the height of the domain. The cell is equipped with a transparent bottom plate heated by a thin oxide layer (for details see Kastner et al. (2018)), which allows us to measure 3C2D velocity fields on ¨a horizontal plane at mid height of the cell. The RBC cell set-up is inserted in the SCALEX facility of TU Ilmenau, a pressure vessel with several optical accesses that can be pressurised up to 10 bars The experiments aim firstly at improving the quality of previous measurements performed in the sameset-up [Kastner et al. (2018), Cierpka et al. (2019)], regarding the accuracy of the out-of-plane velocity ¨component. This has been realised by positioning the cameras at a larger stereo angle (about 25◦), which is possible by placing them inside the pressure vessel. Major challenges of the current measurements are caused by optical distortions due to the temperature gradients that are typical for thermal convection (see Valori (2018), Valori et al. (2019)). Probability Density Functions (PDFs) of ωz from stereo PIV experiments and from DNS data are shown respectively in figure 1(a) and 1(b) for all Rayleigh numbers studied. We can observe that for both kind of data the tails of the PDF becomes wider while increasing the Rayleigh number, which may be connected to intermittency. This crossover from Gaussian to intermittent statistic was recently studied in Valori and Schumacher (2021) from DNS. Figure2(a) shows the temporal evolution of ωz at the position of its largest (extreme) value at Ra = 2.5 × 105, while figure2(b) shows the spatial distribution of ωz at the time of its extreme event in the experiments. The experimental results are able to reproduce well the statistics of DNS data of the same flow, and allow the study of extreme events of ωz.

Unstructured anisotropic mesh adaptation is known to be an efficient way to control discretization errors in computational fluid dynamics simulations. Method verification is required to provide the confidence for routine use in production analysis. The current work aims at verification of anisotropic mesh adaptation for Reynolds-averaged Navier–Stokes simulations over the ONERA M6 wing. The present verification study is performed using four different flow solvers, three different implementations of the metric field, and three mesh mechanics packages. Two of the flow solvers use stabilized finite element discretizations (FUN3D-SFE and general geometry Navier–Stokes), one uses finite volume discretization (FUN3D-FV), and the last one uses mixed finite volume and finite element discretizations (Wolf). The mesh adaptation is based on an error estimator that aims to control the quadratic error term in the linear interpolation of the Mach number. Two sets of adaptations were performed; the first one controls the interpolation error in the norm, and the second one controls the interpolation error in the norm. Convergence studies were performed on the forces and the pitching moment using all four solvers, and the results are compared with previously verified convergence studies on fixed (nonadapted) meshes. Both the forces and pitching moment on adapted meshes are found to be converging to the fine-mesh values faster than those on fixed meshes. In addition to forces and moments, the convergence of surface pressure and skin-friction coefficients at various measurement locations on the wing are also presented. Adapted-mesh surface pressure distributions agree with the fine fixed mesh pressure distributions. Adapted-mesh skin-friction distributions contain high-frequency noise with mean values approaching the fixed mesh pressure skin-friction distributions.

This study numerically investigates the viscous heating mechanism in a nanofluid-filled cavity subjected to external forces applied to the top lid, combined with laminar mixed convection of the nanofluid. The vertical walls of the cavity are assumed to be insulated, non-conductive, and impermeable to mass transfer. The horizontal walls are differentially heated, with the lower wall maintained at a higher temperature while the upper wall remains cooler. The primary objective of this research is to introduce a novel method that accurately incorporates height in the solution of heat transfer equations, using transient analysis for numerical iterations. Although the fluid flow reaches a steady state, the square cavity’s walls are fully insulated, and a constant heat flux is generated by the motion of the top lid. This work aims to analyze the effects of viscous heating in a fully insulated lid-driven cavity with Neumann boundary conditions under both no-slip and free-slip conditions, while varying Rayleigh and Prandtl numbers as independent parameters. The simulations are performed for a specific case where the Prandtl number Pr = 6.2 is fixed, while Rayleigh numbers and the volume fraction of the nanofluid (water mixed with copper nanoparticles) range from 0% to 5%. The time dependent vorticity-stream function and thermal energy equations are discretized and solved using a custom finite volume method combined with the artificial compressibility approach, implemented in MATLAB. Despite viscous heating having a limited effect, the Neumann boundary conditions with no-slip and free-slip assumptions influence heat retention within the insulated cavity. The free-slip condition acts as a lubricant, leading to reduced temperature distribution, particularly under lower Rayleigh numbers and higher Prandtl numbers, compared to the no-slip condition. This is attributed to the free-slip effects under these conditions, which enhance heat dissipation and increase the fluid velocity, further stabilizing the system.

Unsteady analysis of heated inclined fin-plate at an angle of 45° is carried out using ANSYS FLUENT 15. The fin-plate was placed inside a square enclosure with top and bottom walls were adiabatic while the left and right walls were at acooler temperature. The problem was investigated over the complete domain, thevalue of the Prandtl number (Pr) was taken as 0.71. Rayleigh number(Ra) varies from 104 to 106 and aspect ratio chosen was A=0.6 (h/H). Thermal buoyancy was responsible for the heat flow inside the domain. Nusselt number variation, temperature distribution, and flow field were examined by means of isotherm and streamlines. The simulation was affected by various parameters such as Rayleigh number, aspect ratio, fin length. Boussinesq approximation solved by finite volume method and PISO (Pressure-implicit with splitting of operators) is used to investigate heat transfer from finnedplate to the surrounding. Various Engineering applications such as in HVAC, electronic devices etc requires anin-depth understanding of convective heat flow, therefore, free convection is now widely used for designing, durability and reliability of products.

The least square-based finite difference-finite volume (LSFD-FV) method has been developed and successfully applied to solve various two-dimensional flow problems with a high-order of accuracy. In this paper, the extension of the LSFD-FV method to the three-dimensional (3D) case on unstructured grids is presented. Different from other existing high-order methods, the LSFD-FV method combines the good features of the least square-based finite difference (LSFD) scheme for derivative approximation and the finite volume (FV) discretization for conservation of physical laws. Within each control cell, a high-order polynomial resultant from a Taylor series expansion is used to approximate the solution in the FV discretization of governing equations, where the derivatives are approximated by the LSFD scheme. As a result, the mesh-free nature of the LSFD scheme endows the LSFD-FV method with the flexibility on unstructured grids. Additionally, the straightforward algorithm of the LSFD scheme and the direct utilization of the Taylor series polynomial make the LSFD-FV method user-friendly and easy to implement. Furthermore, the inviscid and viscous fluxes are simultaneously evaluated by lattice Boltzmann and gas kinetic flux solvers in this work, which avoids additional and complicated treatment for the viscous discretization. Accuracy studies on unstructured hexahedral and tetrahedral grids validate the third-order of accuracy of the 3D LSFD-FV method. Various 3D incompressible and compressible numerical experiments are also presented. The results show that the proposed method enjoys the higher accuracy than the conventional second-order method on the same mesh. When the same accuracy is achieved, the present high-order method has superior computational efficiency to the second-order counterpart.