A fourth order accurate finite volume scheme for numerical simulations of turbulent Rayleigh–Bénard convection in cylindrical containers

2005 ◽  
Vol 333 (1) ◽  
pp. 17-28 ◽  
Author(s):  
Olga Shishkina ◽  
Claus Wagner
Keyword(s):  
Numerical Simulations ◽  
Finite Volume ◽  
Fourth Order ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Direct numerical simulations of Rayleigh–Bénard convection in water with non-Oberbeck–Boussinesq effects

2019 ◽  
Vol 881 ◽  
pp. 1073-1096 ◽  
Author(s):  
Andreas D. Demou ◽  
Dimokratis G. E. Grigoriadis
Keyword(s):  
Numerical Simulations ◽  
Two Dimensions ◽  
Direct Numerical Simulations ◽  
Wall Region ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Near Wall

Rayleigh–Bénard convection in water is studied by means of direct numerical simulations, taking into account the variation of properties. The simulations considered a three-dimensional (3-D) cavity with a square cross-section and its two-dimensional (2-D) equivalent, covering a Rayleigh number range of $10^{6}\leqslant Ra\leqslant 10^{9}$ and using temperature differences up to 60 K. The main objectives of this study are (i) to investigate and report differences obtained by 2-D and 3-D simulations and (ii) to provide a first appreciation of the non-Oberbeck–Boussinesq (NOB) effects on the near-wall time-averaged and root-mean-squared (r.m.s.) temperature fields. The Nusselt number and the thermal boundary layer thickness exhibit the most pronounced differences when calculated in two dimensions and three dimensions, even though the $Ra$ scaling exponents are similar. These differences are closely related to the modification of the large-scale circulation pattern and become less pronounced when the NOB values are normalised with the respective Oberbeck–Boussinesq (OB) values. It is also demonstrated that NOB effects modify the near-wall temperature statistics, promoting the breaking of the top–bottom symmetry which characterises the OB approximation. The most prominent NOB effect in the near-wall region is the modification of the maximum r.m.s. values of temperature, which are found to increase at the top and decrease at the bottom of the cavity.

Turbulent Rayleigh–Bénard convection in a near-critical fluid by three-dimensional direct numerical simulation

2009 ◽  
Vol 619 ◽  
pp. 127-145 ◽  
Author(s):  
G. ACCARY ◽  
P. BONTOUX ◽  
B. ZAPPOLI
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Thermal Balance ◽  
Transition To Turbulence ◽  
Convective Structures ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper presents state of the art three-dimensional numerical simulations of the Rayleigh–Bénard convection in a supercritical fluid. We consider a fluid slightly above its critical point in a cube-shaped cell heated from below with insulated sidewalls; the thermodynamic equilibrium of the fluid is described by the van der Waals equation of state. The acoustic filtering of the Navier–Stokes equations is revisited to account for the strong stratification of the fluid induced by its high compressibility under the effect of its own weight. The hydrodynamic stability of the fluid is briefly reviewed and we then focus on the convective regime and the transition to turbulence. Direct numerical simulations are carried out using a finite volume method for Rayleigh numbers varying from 106 up to 108. A spatiotemporal description of the flow is presented from the convection onset until the attainment of a statistically steady state of heat transfer. This description concerns mainly the identification of the vortical structures in the flow, the distribution of the Nusselt numbers on the horizontal isothermal walls, the structure of the temperature field and the global thermal balance of the cavity. We focus on the influence of the strong stratification of the fluid on the penetrability of the convective structures in the core of the cavity and on its global thermal balance. Finally, a comparison with the case of a perfect gas, at the same Rayleigh number, is presented.

scholarly journals Comparison of computational codes for direct numerical simulations of turbulent Rayleigh–Bénard convection

2018 ◽  
Vol 166 ◽  
pp. 1-8 ◽  
Author(s):  
Gijs L. Kooij ◽  
Mikhail A. Botchev ◽  
Edo M.A. Frederix ◽  
Bernard J. Geurts ◽  
Susanne Horn ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

scholarly journals Performance of parallel-in-time integration for Rayleigh Bénard convection

2020 ◽  
Vol 23 (1-4) ◽  
Author(s):  
Andrew Clarke ◽  
Chris Davies ◽  
Daniel Ruprecht ◽  
Steven Tobias ◽  
Jeffrey S. Oishi
Keyword(s):  
Numerical Simulations ◽  
High Performance ◽  
Fundamental Problem ◽  
Time Integration ◽  
Time Algorithm ◽  
Bénard Convection ◽  
Benard Convection ◽  
Computational Resources ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractRayleigh–Bénard convection (RBC) is a fundamental problem of fluid dynamics, with many applications to geophysical, astrophysical, and industrial flows. Understanding RBC at parameter regimes of interest requires complex physical or numerical experiments. Numerical simulations require large amounts of computational resources; in order to more efficiently use the large numbers of processors now available in large high performance computing clusters, novel parallelisation strategies are required. To this end, we investigate the performance of the parallel-in-time algorithm Parareal when used in numerical simulations of RBC. We present the first parallel-in-time speedups for RBC simulations at finite Prandtl number. We also investigate the problem of convergence of Parareal with respect to statistical numerical quantities, such as the Nusselt number, and discuss the importance of reliable online stopping criteria in these cases.

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