A Karhunen-Loeve-based approach to numerical simulation of transition in Rayleigh-Benard convection

2003-06-01
Tarman, HI
A Karhunen-Loeve ( K - L) basis is generated empirically, using a database obtained by numerical integration of Boussinesq equations representing Rayleigh - Benard convection in a weakly turbulent state in a periodic convective box with free upper and lower surfaces. This basis is then used to reduce the governing partial differential equation (PDE) into a truncated system of amplitude equations under Galerkin projection. In the generation and implementation of the basis, the symmetries of the PDE and the geometry are fully exploited. The resulting amplitude equations are integrated numerically and it is shown that, with the use of the K - L basis in the present formulation, the known dynamics of the flow in the transition region is completely captured.
NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS

Suggestions

A Karhunen-Loeve analysis of turbulent thermal convection
Tarman, Işık Hakan (1996-01-01)
The Karhunen-Loeve (K-L) procedure is applied to a turbulent thermal convection database which is generated numerically through integration of the Boussinesq equation in a periodic box with stress-free boundary conditions using a Fourier collocation spectral method. This procedure generates a complete set of mutually orthogonal functions in terms of which the turbulent flow fluctuation field is represented optimally in the mean square sense. A study is performed ranging from the direct projection of the dat...
Two-way Fourier Split Step Algorithm over Variable Terrain with Narrow and Wide Angle Propagators
Ozgun, Ozlem; Apaydin, Gökhan; Kuzuoğlu, Mustafa; Sevgi, Levent (2010-07-17)
Helmholtz's wave equation can be approximated by means of two differential equations, corresponding to forward and backward propagating waves each of which is in parabolic wave equation (PWE) form. The standard PWE is very suitable for marching-type numerical solutions. The one-way Fourier split-step parabolic equation algorithm (SSPE) is highly effective in modeling electromagnetic (EM) wave propagation above the Earth's irregular surface through inhomogeneous atmosphere. The two drawbacks of the standard ...
A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations
Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01)
In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
A finite element variational multiscale method for the Navier-Stokes equations
Volker, John; Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01)
This paper presents a variational multiscale method (VMS) for the incompressible Navier-Stokes equations which is defined by a large scale space L-H for the velocity deformation tensor and a turbulent viscosity nu(T). The connection of this method to the standard formulation of a VMS is explained. The conditions on L-H under which the VMS can be implemented easily and efficiently into an existing finite element code for solving the Navier - Stokes equations are studied. Numerical tests with the Smagorinsky ...
A comparative study of modeling of radiative heat transfer using mol solution of dom with gray gas, wide-band correlated-k, and spectral line-based weighted sum of gray gases models
Cayan, Fatma Nihan; Selçuk, Nevin (2007-01-01)
A radiation code based on the method of lines (MOL) solution of the discrete ordinates method (DOM) for the prediction of radiative heat transfer in nongray absorbing-emitting media was developed by incorporation of two different gas spectral radiative property models, wide-band correlated-k (WBCK) and spectral line-based weighted sum of gray gases (SLW) models. Predictive accuracy and computational efficiency of the code were assessed by applying it to one- and two-dimensional test problems and benchmarkin...
Citation Formats
H. Tarman, “A Karhunen-Loeve-based approach to numerical simulation of transition in Rayleigh-Benard convection,” NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS, pp. 567–586, 2003, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63843.