Extensions to Karhunen-Loeve based approximation of complicated phenomena

Extensions to the Karhunen-Loeve transform applied to complicated phenomena are demonstrated on Rayleigh-Benard thermal convection phenomena. The extensions deal with the role of the mean flow, and with the enhancement of the robustness of the Karhunen-Loeve basis when used for a range of parameter values, such as Rayleigh number, other than the particular values at which Karhunen-Loeve basis is generated. (C) 1998 Elsevier Science S.A.


Selçuk, Nevin (1988-07-01)
Three flux-type models for three-dimensional radiative heat transfer were applied to the prediction of the radiative flux density and the source term of a box-shaped enclosure problem based on data reported previously on a large-scale experimental furnace with steep temperature gradients. The models, which are a six-term discrete ordinate model and two Schuster-Schwarzschild type six-flux models, were evaluated from the viewpoints of both predictive accuracy and computational economy by comparing their pred...
A numerical study on magneto-hydrodynamic mixed convection flow
Bozkaya, Canan (2014-01-01)
This paper, describes a study conducted to numerically investigate the two-dimensional, steady, laminar, magneto-hydrodynamic mixed convection flow and heat transfer characteristics in a lid-driven enclosure beneath an externally applied magnetic field. A solid square block is placed inside the cavity. The governing equations in the form of a stream function-vorticity-temperature formulation are solved numerically using the dual reciprocity boundary element method with constant elements. Treatment of nonlin...
A new framework for simulation of heat treatments
Şimşir, Caner; Gür, Cemil Hakan (Inderscience Publishers, 2010-12-01)
In this study, a mathematical framework based on finite element method (FEM) capable of predicting temperature history, evolution of phases and internal stresses during thermal treatment of metals and alloys was developed. The model was integrated into the commercial FEA software MSC.Marc® by user subroutines. The accuracy of the model was verified by simulating the quenching of eccentrically drilled steel cylinders. Simulation results were justified via SEM observations and XRD residual stress measurements.
A theoretical framework for comprehensive modeling of steadily fed evaporating droplets and the validity of common assumptions
Akkus, Yigit; ÇETİN, BARBAROS; Dursunkaya, Zafer (Elsevier BV, 2020-12-01)
A theoretical framework is established to model the evaporation from continuously fed droplets, promising tools in the thermal management of high heat flux electronics. Using the framework, a comprehensive model is developed for a hemispherical water droplet resting on a heated flat substrate incorporating all of the relevant transport mechanisms: buoyant and thermocapillary convection inside the droplet and diffusive and convective transport of vapor in the gas domain. At the interface, mass, momentum, and...
Numerical study of Rayleigh Bènard thermal convection via solenoidal bases
Yıldırım, Cihan; Tarman, Işık Hakan; Department of Engineering Sciences (2011)
Numerical study of transition in the Rayleigh-B\'enard problem of thermal convection between rigid plates heated from below under the influence of gravity with and without rotation is presented. The first numerical approach uses spectral element method with Fourier expansion for horizontal extent and Legendre polynomal for vertical extent for the purpose of generating a database for the subsequent analysis by using Karhunen-Lo\'eve (KL) decomposition. KL decompositions is a statistical tool to decompose the...
Citation Formats
I. H. Tarman, “Extensions to Karhunen-Loeve based approximation of complicated phenomena,” COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, vol. 155, no. 3-4, pp. 359–368, 1998, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/92575.