A New Numerical Method--Asymptotically Simplified Iteration Method With Patching as Applied to Free and Mixed Convection Heat Transfer
Wang, Duan-Fan
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https://hdl.handle.net/2142/70151
Description
Title
A New Numerical Method--Asymptotically Simplified Iteration Method With Patching as Applied to Free and Mixed Convection Heat Transfer
Author(s)
Wang, Duan-Fan
Issue Date
1988
Doctoral Committee Chair(s)
Chen, Michael M.
Department of Study
Mechanical Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Aerospace
Engineering, Mechanical
Abstract
Conventional boundary layer analysis is restricted to problems in which the transverse momentum equation is not important and the streamwise diffusion terms in the momentum and energy equations are negligible. Full Navier-Stokes methods, on the other hand, are computationally expensive due to slow convergence and the lack of an economical means to simulate the infinity boundary condition. In this work, we present an efficient, exact solver of the full Navier-Stokes and energy equations--Asymptotically Simplified Iteration Method with Patching (ASIMP). It is based on the natural structure of high Rayleigh number free convection, which consists of thin thermal and viscous boundary layers surrounded by a region of negligible viscous and conductive influences. Iteration techniques appropriate for each region are obtained from considerations of the asymptotic behavior at high Rayleigh numbers. Alternate iterations of the inner and outer solutions are patched at a pre-selected patching boundary.
For the inner flow, the solution is based on a Residual Correction Scheme with the residuals evaluated using a higher order finite difference formula, but with the corrections computed from an efficient, lower order marching solution scheme. For the outer flow, the analytical solution of the potential flow is utilized with a residual reduction scheme, the Momentum Sources Method. Upon convergence, the full Navier-Stokes and energy equations are satisfied.
Free and mixed convection heat transfer for a simple geometry and a complex geometry with recirculation regions were investigated using the present method. For second order accuracy, the method was found to be about an order of magnitude faster than a standard first order-accurate elliptic solver based on ADI with upwinding. Although the present method is based on the asymptotic behavior at high Rayleigh numbers, it is found that it can be used to solve problems with Rayleigh numbers as low as 10$\sp2$.
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