Commun. Comput. Phys., 14 (2013), pp. 1120-1146.


A TV-Based Iterative Regularization Method for the Solutions of Thermal Convection Problems

Eric T. Chung 1, Jeff C.-F. Wong 1*

1 Department of Mathematics, Lady Shaw Building, The Chinese University of Hong Kong, Shatin, Hong Kong.

Received 27 February 2012; Accepted (in revised version) 31 January 2013
Available online 27 May 2013
doi:10.4208/cicp.270212.310113a

Abstract

Linear/nonlinear and Stokes based-stabilizations for the filter equations for damping out primitive variable (PV) solutions corrupted by uniformly distributed random noises are numerically studied through the natural convection (NC) as well as the mixed convection (MC) environment. The most recognizable filter-scheme is based on a combination of the negative Laplace equation multiplied with the selection of the spatial scale and a linear function in order to preserve the uniqueness of the filtered solution. A more complicated filter-scheme, based on a Stokes problem which couples a filtered velocity and a filtered (artificial) pressure (or Lagrange multiplier) in order to enforce the incompressibility constraint, is also studied. Linear and Stokes based-filters via nested iterative (NI) filters and the consistent splitting scheme (CSS) are proposed for the NC/MC problems. Inspired by the total-variation (TV) model of image diffusion, well preserved feature flow patterns from the corrupted NC/MC environment are obtained by TV-Stokes based-filters together with the CSS. Our experimental results show that our proposed algorithms are effective and efficient in eliminating the unwanted spurious oscillations and preserving the accuracy of thermal convective fluid flows.

AMS subject classifications: 65M60, 76M10

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Key words: Linear/nonlinear differential filter, Stokes differential filters, Leray-alpha model, total-variation regularization.

*Corresponding author.
Email: tschung@math.cuhk.edu.hk (E. T. Chung), jwong@math.cuhk.edu.hk (J. C.-F. Wong)
 

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