Volume 14, Issue 4
A TV-based Iterative Regularization Method for the Solutions of Thermal Convection Problems

Eric T. Chung & Jeff C.-F. Wong

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

Published online: 2013-10

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  • Abstract

Linear/nonlinear and Stokes based-stabilizations for the filter equations for damping outprimitive variable(PV)solutions corruptedby uniformly distributedrandom noises arenumerically 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 basedfilters 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.


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@Article{CiCP-14-1120, author = {Eric T. Chung and Jeff C.-F. Wong}, title = {A TV-based Iterative Regularization Method for the Solutions of Thermal Convection Problems}, journal = {Communications in Computational Physics}, year = {2013}, volume = {14}, number = {4}, pages = {1120--1146}, abstract = {

Linear/nonlinear and Stokes based-stabilizations for the filter equations for damping outprimitive variable(PV)solutions corruptedby uniformly distributedrandom noises arenumerically 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 basedfilters 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.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.270212.310113a}, url = {http://global-sci.org/intro/article_detail/cicp/7196.html} }
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