A TV-Based Iterative Regularization Method for the Solutions of Thermal Convection Problems (Communications in Computational Physics, 2013)
Linear/nonlinear and Stokes based-stabilizations for the filter equations fordamping out primitive variable (PV) solutions corrupted by uniformly distributed random noises are numerically studied through the natural convection (NC) as well as themixed convection (MC) environment. The most recognizable filter-scheme is based ona combination of the negative Laplace equation multiplied with the selection of thespatial scale and a linear function in order to preserve the uniqueness of the filteredsolution. A more complicated filter-scheme, based on a Stokes problem which couplesa filtered velocity and a filtered (artificial) pressure (or Lagrange multiplier) in orderto 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 imagediffusion, well preserved feature flow patterns from the corrupted NC/MC environment are obtained by TV-Stokes based-filters together with the CSS. Our experimentalresults show that our proposed algorithms are effective and efficient in eliminatingthe unwanted spurious oscillations and preserving the accuracy of thermal convectivefluid flows.