Abstract
In this paper, we propose an adaptive defect-correction method for natural convection (NC) equations. A defect-correction method (DCM) is proposed for solving NC equations to overcome the convection dominance problem caused by a high Rayleigh number. To solve the large amount of computation and the discontinuity of the gradient of the numerical solution, we combine a new recovery-type posteriori estimator in view of the gradient recovery and superconvergent theory. The presented reliability and efficiency analysis shows that the true error can be effectively bounded by the recovery-based error estimator. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.
Highlights
Natural convection (NC) equations for buoyancy-driven fluid often appear in practical problems
There has been continuous research on NC equations, such as in [8,10,11,12,13], which studied the natural convection of cavity-filled nanofluids
Ahmad [14] studied the effect of viscosity and thermal conductivity on natural convection in exothermic catalytic chemical reactions on curved surfaces, and in [10,15,16,17,18,19], Singh et al considered the effect of factors such as Lorentz force on natural convection
Summary
Natural convection (NC) equations for buoyancy-driven fluid often appear in practical problems. The stationary NC equation is a coupling equation for the incompressible flow and heat transfer process of viscous fluid, in which the incompressible fluid can be characterized by Boussinesq’s approximation In atmospheric dynamics, it is an important forced dissipative nonlinear system. The defect-correction method (DCM) is an iterative improvement technique for improving the accuracy of computational solutions without introducing mesh refinement [28,29,30,31]. In the case of solving linear systems, the well-known iterative refinement method is an example of a defect-correction technique. The approximate solution computed by the local recovered error estimator ||σh − G(σh)||K is closer to the true solution than the approximate solution of the general finite element method. We use the adaptive defect-correction method to solve NC equations. The validity and reliability of our method are verified by numerical experiments
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