A stabilized semi‐Lagrangian finite element method for natural convection in Darcy flows

2020 ◽  
Author(s):  
Loubna Salhi ◽  
Mofdi El‐Amrani ◽  
Mohammed Seaid
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Lagrangian Finite Element ◽  
Darcy Flows ◽  
Element Method

An efficient iterative algorithm for the natural convection equations based on finite element method

2018 ◽  
Vol 28 (3) ◽  
pp. 584-605 ◽  
Author(s):  
Lei Wang ◽  
Jian Li ◽  
Pengzhan Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Iterative Method ◽  
Error Correction ◽  
Computational Time ◽  
Content Type ◽  
Natural Convection Problem ◽  
New Iterative Method ◽  
Element Method

Purpose This paper aims to propose a new highly efficient iterative method based on classical Oseen iteration for the natural convection equations. Design/methodology/approach First, the authors solve the problem by the Oseen iterative scheme based on finite element method, then use the error correction strategy to control the error arising. Findings The new iterative method not only retains the advantage of the Oseen scheme but also saves computational time and iterative step for solving the considered problem. Originality/value In this work, the authors introduce a new iterative method to solve the natural convection equations. The new algorithm consists of the Oseen scheme and the error correction which can control the errors from the iterative step arising for solving the nonlinear problem. Comparing with the classical iterative method, the new scheme requires less iterations and is also capable of solving the natural convection problem at higher Rayleigh number.

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