Superconsistent collocation methods with applications to convection-dominated convection–diffusion equations

2021 ◽  
Vol 391 ◽  
pp. 113367
Author(s):  
François De l’Isle ◽  
Robert G. Owens
Keyword(s):  
Collocation Methods ◽  
Diffusion Equations ◽  
Convection Diffusion ◽  
Convection Dominated

An assessment of discretizations for convection-dominated convection–diffusion equations

2011 ◽  
Vol 200 (47-48) ◽  
pp. 3395-3409 ◽  
Author(s):  
Matthias Augustin ◽  
Alfonso Caiazzo ◽  
André Fiebach ◽  
Jürgen Fuhrmann ◽  
Volker John ◽  
...  
Keyword(s):  
Diffusion Equations ◽  
Convection Diffusion ◽  
Convection Dominated

A Compact Higher-Order Scheme for Two-Dimensional Unsteady Convection–Diffusion Equations

2019 ◽  
Vol 17 (07) ◽  
pp. 1950025
Author(s):  
Yon-Chol Kim
Keyword(s):  
Stability Analysis ◽  
Numerical Study ◽  
Higher Order ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Order Scheme ◽  
Higher Order Scheme ◽  
Convection Dominated ◽  
Diffusion Problems

In this paper, we study a compact higher-order scheme for the two-dimensional unsteady convection–diffusion problems using the nearly analytic discrete method (NADM), especially, focusing on the convection dominated-diffusion problems. The numerical scheme is constructed and the stability analysis is implemented. We find the order of accuracy of scheme is [Formula: see text], where [Formula: see text] is the size of time steps and [Formula: see text] the size of spacial steps, especially, making clear the relation between [Formula: see text] and [Formula: see text] is according to the different values of diffusion parameter [Formula: see text] through von Neumann stability analysis. The obtained numerical results for several benchmark problems show that our method makes progress in the numerical study of NADM for convection–diffusion equation and is to be effective and helpful particularly in computations for the convection dominated-diffusion equations and, furthermore, valuable in the numerical treatment of many real-world problems such as MHD natural convection flow.

scholarly journals SUPG-YZβ formulation for solving convection-dominated steady linear reaction-convection-diffusion equations

2021 ◽  
Author(s):  
Suleyman Cengizci ◽  
Ömür Uğur ◽  
Natesan Srinivasan
Keyword(s):  
Finite Element ◽  
Computational Study ◽  
Diffusion Equations ◽  
Stabilized Finite Element ◽  
Convection Diffusion ◽  
Linear Reaction ◽  
Additional Stability ◽  
Supg Formulation ◽  
Spurious Oscillations ◽  
Convection Dominated

In this computational study, stabilized finite element solutions of convection-dominated steady linear reaction-convection-diffusion equations are examined. Although the standard Galerkin finite element method (GFEM) is one of the most robust, efficient, and reliable methods for many engineering simulations, it suffers from instability issues in solving convection-dominated problems. To this end, this work deals with a stabilized version of the standard GFEM, called the streamline-upwind/Petrov-Galerkin (SUPG) formulation, to overcome the instability issues in solving such problems. The stabilized formulation is further supplemented with YZβ shock-capturing to provide additional stability around sharp gradients. A comprehensive set of test computations is provided to compare the results obtained by using the GFEM, SUPG, and SUPG-YZβ formulations. It is observed that the GFEM solutions involve spurious oscillations for smaller values of the diffusion parameter, as expected. These oscillations are significantly eliminated when the SUPG formulation is employed. It is also seen that the SUPG-YZβ formulation provides better solution profiles near steep gradients, in general.

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