scholarly journals Very high‐order accurate finite volume scheme for the convection‐diffusion equation with general boundary conditions on arbitrary curved boundaries

2018 ◽  
Vol 117 (2) ◽  
pp. 188-220 ◽  
Author(s):  
Ricardo Costa ◽  
João M. Nóbrega ◽  
Stéphane Clain ◽  
Gaspar J. Machado ◽  
Raphaël Loubère
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Finite Volume ◽  
Finite Volume Scheme ◽  
General Boundary Conditions ◽  
Curved Boundaries ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Volume Scheme ◽  
Very High

scholarly journals Nonlinear Finite Volume Scheme Preserving Positivity for 2D Convection-Diffusion Equations on Polygonal Meshes

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Bin Lan ◽  
Jianqiang Dong
Keyword(s):  
Finite Volume ◽  
Upper Bound ◽  
Finite Volume Scheme ◽  
Polygonal Meshes ◽  
Present Scheme ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Volume Scheme ◽  
Arbitrary Convex ◽  
Steady Convection

In this paper, a nonlinear finite volume scheme preserving positivity for solving 2D steady convection-diffusion equation on arbitrary convex polygonal meshes is proposed. First, the nonlinear positivity-preserving finite volume scheme is developed. Then, in order to avoid the computed solution beyond the upper bound, the cell-centered unknowns and auxiliary unknowns on the cell-edge are corrected. We prove that the present scheme can avoid the numerical solution beyond the upper bound. Our scheme is locally conservative and has only cell-centered unknowns. Numerical results show that our scheme preserves the above conclusion and has second-order accuracy for solution.

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