scholarly journals Finite volume discretisation for the one-dimensional convection diffusion-dissipation equation

2016 ◽  
Vol 5 (4) ◽  
pp. 206
Author(s):  
Bienvenu ONDAMI
Keyword(s):  
Finite Volume ◽  
Water Table ◽  
Method Of Lines ◽  
Finite Volume Scheme ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Volume Scheme ◽  
The One ◽  
Dissipation Equation

This paper is devoted to analysis of a finite volume scheme for a one-dimensional convection-diffusion-dissipation equation having application in pollution of water table. We analyse a scheme corresponding to a semi-descretization, also called method of lines. Results of umerical experiments using this approach are reported.

scholarly journals On the use of a cell-centered finite-volume scheme on prismatic meshes in boundary layers

2021 ◽  
pp. 1-44
Author(s):  
Pavel Alexeevisch Bakhvalov
Keyword(s):  
Reynolds Number ◽  
Finite Volume ◽  
High Reynolds Number ◽  
Finite Volume Scheme ◽  
Wall Surface ◽  
One Dimensional ◽  
Volume Scheme ◽  
Dimensional Reconstruction ◽  
A Cell ◽  
High Reynolds

We consider the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction and generalize it to anisotropic prismatic meshes suitable for high-Reynolds-number problems. We offer a new algorithm of flux computation based on the reconstruction along the wall surface, whereas in the original schemes it was along the tangent to the wall surface. We also study how does the curvature of mesh elements influence the accuracy if taken into account.

scholarly journals Mixed and Hybrid Finite Element Methods for Convection-Diffusion Problems and Their Relationships with Finite Volume: The Multi-Dimensional Case

2017 ◽  
Vol 9 (1) ◽  
pp. 68 ◽  
Author(s):  
Michel Fortin ◽  
Abdellatif Serghini Mounim
Keyword(s):  
Finite Volume ◽  
Numerical Approximation ◽  
Dimensional Case ◽  
Parabolic Problems ◽  
Finite Volume Schemes ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Hybrid Finite Element ◽  
The One ◽  
Diffusion Problems

We introduced in (Fortin & Serghini Mounim, 2005) a new method which allows us to extend the connection between the finite volume and dual mixed hybrid (DMH) methods to advection-diffusion problems in the one-dimensional case. In the present work we propose to extend the results of (Fortin & Serghini Mounim, 2005) to multidimensional hyperbolic and parabolic problems. The numerical approximation is achieved using the Raviart-Thomas (Raviart & Thomas, 1977) finite elements of lowest degree on triangular or rectangular partitions. We show the link with numerous finite volume schemes by use of appropriate numerical integrations. This will permit a better understanding of these finite volume schemes and the large number of DMH results available could carry out their analysis in a unified fashion. Furthermore, a stabilized method is proposed. We end with some discussion on possible extensions of our schemes.

scholarly journals Numerical Analysis of a Nonlinear Free-Energy Diminishing Discrete Duality Finite Volume Scheme for Convection Diffusion Equations

2018 ◽  
Vol 18 (3) ◽  
pp. 407-432 ◽  
Author(s):  
Clément Cancès ◽  
Claire Chainais-Hillairet ◽  
Stella Krell
Keyword(s):  
Finite Volume ◽  
Diffusion Equations ◽  
Finite Volume Scheme ◽  
Time Behavior ◽  
Convection Diffusion ◽  
Volume Scheme ◽  
Existence Of Positive Solutions ◽  
Long Time ◽  
Nonlinear Form ◽  
Compactness Arguments

AbstractWe propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy/energy dissipation relation. This relation is of paramount importance to capture the long-time behavior of the problem in an accurate way. To enforce it, the linear convection diffusion equation is rewritten in a nonlinear form before being discretized. We establish the existence of positive solutions to the scheme. Based on compactness arguments, the convergence of the approximate solution towards a weak solution is established. Finally, we provide numerical evidences of the good behavior of the scheme when the discretization parameters tend to 0 and when time goes to infinity.

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