Transport Schemes in GungHo

2021 ◽  
Author(s):  
James Kent
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Mixed Finite Element ◽  
Method Of Lines ◽  
Finite Volume Methods ◽  
Kutta Method ◽  
Finite Volume Schemes ◽  
Dynamical Core ◽  
Runge Kutta Method ◽  
The Stability

<p>GungHo is the mixed finite-element dynamical core under development by the Met Office. A key component of the dynamical core is the transport scheme, which advects density, temperature, moisture, and the winds, throughout the atmosphere. Transport in GungHo is performed by finite-volume methods, to ensure conservation of certain quantaties. There are a range of different finite-volume schemes being considered for transport, including the Runge-Kutta/method-of-lines and COSMIC/Lin-Rood schemes. Additional horizontal/vertical splitting approaches are also under consideration, to improve the stability aspects of the model. Here we discuss these transport options and present results from the GungHo framework, featuring both prescribed velocity advection tests and full dry dynamical core tests. </p>

scholarly journals Mixed finite element-finite volume methods

2010 ◽  
Vol 17 (3) ◽  
pp. 385-410
Author(s):  
Khadija Zine Dine ◽  
Naceur Achtaich ◽  
Mohamed Chagdali
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Mixed Finite Element ◽  
Finite Volume Methods

Combined mixed finite element and nonconforming finite volume methods for flow and transport in porous media

Analysis ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Omar El Moutea ◽  
Hassan El Amri
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Finite Volume ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Coupled System ◽  
Finite Volume Methods ◽  
Flow Equation ◽  
Heterogeneous Porous Media ◽  
Flow And Transport

Abstract This paper is concerned with numerical methods for a coupled system of two partial differential equations (PDEs), modeling flow and transport of a contaminant in porous media. This coupled system, arising in modeling of flow and transport in heterogeneous porous media, includes two types of equations: an elliptic and a diffusion-convection equation. We focus on miscible flow in heterogeneous porous media. We use the mixed finite element method for the Darcy flow equation over triangles, and for the concentration equation, we use nonconforming finite volume methods in unstructured mesh. Finally, we show the existence and uniqueness of a solution of this coupled scheme and demonstrate the effectiveness of the methodology by a series of numerical examples.

scholarly journals Finite volume schemes for diffusion equations: Introduction to and review of modern methods

2014 ◽  
Vol 24 (08) ◽  
pp. 1575-1619 ◽  
Author(s):  
Jerome Droniou
Keyword(s):  
Finite Volume ◽  
Approximate Solutions ◽  
Finite Volume Methods ◽  
Diffusion Equations ◽  
Maximum Principles ◽  
Finite Volume Schemes ◽  
Real World Applications ◽  
Continuous Equation ◽  
The Stability ◽  
Main Ideas

We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construction principles of the methods, we review some literature results, focusing on two important properties of schemes (discrete versions of well-known properties of the continuous equation): coercivity and minimum–maximum principles. Coercivity ensures the stability of the method as well as its convergence under assumptions compatible with real-world applications, whereas minimum–maximum principles are crucial in case of strong anisotropy to obtain physically meaningful approximate solutions.

scholarly journals A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS

2010 ◽  
Vol 20 (02) ◽  
pp. 265-295 ◽  
Author(s):  
JÉRÔME DRONIOU ◽  
ROBERT EYMARD ◽  
THIERRY GALLOUËT ◽  
RAPHAÈLE HERBIN
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Finite Volume ◽  
Mixed Finite Element ◽  
Finite Volume Methods ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Common Framework ◽  
Finite Element Schemes ◽  
Unified Method

We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids. We prove that the Mimetic Finite Difference scheme, the Hybrid Finite Volume scheme and the Mixed Finite Volume scheme are in fact identical up to some slight generalizations. As a consequence, some of the mathematical results obtained for each of the methods (such as convergence properties or error estimates) may be extended to the unified common framework. We then focus on the relationships between this unified method and nonconforming Finite Element schemes or Mixed Finite Element schemes. We also show that for isotropic operators, on particular meshes such as triangular meshes with acute angles, the unified method boils down to the well-known efficient two-point flux Finite Volume scheme.

Sign in / Sign up

Export Citation Format

Share Document