### An Edge-Based Unstructured Finite Volume Method For The Solution Of Potential Problems.

#### Abstract

The FV formulation is very flexible to deal with any kind of control volume and so

any kind of unstructured meshes, including triangular, quadrilateral, mixed or even dual

meshes. The element-based finite volume methods are usually either a node/vertex centered,

where the unknowns are defined at the nodes of the mesh, or element/cell centered where the

unknowns are defined within the element, usually at the element centroid. Both options have

advantages and disadvantages, but in two-dimensional applications all of them have basically

the same computational cost, which is proportional to the number of edges of the mesh. However,

the node-centered formulation has a strong connection with an edge-based finite element

formulation, when linear triangular elements are used, and requires less memory and

computations when extended for three-dimensional tetrahedral meshes. In this article an unstructured

finite volume node centered formulation, implemented using an edge-based data

structure, is adapted and detailed for the solution of two-dimensional potential problems. The

whole formulation is fully described considering triangular meshes, but it can directly be extended

and applied to any conform two-dimensional meshes. A straight extension for threedimension

is also possible but not attempted here. In order to demonstrate the potentiality of

the presented procedure some model problems are investigated.

any kind of unstructured meshes, including triangular, quadrilateral, mixed or even dual

meshes. The element-based finite volume methods are usually either a node/vertex centered,

where the unknowns are defined at the nodes of the mesh, or element/cell centered where the

unknowns are defined within the element, usually at the element centroid. Both options have

advantages and disadvantages, but in two-dimensional applications all of them have basically

the same computational cost, which is proportional to the number of edges of the mesh. However,

the node-centered formulation has a strong connection with an edge-based finite element

formulation, when linear triangular elements are used, and requires less memory and

computations when extended for three-dimensional tetrahedral meshes. In this article an unstructured

finite volume node centered formulation, implemented using an edge-based data

structure, is adapted and detailed for the solution of two-dimensional potential problems. The

whole formulation is fully described considering triangular meshes, but it can directly be extended

and applied to any conform two-dimensional meshes. A straight extension for threedimension

is also possible but not attempted here. In order to demonstrate the potentiality of

the presented procedure some model problems are investigated.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**