Discretization

From FVCOM Wiki

(Difference between revisions)
Jump to: navigation, search
(Created page with "The original version of FVCOM was developed in the σ-coordinate transformation system. The code was subsequently upgraded to the generalized terrain-following coordinate system ...")
(Discretization Stencil)
Line 4: Line 4:
Similar to a triangular finite element method, the horizontal numerical computational domain is subdivided into a set of non-overlapping unstructured triangular cells. An unstructured triangle is comprised of three nodes, a centroid, and three sides (Fig. 3.1). Let N and M be the total number of centroids and nodes in the computational domain, respectively, then the locations of centroids can be expressed as:
Similar to a triangular finite element method, the horizontal numerical computational domain is subdivided into a set of non-overlapping unstructured triangular cells. An unstructured triangle is comprised of three nodes, a centroid, and three sides (Fig. 3.1). Let N and M be the total number of centroids and nodes in the computational domain, respectively, then the locations of centroids can be expressed as:
 +
<math>[X(i),Y(i)], i=1:N</math>
<math>[X(i),Y(i)], i=1:N</math>
and the location of the nodes can be specified as:
and the location of the nodes can be specified as:
 +
<math>[Xn(j),Yn(j)],j=1:M</math>
<math>[Xn(j),Yn(j)],j=1:M</math>

Revision as of 20:16, 13 November 2011

The original version of FVCOM was developed in the σ-coordinate transformation system. The code was subsequently upgraded to the generalized terrain-following coordinate system in 2006. The discretization forms of governing equations have been significantly modified in this new coordinate system. When the non-hydrostatic version of FVCOM was developed, we implemented a semi-implicit solver, so the current version of FVCOM has two options for the time integration: 1) mode-split and 2) semi-implicit. In this chapter, we provide an example of the discrete forms of the hydrostatic FVCOM in the σ-coordinate transformation system for the mode-split solver. The σ-coordinate transformation is one selection of the generalized terrain-following coordinates, so learning the details of the discretization forms in this coordinate system can make users it easy to learn how the generalized terrain-following coordinates work in FVCOM. A brief description of the semi-implicit solver is given in Chapter 4 when the non-hydrostatic solver is introduced. Users, who are interested in learning the details of discretization forms in the generalized terrain-following coordinate system, can examine the source code directly.

Discretization Stencil

Similar to a triangular finite element method, the horizontal numerical computational domain is subdivided into a set of non-overlapping unstructured triangular cells. An unstructured triangle is comprised of three nodes, a centroid, and three sides (Fig. 3.1). Let N and M be the total number of centroids and nodes in the computational domain, respectively, then the locations of centroids can be expressed as:

[X(i),Y(i)],i = 1:N and the location of the nodes can be specified as:

[Xn(j),Yn(j)],j = 1:M

Personal tools