ShortleyWeller discretization for Skewed Structured Grids - PowerPoint PPT Presentation
1 / 11
Title:
ShortleyWeller discretization for Skewed Structured Grids
Description:
Shortley-Weller Approximation. Let the boundary value Problem. be given for an arbitrary domain O. ... One obtains the difference scheme of Shortley and Weller: ... – PowerPoint PPT presentation
Number of Views:114
Avg rating:3.0/5.0
Title: ShortleyWeller discretization for Skewed Structured Grids
1
Shortley-Weller discretization for Skewed
Structured Grids
- _____Swathi
2
Structured Grid
3
Skewed Structured Grid
4
Shortley-Weller Approximation
- Let the boundary value Problem
- be given for an arbitrary domain O.
- If one places a square grid of step size h over O
one obtains - As the set of grid points.
5
- By contrast the set of of boundary points
must be defined differently from the case of a
square.
6
- The left ,right ,lower and upper neighbour points
can be boundary points of the following form - We set
- A grid point possessing a
neighbour from ,is said to be near the
boundary. All other points of O are said to be
far from the boundary.
7
(No Transcript)
8
- To set up the difference equation for
- we use the neighbouring points.
- The subscripts to the s are suggest respectively
left, right, under and over. For points far from
the boundary - S1holds for points near the boundary (x,y) at
least one neighbour lies on and the
corresponding distances Sh may be smaller than
h.
9
- One obtains the difference scheme of Shortley and
Weller
10
- The discrete boundary value problem assumes the
form - The five coefficients on the right side of
equation define the matrix elements - The right side of the system of equations.
11
- Thank you
