ShortleyWeller discretization for Skewed Structured Grids

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Shortley-Weller discretization for Skewed
Structured Grids

• _____Swathi

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Structured Grid
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Skewed Structured Grid
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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.

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• By contrast the set of of boundary points
  must be defined differently from the case of a
  square.

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• 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.

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• 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.

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• One obtains the difference scheme of Shortley and
  Weller

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• 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.

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• Thank you