Chemical Engineering Hand Written_Notes_Part_116

Chemical Engineering Hand Written_Notes_Part_116 - 234 5...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
234 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES In two dimension, the simplest element divides region into triangles on which simple polynomials are f tted. For example, u ( x, y ) canbeapprox imatedas (10.75) b u ( x, y )= a + bx + cy where vertices a, b, c can be expressed in terms of values of b u ( x, y ) at the tri- angle vertices. For example, consider triangle de f ned by ( x i ,y j ) , ( x i +1 ,y j ) and ( x i ,y j +1 ) . The value of the approximate solution at the corner points is denoted by b u i,j = b u ( x i ,y j ); b u i +1 ,j = b u ( x i +1 ,y j ); b u i,j +1 = b u ( x i ,y j +1 ) Then, b u ( x, y ) canbewr ittenintermso fshapefunct ionsasfo l lows b u ( x, y )= b u i,j + b u i +1 ,j b u i,j h ( x x i,j )+ b u i,j +1 b u i,j h ( y y i,j ) (10.76) = b u i,j 1 ( x x i,j ) h ( y y i,j ) h ¸ + b u i +1 ,j ( x x i,j ) h ¸ + b u i,j +1 ( y y i,j ) h ¸ (10.77) Now, coe
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

Page1 / 2

Chemical Engineering Hand Written_Notes_Part_116 - 234 5...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online