Chemical Engineering Hand Written_Notes_Part_116

# Chemical Engineering Hand Written_Notes_Part_116 - 234 5...

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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

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## 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.

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Chemical Engineering Hand Written_Notes_Part_116 - 234 5...

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