Page 200 - Basic Structured Grid Generation

Moving grids and time-dependent co-ordinate systems 189

which is similar to eqn (1.102). The required second derivatives are
2
2
∂ x ∂ x
= = 0,
∂t∂ξ ∂t∂η
2
2
2
∂ y ∂ y a ∂ y ∂y a
= l(1 − η) , =− . (7.49)
∂t∂ξ ∂t∂x ∂t∂η ∂t
Hence from eqn (7.48) we obtain
1 = 1 = 1 = 1 = 0,
10 01 20 02
2
∂ y a
2
2 10 = 01 = l(y b − y a ) −1 (1 − η) , (7.50)
∂t∂x
2
2 20 = 02 =−(y b − y a ) −1 ∂y a .
∂t
In this example the moving grid has been generated essentially by algebraic interpola-
tion from the known moving boundaries.