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where P and Q are terms that control the point spacing on the interior of the domain. If we transform the above equation by interchanging the roles of the dependent and independent variables, we get where aree-2pre+'r, =-I.I'(Pre+Qr,) aztf -2/#zj +yz,,=- I I(PzE+Qz,) (3.4) a=r + P/= rr + zez, =r+z The above equations are partial differential equations of elliptic type and they can be solved iteratively. 3.2 The Elliptic Solver Eq.(2.23) for the stream function and Eq.(2.26) for the periodic velocity potential are non-linear partial differential equations. The Finite Element Method is used to solve them. The procedure used is that all the nonlinear terms are transposed to the right hand sides of the equations to become the "forcing functions" of the equations. Since the left hand sides are now linear, they can be solved by a finite element method. The RHS is then recomputed based on newly obtained solutions; such a procedure is repeated until the solution converges. Here, we use a 4-node isoparametric element to interpolate the variables. The coordinates r and z are expressed in terms of the coordinates of the four corner nodes by {r}= (1+ )(1+ mi) }N= T } (3.5)PDF Image | Radial Inflow Splitter Blades in Three-Dimensional
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