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 jvn August 16, 2004 17:32

Incorrect wave angle, but proper conditions

I've written a program (using MacCormack's explicit predictor/corrector finite difference scheme) to solve for inviscid supersonic flow over a wedge. The solver reads a structured grid, calculates the metrics, sets ICs, then marches in time. For simplicity, I've started with uniform Cartesian grids and a square domain such that the left and upper edges of the domain are inflow, the right edge is outflow, and the lower edge is a solid boundary. Inflow angle is set to -(wedge half angle). Thus, with wedge half angle of 15 degrees and M(inf)=2.0, I expect to get an attached shock, the wave angle between shock and solid boundary being approximately equal to 30 degrees. Instead, that angle keeps going to about 45 degrees... though the properties across the shock rho/rhoinf, p/pinf, M/Minf, etc. are correct. Any suggestions as to the cause of the problem? Thanks, jvn

 Doctor Blade August 17, 2004 10:43

Re: Incorrect wave angle, but proper conditions

Hey!. Are you solving the Prandtl-Mayer expansion of Anderson's book?.

Anyway, I have a similar problem too. Perhaps I could not help you because I have not reach any result yet, not like you. I am solving with the same algorithm the Prandtl-Mayer expansion over a corner. Using strong conservative formulation (I solve in F and G), and arranging the appropriate metrics, when I reach the corner abcissae, the flow does not feel the expansion. I mean, before the corner, F and G flux are constant over the transversal coordinate (named "eta"); all F and G numerical derivatives respect to eta are zero. So that, F and G remains constant until the corner is reached. At the corner, the metric value changes rapidly. But either in Predictor step, where I get zero for F and G derivatives, or Corrector step, where I get another time zero values for F and G derivatives, it does not yield a F longitudinal variation. As a result of cancelling all transversal derivatives straightforward, I obtain F and G are constant over the expansion corner. Altough I thought about the metrics changes, these ones only multiply G and F transversal derivatives OUT of the respective numeric derivatives. Sorry for not being able to help you, but if I solve my problem I may as well be capable of help you then.

 jvn August 17, 2004 13:31

Re: Incorrect wave angle, but proper conditions

I'm not solving Anderson's problem, though it is similar. The two important differences are that 1) my domain is square, whereas Anderson's is not; and 2) I'm solving for a compressive flow with shock, whereas Anderson's problem is for a centered expansion. I could have made the domain similar to JA's, a square domain with clipped corner. Problem is, Abbett's boundary condition does not work well at all unless the turning angle is very small... and my turning angle is 15 degrees. On my domain, I just specify the inflow conditions as uinf=cos(alpha), vinf=sin(alpha), and the BC at wall as rho*u=0.

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