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326 10. Inviscid Compressible Flow

References

[1] Hirsch, C : Numerical Computation of Internal and External Flows. John Wiley &
Sons, 1990.
[2] Murman, E. M. and Cole, J.D.: Calculation of Plane Steady Transonic Flows, AIAA
J. 9(1), 114-121, 1971.
[3] Jameson, A.: Iterative Solutions of Transonic Flows over Airfoils and Wings, including
flows at Mach 1. Comm. Pure and Applied Mathematics 27, 283-309, 1974.
[4] Jameson, A.: Transonic Potential Flow Calculations using Conservative Form. Pro-
ceedings of the AIAA Second Computational Fluid Dynamics Conference, Hartford,
pp. 148-161, 1975.
[5] Hoist, T.L. and Ballhaus, W. F.: Fast Conservative Schemes for the Full Potential
Equation Applied to Transonic Flows. AIAA J. 17, 145-152, 1979.
[6] Liepmann, H.W. and Roshko, A.: Elements of Gasdynamics. John Wiley & Sons,
1957.

Problems

10-1. Show that, when central difference operators are applied to the TSD
equation, the discretized equations are of similar form whether the conservative
Eq. (10.4.1) or non-conservative Eq. (10.4.2) forms are used.
Hint: write the conservative operator (\ip^) x using the stencil cp x = ^i+1/2 ~~
Vi-1/2 a n d compare your result with the non-conservative operator (fx^fxx writ-
ten with the standard central difference operator 6 xtp = ^ + 1 — ^p%-\.

10-2. Solve the model problem 10.4 by introducing the boundary conditions
through modification of the constants a, 6, c in Eq. (10.5.8), instead of using
halo cells.

10-3. Solve the model Problem 10.4 using the non-conservative full-potential
equation for the case K = 2.5, and compare your results with those obtained
with the TSD equation.

10-4. Examine the effect of using the reverse predictor-corrector steps (10.6.5)-
(10.6.6) on the model Problems 10.11 and 10.14.

10-5. Repeat the model Problems 10.11 and 10.14 for the following inflow/out-
flow boundary conditions: Supersonic/Supersonic, Subsonic/Subsonic, Sub-
sonic/Supersonic.