Stability and accuracy studies on a second-order method of characteristics scheme for three-dimensional, steady, supersonic flow
A new explicit method of characteristics (MOC) numerical scheme for three-dimensional steady flow has been developed which has second-order accuracy. A complete numerical algorithm has been developed for computing internal supersonic flows. A comprehensive stability analysis was conducted in which both the Courant-Friedrichs-Lewy (CFL) stability criterion and the von Neumann stability analysis were applied. Although necessary and sufficient criteria for stability exist only for linear difference equations and analytic initial data, experience has indicated that these same criteria are appropriate for nonlinear systems when applied locally to the linearized form of the equations. This thesis is supported by the results of the present research in which the nonlinear scheme was found to be stable only when the analysis of the linearized system indicated stability. The numerical scheme has been tested for order of accuracy using exact solutions for source flow and Prandtl-Meyer flow. The results of these tests have verified the second-order accuracy of the scheme. Additional tests using axisymmetric flows have shown that the accuracy of the scheme is comparable to that of a proven second-order two-dimensional MOC scheme.
KeywordsMach Number Numerical Scheme Linear Difference Equation Source Flow Hyperbolic Partial Differential Equation
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