Implicit finite-difference method for the calculation of unsteady transonic potential flow about 2D airfoils: A discussion

Implicit finite-difference method for the calculation of unsteady transonic potential flow about 2D airfoils: A discussion

van der Vooren, J.
Schippers, H.

National Aerospace Laboratory NLR

1983-09-23

A thorough discussion of the mathematical modelling of unsteady transonic flow is presented. Starting from the Euler equations potential theory is derived and applied to the flow about a 2D airfoil. Motions considered include rigid body motions as well as deformations of the airfoil itself. The full-potential equation is formulated on curvilinear coordinates maintaining strong conservation form. Ample attention is given to the boundary conditions on the airfoil, the wake conditions and radiation type far-field conditions. The paper is completed with the description of a numerical method based upon time-linearization of the differential equation upto second order accuracy. The resulting equation can be integrated numerically by an implicit locally one-dimensional split method. Finally, the approximation of spatial derivatives by fully conservative finite difference schemes employing mass-flux splitting for the capture of shocks is discussed. Numerical results for the steady flow about the Onera M6 airfoil illustrate that an Engquist-Osher type scheme at the sonic line is a prerequisite to rigorously suppress non-physical expansion shocks.

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Nationaal Lucht- en Ruimtevaartlaboratorium

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Aerospace Engineering Reports

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(c) 1983 National Aerospace Laboratory NLR