Abstract
Analysis of the transonic flow past an airfoil can be based on the partial differential equation
for the velocity potential φ. Weak solutions modeling shock waves are calculated by adding artificial viscosity. This can be accomplished with a full conservation form (FCF) of the equation, but a simpler version not in conservation form (NCF) is sometimes more useful [2,9, 10,16,25]. To handle the boundary conditions it is convenient to map the region of flow conformally onto the interior of the unit circle and use polar coordinates r and ω there. The simplest way of introducing artificial viscosity numerically, suggested first by Murman and Cole in a fundamental paper [26], is to use finite difference approximations that are retarded in the direction of the flow. This does not perturb the Neumann boundary condition on φ.
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© 1977 Springer-Verlag Berlin Heidelberg
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Bauer, F., Garabedian, P., Korn, D. (1977). Two-Dimensional Analysis Code. In: Supercritical Wing Sections III. Lecture Notes in Economics and Mathematical Systems, vol 150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48852-8_4
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DOI: https://doi.org/10.1007/978-3-642-48852-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08533-1
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