Abstract
This contribution deals with the modern finite volume schemes solving the Euler and Navier-Stokes equations for transonic flow problems. We will mention the TVD theory for first order and higher order schemes and some numerical examples obtained by 2D central and upwind schemes for 2D transonic flows in the GAMM channel or through the SE 1050 turbine cascade of Skoda Plzeñ.
In the next part two new 2D finite volume schemes are presented. Explicit composite scheme on a structured triangular mesh and implicit scheme realized on a general unstructured mesh. Both schemes are used for the solution of inviscid transonic flows in the GAMM channel and the implicit scheme also for the flows through the SE 1050 turbine cascade using both triangular and quadrilateral meshes. For the case of the flows through the SE 1050 turbine we compare the numerical results with the experiment.
The TVD MacCormack method as well as a finite volume composite scheme are extended to a 3D method for solving flows through channels and turbine cascades.
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Fürst, J., Janda, M., Kozel, K. (2001). Finite Volume Solution of 2D and 3D Euler and Navier-Stokes Equations. In: Neustupa, J., Penel, P. (eds) Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8243-9_7
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DOI: https://doi.org/10.1007/978-3-0348-8243-9_7
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