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A two dimensional euler flow solver on adaptive cartesian grids

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2008
Siyahhan, Bercan
In the thesis work, a code to solve the two dimensional compressible Euler equations for external flows around arbitrary geometries have been developed. A Cartesianmesh generator is incorporated to the solver. Hence the pre-processing can be performed together with the solution within a single code. The code is written in the C++ programming language and its object oriented capabilities have been exploited to save memory in the data structure developed. The Cartesian mesh is formed by dividing squares successively into its four quadrants. The main advantage of using this type of a mesh is the ability to generate meshes around geometries of arbitrary complexity quickly and to adapt the mesh easily based on the solution. The main disadvantage of this method is that the treatment of the cells that are cut by the geometry. For the solution procedure Roe’s method as well as flux vector splitting methods are used for the flux evaluation. The flux vector splitting schemes used are van Leer, AUSM, AUSMD and AUSMV methods. Time discretization is performed using a multi-stage method. To increase the accuracy least squares reconstruction is employed. The code is validated by performing calculations around a NACA0012 airfoil profile. The effect of reconstruction is demonstrated by plotting the pressure coefficient on the airfoil. The distribution obtained using reconstruction is very close to the experimental one while there is a considerable deviation for the case without reconstruction. Also the shock capturing capabilities of different methods have been investigated. In addition the performance of each method is analyzed for flow around an NLR 7301 airfoil with a flap.