Implementation and assessment of the generalized Riemann problem method in an unstructured solver

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2022-9

Author

Ayan, Ulaş Canberk

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High-order accuracy in the Computational Fluid Dynamics (CFD) solvers became an important necessity with increasing computational resources and algorithms. Resolving discontinuities and regions where high gradients formed accurately is the main topic for high-order schemes. The Generalized Riemann Problem (GRP) method came to the fore with its ability to improve the accuracy in these regions and discontinuities. With the GRP method, the second-order accuracy is not achieved by the piece-wise linear reconstruction method only but also by time variation of flux and resolved state. In this thesis, the GRP method is implemented in a finite volume, open-source CFD solver. The generalized MINMOD limiter is implemented in the solver and investigated since it is a key ingredient of the GRP method. The robustness and accuracy of the implemented method are tested with five cases in one dimension and compared with analytical solutions and reference solutions. The implemented method is validated for the two-dimensional domain with well-known benchmark tests such as; the inviscid Prandtl-Meyer expansion fan case for evaluating the two-dimensional (2D) performance on rarefaction wave accuracy, inviscid Wedge case for investigating the 2D performance on shock wave accuracy, and RAE 2822 airfoil case for examining the aerodynamic performance for viscous flows. A three-dimensional study is conducted with ONERA M6 Wing. The results are in good agreement with the experimental results and analytical solutions. Finally, an assessment and discussion are presented for the limiter used in the GRP method.

Subject Keywords

GRP, Riemann solver, Godunov method, CFD, High-resolution

URI

https://hdl.handle.net/11511/99716

Collections

Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

U. C. Ayan, “Implementation and assessment of the generalized Riemann problem method in an unstructured solver,” M.S. - Master of Science, Middle East Technical University, 2022.