Progress on unstructured-grid based high-order CFD method

Yang, Hong
Major Professor
Zhi-jian Wang
Committee Member
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Aerospace Engineering
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Aerospace Engineering

Several new methods have been developed to meet the critical and diversified challenges in the state-of-art unstructured-grids based high-order methods for 3D real-world applications, including 1) parameter-free high-order generalized moment limiter for arbitrary mesh; 2) efficient line implicit method; 3) efficient quadrature-free SV method; 4) novel high-order mesh generation method for 3D hexahedral mesh. The parameter-free high-order generalized moment limiter does not need any user-specified free parameter to detect the discontinuities and exclude the smooth extrema. The present limiter has been designed to be naturally generic, compact, and efficient, which can be applied for arbitrary mesh and general unstructured-grids based high-order methods. The present low-storage line implicit BLU-SGS method significantly overcomes the anisotropy stiffness due to highly stretched wall grids in high Reynolds number flows. Improved robustness and up to 3 times of savings on CPU time have been demonstrated comparing with the cell BLU-SGS solver. This line implicit method preserves the favorable feature of high compactness from the cell BLU-SGS method, and can be programmed as a black box so as to be easily applied in general high-order methods. The quadrature-free SV method has improved the original SV method by replacing the large number of quadrature for face integrals in 3D case with many less nodal operations based on analytical shape functions. Finally for high-order unstructured mesh generation, the present novel and fully automatic algorithm guarantee to resolve the self-intersection problem for non-linear quadrilateral or hexahedral mesh with strong robustness. The algorithm also offers the advantage of correcting grid self-intersection without changing the basic aspect ratio of the original grids or degrading the original grid quality.