Efficient Implementation of High-Order Accurate Numerical by Wanai Li

By Wanai Li

This thesis makes a speciality of the improvement of high-order finite quantity equipment and discontinuous Galerkin equipment, and provides attainable suggestions to a few vital and customary difficulties encountered in high-order equipment, comparable to the shock-capturing method and curved boundary therapy, then applies those how you can clear up compressible flows.

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Extra resources for Efficient Implementation of High-Order Accurate Numerical Methods on Unstructured Grids (Springer Theses)

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The 3rd and 4th order schemes are used to compute the pressure and skin friction distributions. The results are shown in Fig. 10, where the coefficients can match the reference values quite well. 0193176 Fig. 8 1 x Fig. 4 Sound Field Generated by the Flow Around a Circular Cylinder This test case concerns about the sound field generated by the unsteady Kármon street vortex. 2. Since the pressure fluctuation computation requires high accuracy numerical schemes, the 4th order FV scheme is used in the computation where the curved boundary is approximated using 3rd order polynomials for each segment.

13) show that the SR can be constructed analytically. Therefore, the SR is very efficient, in fact, much more efficient than performing a new reconstruction on a manually selected stencil. 3 The Quadrature-Free K-Exact WENO Limiters The WENO scheme gains great success on structured grids. For the unstructured meshes, there are two types of WENO schemes designed. In the first type of WENO schemes (referred to as WENO-1 hereafter) [13–15], the order accuracy of the WENO reconstruction is the same as that of the reconstruction on each candidate stencil.

The TVD-MUSCL discretization captures the discontinuities in very high resolution but is difficult to be applied directly on unstructured grids. The BAP of Choi and Liu [18] is a limiting procedure that can suppress the oscillation near the discontinuity and can be applied on unstructured grids. 23) where L is defined by L(a0 , a1 ) = B −1 ⎤ ⎦ B(a0 ) + B(a1 ) . 4 The WBAP Limiters 51 The function B is called the biased function. There are many possible biased functions, and one example is B(x) = √ x 1+ x2 x , B −1 (x) = √ .

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