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By Wanai Li

This thesis makes a speciality of the improvement of high-order finite quantity equipment and discontinuous Galerkin equipment, and offers attainable ideas to a few vital and customary difficulties encountered in high-order equipment, akin to the shock-capturing method and curved boundary remedy, then applies those the way to remedy compressible flows.

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Efficient Implementation of High-Order Accurate Numerical Methods on Unstructured Grids

This thesis makes a speciality of the improvement of high-order finite quantity equipment and discontinuous Galerkin equipment, and offers attainable ideas to a couple of vital and customary difficulties encountered in high-order tools, similar to the shock-capturing method and curved boundary remedy, then applies those ways to remedy compressible flows.

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The SR has been proposed in Sect. 2 from a different perspective to show its construction better. (2) Compactness. From the point of view of practical implementation, the limiting procedure should be as compact as possible. In this chapter, the implementation of the limiter only uses the information of current cell and its direct face neighbors. The compactness of the present procedure relies on the compactness of the SR. The SR is a special continuation of the PR on a neighboring cell. Referring to Fig.

The biased functions of WBAP are also different with those of BAP. By the introduction of the parameter ε, the asymptotic behavior of WBAP can be studied to reveal its mechanism for suppressing the numerical oscillations, which will be discussed in the next section. Remark 3 The WBAP is continuously differentiable. The nondifferentiable limiters are sensitive to small perturbations and may cause slow convergence, while the differentiable one enables a smooth transition from the high-order solution in smooth region to the first order solution in the vicinity of discontinuity.

In the following section, we will improve these two parts to make an easily implemented k-exact WENO scheme. The main features for this scheme are that it uses the efficient secondary reconstruction to construct the candidate polynomials and the quadrature-free way to compute the WENO smooth indicator. 44 3 Accuracy Preserving Limiters for High-Order Finite Volume Methods (a) (b) 1b 1a 1b i 3b 3a 3c 4b 8c 6b i 2a 2b 1a 2c 3b 9c 1c 2b 5b 4c 6b 2a 3a 4b 5b 5c 7c 6c Fig. 1 The secondary reconstruction stencils for the third (left) and fourth (right) order schemes in two-dimensional grids.

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