中国科学技术大学学术报告

题目： Hybrid Weighted Essentially Non-Oscillatory Schemes with
different indicators

报告人: 邱建贤 教授
厦门大学数学科学学院

时间：2011年8月30日 16:30

地点：管理科研楼1518室

摘要:
A key idea in finite difference weighted essentially non-oscillatory (WENO) schemes is a combination of lower
order fluxes to obtain a higher order approximation. The choice of the weight to each candidate stencil, which is a nonlinear function
of the grid values, is crucial to the success of WENO. For the system case, WENO schemes are based on local characteristic
decompositions and flux splitting to avoid spurious oscillation. But the cost of computation of nonlinear weights and local
characteristic decompositions is very high. In this paper, we investigate hybrid schemes of WENO schemes with high order up-wind
linear schemes using different discontinuity indicators and explore the possibility in avoiding the local characteristic decompositions
and the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for
problems with strong shocks. The idea is to identify discontinuity by an discontinuity indicator, then reconstruct numerical flux by
WENO approximation in discontinuous regions and up-wind linear approximation in smooth regions. These indicators are mainly based
on the troubled-cell indicators for discontinuous Galerkin (DG) method which are listed in the paper by Qiu and Shu /{{/em SIAM J.
Sci. Comput. 27 (2005) 995-1013}/}. The emphasis of the paper is on comparison of the performance of hybrid scheme using different
indicators, with an objective of obtaining efficient and reliable indicators to obtain better performance of hybrid scheme to save
computational cost. Detail numerical studies in one- and two-dimensional cases are performed, addressing the issues of
efficiency (less CPU time and more accurate numerical solution), non-oscillatory property.

主办单位：中国科学技术大学数学科学学院

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