Dissertation > Mathematical sciences and chemical > Mechanics > Fluid Mechanics

Construction and Application of High Numerical Perturbation Accuration of WENO Schemes

Author WangXiangYang
Tutor LiMingJun
School Xiangtan University
Course Computational Mathematics
Keywords WENO scheme Euler equation Numerical perturbation withhigh precision reconstruction Richtmyer-Meshkov instability
Type Master's thesis
Year 2012
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The computational fluid dynamics has important applications in scientificcomputing and practical engineering. Numerical schemes with low precision willproduce oscillations in the practical applications. Thus, it is important to increasethe accuracy of the low-level algorithm.In the second chapter of this paper, for the three order WENO finite difer-ence scheme, we make use of the numerical perturbation algorithm presented byGao Zhi to deal with the reconstruction of the numerical perturbation high preci-sion and obtain a new third order WENO numerical perturbation finite diferencescheme with forth order precision. And the numerical examples are presented toprove that the scheme can achieve ideal calculational accuracy. At the sametime, we use it to simulate RMI problems in the refined meshes and obtain goodcomputational results.The finite volume WENO scheme has good robustness, real high precisioncan be obtained in the smooth areas and when solving discontinuous problems, itcan get the numerical solution of non-physical shock. In the third chapter of thispaper, Firstly, we introduce the construction process of five order finite volumeWENO scheme for scalar conservational type equations in2-D. The correspond-ing numerical examples are presented to prove that this scheme has high accuracy,this scheme is used to simulate RMI problems under the action of the shock. Fi-nally, comparing to the computational results of finite diference WENO scheme,we obtain that the fifth finite volume WENO scheme has good performance tocalculate discontinuous problems.

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