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Research of influence of reduced-order boundary on accuracy and solution of interior points

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Abstract

The flow field with a high order scheme is usually calculated so as to solve complex flow problems and describe the flow structure accurately. However, there are two problems, i.e., the reduced-order boundary is inevitable and the order of the scheme at the discontinuous shock wave contained in the flow field as the supersonic flow field is low. It is questionable whether the reduced-order boundary and the low-order scheme at the shock wave have an effect on the numerical solution and accuracy of the flow field inside. In this paper, according to the actual situation of the direct numerical simulation of the flow field, two model equations with the exact solutions are solved, which are steady and unsteady, respectively, to study the question with a high order scheme at the interior of the domain and the reduced-order method at the boundary and center of the domain. Comparing with the exact solutions, it is found that the effect of reduced-order exists and cannot be ignored. In addition, the other two model equations with the exact solutions, which are often used in fluid mechanics, are also studied with the same process for the reduced-order problem.

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Authors and Affiliations

  1. Department of Mechanics, Tianjin University, Tianjin, 300072, China

    Yunlong Li & Wei Cao

Authors
  1. Yunlong Li
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  2. Wei Cao
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Correspondence to Wei Cao.

Additional information

Project supported by the National Key Research and Development Project of China (No. 2016YFA0401200) and the National Natural Science Foundation of China (Nos.11672205 and 11332007)

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Li, Y., Cao, W. Research of influence of reduced-order boundary on accuracy and solution of interior points. Appl. Math. Mech.-Engl. Ed. 38, 111–124 (2017). https://doi.org/10.1007/s10483-017-2153-6

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  • DOI: https://doi.org/10.1007/s10483-017-2153-6

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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