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Grid Average and Nodal Value in High Order Scheme

Published online by Cambridge University Press:  02 August 2018

Z. Liu  and
Q. Cai
Z. Liu
Affiliation:
College of Engineering Peking University Beijing, China
Q. Cai*
Affiliation:
Center for Applied Physics and Technology Beijing, China State Key Laboratory for Turbulence and Complex System Beijing, China
*
*Corresponding author (caiqd@pku.edu.cn)
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Abstract

The concepts of nodal value and grid average in cell centered finite volume method (FVM) are clarified in this work, strict distinction between the two concepts in constructing numerical schemes is made, and common fault in misidentifying the two concepts is pointed out. The expansion based on grid average, similar to Taylor’s expansion, is deduced to construct correct scheme in terms of grid average and to obtain modified partial differential equation (MPDE) which determines the order of accuracy of numerical scheme theoretically. Correct high order scheme, taking QUICK (Quadratic Upstream Interpolation for Convective Kinematics) scheme as an example, is constructed in different approaches. Furthermore, the property of interpolation coefficients is analyzed. We also pointed out that for high order schemes, round-off error dominates the absolute error in fine grid and truncation error dominates the absolute error in coarse grid.

Keywords

Grid averageNodal valueHigh order schemeError analysis
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 3 , June 2019 , pp. 335 - 342
Copyright
© The Society of Theoretical and Applied Mechanics 2018 

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References

REFERENCES

Remi, A., Adam, L. and Mario, R., “Construction of Very High Order Residual Distribution Schemes for Steady Inviscid Flow Problems on Hybrid Unstructured Meshes,” Journal of Computational Physics, 230, pp. 4103–4136 (2011).Google Scholar
Brian, P. L., “A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation,” Computer Methods in Applied Mechanics and Engineering, 19, pp.59–98 (1979).Google Scholar
Peter, D. L. and Robert, D. R., “Survey of the Stability of Linear Finite difference equations,” Communications on Pure and Applied Mathematics, 9, pp. 267–293 (1956).Google Scholar
Li, J., Zeng, Q. and Chou, J., “Computational Uncertainty Principle in Nonlinear Ordinary differential Equations,” Science in China Series E: Technological Sciences, 44, 55–74 (2001).Google Scholar
Liu, R. and Shu, Q., Several New Methods on Computational Fluid Dynamics (in Chinese), Science Press (2003).Google Scholar