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Grid Average and Nodal Value in High Order Scheme

Published online by Cambridge University Press:  02 August 2018

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
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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.

Type
Research Article
Copyright
© The Society of Theoretical and Applied Mechanics 2018 

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References

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