Abstract
ABSTRACTThe 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
