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The Parabolic Spline Method (PSM) for conservative transport problems

✍ Scribed by M. Zerroukat; N. Wood; A. Staniforth

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
235 KB
Volume
51
Category
Article
ISSN
0271-2091

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✦ Synopsis

A new and e cient parabolic spline based remapping algorithm is developed and tested herein. To ensure mass conservation, the scheme solves an integral form of the transport equation rather than the di erential form. The integrals are computed from reconstructed parabolic splines with mass conservation constraints. For higher dimensions, this remapping can be used within a standard directional splitting methodology or within the ow-dependent cascade splitting approach. A grid and sub-grid based monotonic ÿlter is also incorporated into the overall scheme. A truncation error analysis of the scheme is presented and discussed in terms of results from test cases. The analysis shows that although it has a similar truncation error in the converged limit as that of the widely used Piecewise Parabolic Method (PPM) for inÿnitely di erentiable functions, PSM is more accurate than PPM for problems with slow spectral decay. Additionally, an operation count of the scheme is given which demonstrates the computational advantage of PSM compared to PPM. ?

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