The monotonic Quartic Spline Method (QSM) for conservative transport problems

A quartic spline based remapping algorithm is developed and illustrative tests of it are presented herein. To ensure mass conservation, the scheme solves an integral form of the transport equation rather than the differential form. The integrals are computed from reconstructed quartic splines with m...

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Bibliographic Details
Published inJournal of computational physics Vol. 229; no. 4; pp. 1150 - 1166
Main Authors Zerroukat, M., Staniforth, A., Wood, N.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Inc 20.02.2010
Elsevier
Subjects
Advection
Computational techniques
Conservation
Exact sciences and technology
Mathematical methods in physics
Monotonicity
Physics
PPM
PSM
Remapping
02.70.Bf
Advection
92.30.Ef
Remapping
Conservation
02.60.Lj
47.11.Df
PSM
PPM
Monotonicity
Transport equation
Differential form
Spline
Calculation methods
Algorithms
Calculation
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Summary:A quartic spline based remapping algorithm is developed and illustrative tests of it are presented herein. To ensure mass conservation, the scheme solves an integral form of the transport equation rather than the differential form. The integrals are computed from reconstructed quartic splines with mass conservation constraints. For higher dimensions, this remapping can be used within a standard directional splitting methodology or within the flow-dependent cascade splitting approach. A high-order grid and sub-grid based monotonic filter is also incorporated into the overall scheme. This filter is independent of the underlying spline representation adopted here, and is of more general application.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2009.10.018