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A local adaptive Catmull–Rom to reduce numerical dissipation of semi‐Lagrangian advection
Author(s) -
Huang Zhanpeng,
Han Liang,
Gong Guanghong
Publication year - 2013
Publication title -
computer animation and virtual worlds
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.225
H-Index - 49
eISSN - 1546-427X
pISSN - 1546-4261
DOI - 10.1002/cav.1559
Subject(s) - computer science , stability (learning theory) , advection , overshoot (microwave communication) , monotonic function , interpolation (computer graphics) , mathematics , mathematical optimization , artificial intelligence , mathematical analysis , physics , machine learning , thermodynamics , motion (physics) , telecommunications
We propose an adaptive Catmull–Rom interpolation to improve accuracy of semi‐Lagrangian advection for smoke simulation. Original Catmull–Rom improves numerical accuracy but overshoot violates global stability. Monotonic Catmull–Rom is unconditionally stable, whereas it sweeps out detail features due to overly suppression operations. Our method modifies original Catmull–Rom to obtain second‐order accuracy and unconditional stability. It flattens locations where interpolations might break through global bounds but maintains local overshoots to conserve diversity of fluid flow. The scheme is easy to collaborate with existing fluid simulators to improve small features. Copyright © 2013 John Wiley & Sons, Ltd.