A local adaptive Catmull–Rom to reduce numerical dissipation of semi‐Lagrangian advection†. (11th October 2013) - Huang, Zhanpeng; Han, Liang; Gong, Guanghong
Abstract 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.