Imperial College London
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ProfessorColinCotter

Faculty of Natural Sciences, Department of Mathematics

Professor of Computational Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 3468colin.cotter

 
 
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Location

 

755Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Cotter:2019:10.1137/18M1167929,
author = {Cotter, CJ and Crisan, D and Holm, DD and Pan, W and Shevchenko, I},
doi = {10.1137/18M1167929},
journal = {SIAM Journal on Scientific Computing},
pages = {192--232},
title = {Numerically modelling stochastic lie transport in fluid dynamics},
url = {http://dx.doi.org/10.1137/18M1167929},
volume = {17},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We present a numerical investigation of stochastic transport in ideal fluids.According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principlesof transformation theory and multi-time homogenisation, respectively, imply aphysically meaningful, data-driven approach for decomposing the fluid transportvelocity into its drift and stochastic parts, for a certain class of fluidflows. In the current paper, we develop new methodology to implement thisvelocity decomposition and then numerically integrate the resulting stochasticpartial differential equation using a finite element discretisation forincompressible 2D Euler fluid flows. The new methodology tested here is foundto be suitable for coarse graining in this case. Specifically, we performuncertainty quantification tests of the velocity decomposition of Cotter et al.(2017), by comparing ensembles of coarse-grid realisations of solutions of theresulting stochastic partial differential equation with the "true solutions" ofthe deterministic fluid partial differential equation, computed on a refinedgrid. The time discretization used for approximating the solution of thestochastic partial differential equation is shown to be consistent. We includecomprehensive numerical tests that confirm the non-Gaussianity of the streamfunction, velocity and vorticity fields in the case of incompressible 2D Eulerfluid flows.
AU  - Cotter,CJ
AU  - Crisan,D
AU  - Holm,DD
AU  - Pan,W
AU  - Shevchenko,I
DO  - 10.1137/18M1167929
EP  - 232
PY  - 2019///
SN  - 1064-8275
SP  - 192
TI  - Numerically modelling stochastic lie transport in fluid dynamics
T2  - SIAM Journal on Scientific Computing
UR  - http://dx.doi.org/10.1137/18M1167929
UR  - http://arxiv.org/abs/1801.09729v2
UR  - http://hdl.handle.net/10044/1/66472
VL  - 17
ER  -
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