Abstract
Our aim is to simulate a nonlinear system of ODEs describing the flow in smectic liquid crystals. The nonlinear system is first linearized. We present a direct approach to compute the exact analytic solution of this linear system and use this solution as a starting profile in the MATLAB package bvpsuite2.0 to obtain the approximate solution to the nonlinear system. Although, the solution of the nonlinear system has steep boundary layers and therefore is difficult to resolve, we demonstrate that bvpsuite2.0 can cope with the problem and provide an approximation with reasonable accuracy.
| Language | English |
|---|---|
| Pages | 154-162 |
| Number of pages | 9 |
| Journal | Applied Numerical Mathematics |
| Volume | 132 |
| Early online date | 29 May 2018 |
| DOIs | |
| Publication status | Published - 31 Oct 2018 |
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Keywords
- adaptive grids
- boundary value problems in ODEs
- collocation method
- flow dynamics
- smectic A liquid crystals
Cite this
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Numerical simulation of flow in smectic liquid crystals. / Fallahpour, Merlin; McKee, Sean; Weinmüller, Ewa B.
In: Applied Numerical Mathematics, Vol. 132, 31.10.2018, p. 154-162.Research output: Contribution to journal › Article
TY - JOUR
T1 - Numerical simulation of flow in smectic liquid crystals
AU - Fallahpour, Merlin
AU - McKee, Sean
AU - Weinmüller, Ewa B.
PY - 2018/10/31
Y1 - 2018/10/31
N2 - Our aim is to simulate a nonlinear system of ODEs describing the flow in smectic liquid crystals. The nonlinear system is first linearized. We present a direct approach to compute the exact analytic solution of this linear system and use this solution as a starting profile in the MATLAB package bvpsuite2.0 to obtain the approximate solution to the nonlinear system. Although, the solution of the nonlinear system has steep boundary layers and therefore is difficult to resolve, we demonstrate that bvpsuite2.0 can cope with the problem and provide an approximation with reasonable accuracy.
AB - Our aim is to simulate a nonlinear system of ODEs describing the flow in smectic liquid crystals. The nonlinear system is first linearized. We present a direct approach to compute the exact analytic solution of this linear system and use this solution as a starting profile in the MATLAB package bvpsuite2.0 to obtain the approximate solution to the nonlinear system. Although, the solution of the nonlinear system has steep boundary layers and therefore is difficult to resolve, we demonstrate that bvpsuite2.0 can cope with the problem and provide an approximation with reasonable accuracy.
KW - adaptive grids
KW - boundary value problems in ODEs
KW - collocation method
KW - flow dynamics
KW - smectic A liquid crystals
UR - http://www.scopus.com/inward/record.url?scp=85047986078&partnerID=8YFLogxK
UR - https://www.sciencedirect.com/journal/applied-numerical-mathematics
U2 - 10.1016/j.apnum.2018.05.014
DO - 10.1016/j.apnum.2018.05.014
M3 - Article
VL - 132
SP - 154
EP - 162
JO - Applied Numerical Mathematics
T2 - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
ER -