# A fictitious domain method for the numerical two-dimensional simulation of potential flows past sails

Alfredo Bermúdez; Rodolfo Rodríguez; María Luisa Seoane

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 45, Issue: 6, page 1033-1058
- ISSN: 0764-583X

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topBermúdez, Alfredo, Rodríguez, Rodolfo, and Seoane, María Luisa. "A fictitious domain method for the numerical two-dimensional simulation of potential flows past sails." ESAIM: Mathematical Modelling and Numerical Analysis 45.6 (2011): 1033-1058. <http://eudml.org/doc/276353>.

@article{Bermúdez2011,

abstract = {
This paper deals with the mathematical and numerical analysis of a
simplified two-dimensional model for the interaction between the wind
and a sail. The wind is modeled as a steady irrotational plane flow past
the sail, satisfying the Kutta-Joukowski condition. This condition
guarantees that the flow is not singular at the trailing edge of the
sail. Although for the present analysis the position of the sail is
taken as data, the final aim of this research is to develop tools to
compute the sail shape under the aerodynamic pressure exerted by the
wind. This is the reason why we propose a fictitious domain formulation
of the problem, involving the wind velocity stream function and a
Lagrange multiplier; the latter allows computing the force density
exerted by the wind on the sail. The Kutta-Joukowski condition is
imposed in integral form as an additional constraint. The resulting
problem is proved to be well posed under mild assumptions. For the
numerical solution, we propose a finite element method based on
piecewise linear continuous elements to approximate the stream function
and piecewise constant ones for the Lagrange multiplier. Error estimates
are proved for both quantities and a couple of numerical tests
confirming the theoretical results are reported. Finally the method is
used to determine the sail shape under the action of the wind.
},

author = {Bermúdez, Alfredo, Rodríguez, Rodolfo, Seoane, María Luisa},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Finite element approximation; fluid-structure interaction;
fictitious domain; flow past sails; finite element approximation; fictitious domain},

language = {eng},

month = {6},

number = {6},

pages = {1033-1058},

publisher = {EDP Sciences},

title = {A fictitious domain method for the numerical two-dimensional simulation of potential flows past sails},

url = {http://eudml.org/doc/276353},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Bermúdez, Alfredo

AU - Rodríguez, Rodolfo

AU - Seoane, María Luisa

TI - A fictitious domain method for the numerical two-dimensional simulation of potential flows past sails

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2011/6//

PB - EDP Sciences

VL - 45

IS - 6

SP - 1033

EP - 1058

AB -
This paper deals with the mathematical and numerical analysis of a
simplified two-dimensional model for the interaction between the wind
and a sail. The wind is modeled as a steady irrotational plane flow past
the sail, satisfying the Kutta-Joukowski condition. This condition
guarantees that the flow is not singular at the trailing edge of the
sail. Although for the present analysis the position of the sail is
taken as data, the final aim of this research is to develop tools to
compute the sail shape under the aerodynamic pressure exerted by the
wind. This is the reason why we propose a fictitious domain formulation
of the problem, involving the wind velocity stream function and a
Lagrange multiplier; the latter allows computing the force density
exerted by the wind on the sail. The Kutta-Joukowski condition is
imposed in integral form as an additional constraint. The resulting
problem is proved to be well posed under mild assumptions. For the
numerical solution, we propose a finite element method based on
piecewise linear continuous elements to approximate the stream function
and piecewise constant ones for the Lagrange multiplier. Error estimates
are proved for both quantities and a couple of numerical tests
confirming the theoretical results are reported. Finally the method is
used to determine the sail shape under the action of the wind.

LA - eng

KW - Finite element approximation; fluid-structure interaction;
fictitious domain; flow past sails; finite element approximation; fictitious domain

UR - http://eudml.org/doc/276353

ER -

## References

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