Iterative solver approach for turbine interactions: application to wind or marine current turbine farms

Type Article
Date 2017-01
Language English
Author(s) Mycek Paul1, Pinon Gregory2, Lothode Corentin3, 4, Dezotti Alexandre5, Carlier Clement2, 6
Affiliation(s) 1 : Duke Univ, MEMS Dept, 144 Hudson Hall,Box 90300, Durham, NC 27708 USA.
2 : Univ Havre, Lab Ondes & Milieux Complexes, UMR 6294, CNRS, 53 Rue Prony,BP 540, F-76058 Le Havre, France.
3 : INSA Rouen, Lab Optimisat & Fiabilite Mecan Struct, EA 3828, Ave Univ,BP 08, F-76801 St Etienne, France.
4 : K Epsilon, WTC Batiment 1 Entree E,1300 Route Cretes, F-06560 Valbonne, France.
5 : Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England.
6 : IFREMER, Marine Struct Lab, 150 Quai Gambetta,BP 699, F-62321 Boulogne Sur Mer, France.
Source Applied Mathematical Modelling (0307-904X) (Elsevier Science Inc), 2017-01 , Vol. 41 , P. 331-349
DOI 10.1016/j.apm.2016.08.027
WOS© Times Cited 5
Keyword(s) Iterative solver, Bi-GCSTAB, Preconditioner, Lagrangian vortex method, Wind turbine, Marine current turbine
Abstract This paper presents a numerical investigation for the computation of wind or marine current turbines in a farm. A 3D unsteady Lagrangian vortex method is used together with a panel method in order to take into account for the turbines. In order to enforce the boundary condition onto the panel elements, a linear matrix system is defined. Solving general linear matrix systems is a topic with important scientific literature. But the main concern here is the application to a dedicated matrix which is non-sparse, non-symmetric, neither diagonally dominant nor positive-definite. Several iterative approaches were tested and compared. But after some numerical tests, a Bi-CGSTAB method was finally chosen. The main advantage of the presented method is the use of a specific preconditioner well suited for the desired application. The chosen implementation proved to be very efficient with only 3 iterations of our preconditioned Bi-CGSTAB algorithm whatever the turbine geometrical configuration. Although developed for wind or marine turbines, the proposed algorithm is absolutely not restricted to these cases, and can be applied to many others. At the end of the paper, some applications (specifically, wake computations) in a farm are presented, along with a quantitative assessment of the computational time savings brought by the iterative approach
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