A self-regularising DVM–PSE method for the modelling of diffusion in particle methods

Mycek, Paul; Pinon, Grégory; Germain, Grégory; Rivoalen, Elie

doi:10.1016/j.crme.2013.08.002

Cited by 4 publications

(6 citation statements)

References 28 publications

(45 reference statements)

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“…Finally, the diffusion term of equation ( 1), ν∆ω, can be modeled by means of the broadly-used particle strength exchange (PSE) method [23][24][25][26]. Alternatively, the diffusion velocity method (DVM) [27][28][29][30][31] may be used instead. Both of these methods may be modified in order to incorporate a LES turbulence model [5,32].…”

Section: Description Of the Numerical Methodsmentioning

confidence: 99%

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

Mycek

Pinon

Lothodé

et al. 2017

Applied Mathematical Modelling

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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, nonsymmetric, 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 Highlights ► Numerical computation of wind or marine current turbines in a farm is investigated. ► A Vortex method together with a panel method is considered. ► Iterative approaches are compared for the solving of the so-called influence system. ► A specific preconditioner, well suited for the desired application, is proposed. ► CPU times of computations involving up to 10 turbines are compared.

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Section: Description Of the Numerical Methodsmentioning

confidence: 99%

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

Mycek

Pinon

Lothodé

et al. 2017

Applied Mathematical Modelling

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“…In such cases, DVM suffers from a severe singularity problem and shows dramatically unstable behaviours -computations are likely to collapse. This issue has been discussed for the original DVM scheme in one dimension, and a weighted self-regularising DVM-PSE hybrid model was proposed to overcome such problems by Mycek et al (2013). This hybrid model should be straightforwardly extendable to the 3D diffusion of a vector field.…”

Section: Resultsmentioning

confidence: 99%

“…with ν * = ν or ν * = ν + ν t ), a singular behaviour is likely to occur when the quantity to diffuse (either c or components of ω) crosses zero (changes sign). This issue has been addressed in (Mycek et al 2013).…”

Section: Large Eddy Simulation (Les) Modellingmentioning

confidence: 99%

Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations

et al. 2014

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. Formulation and analysis of a diffusionvelocity particle model for transport-dispersion equations. Computational and Applied Mathematics, Springer Verlag, 2016, 35 (2), pp.447-473. 10.1007/s40314-014-0200-5. hal-01087854 Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations Paul Mycek · Grégory Pinon · Grégory Germain · Elie Rivoalen Abstract The modelling of diffusive terms in particle methods is a delicate matter and several models were proposed in the literature to take such terms into account. The Diffusion Velocity Method (DVM), originally designed for the diffusion of passive scalars, turns diffusive terms into convective ones by expressing them as a divergence involving a so-called diffusion velocity. In this paper, DVM is extended to the diffusion of vectorial quantities in the three-dimensional NavierStokes equations, in their incompressible, velocity-vorticity formulation. The integration of a Large Eddy Simulation (LES) turbulence model is investigated and a DVM general formulation is proposed. Either with or without LES, a novel expression of the diffusion velocity is derived, which makes it easier to approximate and which highlights the analogy with the original formulation for scalar transport. From this statement, DVM is then analysed in one dimension, both analytically and numerically on test cases to point out its good behaviour.

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“…This term is handled via the particle strength exchange (PSE) method developed and detailed in previous studies. [42][43][44][45] This method allows to account for non-uniform viscous coefficients that may depend on position and time. In the presented computations, the turbulent viscosity (ν T ð x !…”

Section: Lagrangian Vortex Particle Formulation Of Navier-stokes Equa...mentioning

confidence: 99%

Development and validation of a lifting‐line code associated with the vortex particle method software Dorothy

Dufour,

Pinon,

Rivoalen

et al. 2024

Wind Energy

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This paper presents a lifting‐line implementation in the framework of a Lagrangian vortex particle method (LL‐VP). The novelty of the present implementation lies in the fluid particles properties definition and in the particles shedding process. In spite of mimicking a panel method, the LL‐VP needs some peculiar treatments described in the paper. The present implementation converges rapidly and efficiently during the shedding sub‐iteration process. This LL‐VP method shows good accuracy, even with moderate numbers of sections. Compared to its panel or vortex filaments counterparts, more frequently encountered in the literature, the present implementation inherently accounts for the diffusion term of the Navier‐Stokes equations, possibly with a turbulent viscosity model. Additionally, the present implementation can also account for more complex onset flows: upstream ambient turbulence and upstream turbine wakes. After validation on an analytical elliptic wing configuration, the model is tested on the Mexnext‐III wind turbine application, for three reduced velocities. Accurate results are obtained both on the analytical elliptic wing and on the New MEXICO rotor cases in comparison with other similar numerical models. A focus is made on the Mexnext‐III wake analysis. The numerical wake obtained with the present LL‐VP is close to other numerical and experimental results. Finally, a last configuration with three tidal turbines in interaction is considered based on an experimental campaign carried out at the IFREMER wave and current flume tank. Enhanced turbine‐wake interactions are highlighted, with favourable comparisons with the experiment. Hence, such turbine interactions in a farm are accessible with this LL‐VP implementation, be it wind or tidal energy field.

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A self-regularising DVM–PSE method for the modelling of diffusion in particle methods

Cited by 4 publications

References 28 publications

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

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

Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations

Development and validation of a lifting‐line code associated with the vortex particle method software Dorothy

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