Distributed Control for Shear-Thinning Non-Newtonian Fluids

Guerra, Telma

doi:10.1007/s00021-012-0101-6

Cited by 9 publications

(3 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the two-dimensional unsteady case, we refer to [23], and to [18] for three-dimensional coupled modified Navier-Stokes and Maxwell equations. Furthermore, for distributed control on three-dimensional domains we cite [1] and [16]. None of the cited authors focused on the boundary control problem for the nonlinear system (7).…”

Section: The Da Methodsmentioning

confidence: 99%

Optimal control in blood flow simulations

Guerra

Tiago

Sequeira

2014

International Journal of Non-Linear Mechanics

Self Cite

View full text Add to dashboard Cite

Blood flow simulations can be improved by integrating known data into the numerical simulations. Data assimilation techniques based on a variational approach play an important role in this issue. We propose a nonlinear optimal control problem to reconstruct the blood flow profile from partial observations of known data in idealized 2D stenosed vessels. The wall shear stress is included in the cost function, which is considered as an important indicator for medical purposes. To simplify we assume blood flow as an homogeneous fluid with non-Newtonian behavior. Using a Discretize then Optimize (DO) approach, we solve the nonlinear optimal control problem and we propose a weighted cost function that accurately recovers both the velocity and the wall shear stress profiles. The robustness of such cost function is tested with respect to different velocity profiles and degrees of stenosis. The filtering effect of the method is also confirmed. We conclude that this approach can be successfully used in the 2D case.

show abstract

Section: The Da Methodsmentioning

confidence: 99%

Optimal control in blood flow simulations

Guerra

Tiago

Sequeira

2014

International Journal of Non-Linear Mechanics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Such type of optimal control problems has been a subject of intensive research in the past decades. For non-Newtonian fluid equations we mention the results in [1], [3], [4], [8], [9], [12] and [16] where the authors used several techniques to deal properly with the shear-thinning and shear-thickening viscosity laws, defined both in 2D and 3D domains. For the existence of solution, such techniques consist in exploring correctly the properties of the tensor S in order to establish compactness results necessary for the application of the direct method of the Calculus of Variations.…”

Section: Introductionmentioning

confidence: 99%

On the optimal control of a class of non-Newtonian fluids

Guerra¹,

Tiago

Sequeira

2013

Ann Univ Ferrara

Self Cite

View full text Add to dashboard Cite

show abstract

“…These considerations have led Slawig [25] and Wachsmuth and Roubíček [26], by exploiting the regularity results established in [17] and [16], to restrict their studies to the case n = 2. Similarly, by using regularity results established in [7] for the very special case of a viscosity obeying the Carreau's law, a problem describing threedimensional shear-thinning fluids was studied in [13]. To guarantee the uniqueness of the state variable, restrictions on the set of admissible controls are imposed in [25], [26], and [13] with an additional restriction in [13] to ensure the regularity of the weak solution of the state equation.…”

mentioning

confidence: 99%