An immersed methodology for fluid-structure interaction using NURBS and T-splines: theory, algorithms, validation, and application to blood flow at small scales
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- Teses de doutoramento [2079]
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An immersed methodology for fluid-structure interaction using NURBS and T-splines: theory, algorithms, validation, and application to blood flow at small scalesAuthor(s)
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Gómez Díaz, HéctorDate
2016Center/Dept./Entity
Universidade da Coruña. Departamento de Métodos Matemáticos e de RepresentaciónAbstract
[Abstract]
Mesh-based immersed approaches shine in a variety of fluid-structure interaction (FSI) applications such
as, e.g., simulations where the solid undergoes large displacements or rotations, particulate flow problems,
and scenarios where the topology of the region occupied by the fluid varies in time. In this thesis, a new
mesh-based immersed approach is proposed which is based on the use of di erent types of splines as basis
functions. This approach is put forth for modeling and simulating di erent types of biological cells in blood
flow at small scales.
The specific contributions of this thesis are outlined as follows. Firstly, a hybrid variational-collocation
immersed technique using nonuniform rational B-splines (NURBS) is presented. Newtonian viscous incompressible
fluids and nonlinear hyperelastic incompressible solids are considered. Our formulation boils
down to three coupled equations which are the linear momentum balance equation, the mass conservation
equation, and the kinematic equation that relates the Lagrangian displacement with the Eulerian velocity.
The latter is discretized in strong form using isogeometric collocation and the other two equations are discretized
using the variational multiscale (VMS) paradigm. As usual in immersed FSI approaches, we define
a background mesh on the whole computational domain and a Lagrangian mesh tailored to the region occupied
by each solid. Besides of using NURBS for creating these meshes, the data transfer between the
background mesh and the Lagrangian meshes is carried out using NURBS functions in such a way that no
interpolation or projection is needed, thus avoiding the errors associated with these procedures. Regarding
the time discretization, the generalized- method is used which leads to a fully-implicit and second-order
accurate method. The methodology is validated in two- and three-dimensional settings comparing the terminal
velocity of free-falling bulky solids obtained in our simulations with its theoretical value. Secondly,
we extend our algorithms in order to use analysis-suitable T-splines (ASTS) as basis functions instead of
NURBS. This required to develop isogeometric collocation methods for ASTS which was an open problem.
The data transfer between meshes changes significantly from NURBS to ASTS due to the fact that their
geometrical mappings are local to patches and elements, respectively. ASTS possess two main advantages
with respect to NURBS: (1) ASTS support local h-refinement and (2) ASTS are unstructured. The ASTSbased
method is validated solving again the aforementioned benchmark problems and showing the potential
of ASTS to decrease the amount of elements needed, thus enhancing the e ciency of the method. Thirdly,
capsules, modeled as solid-shell NURBS elements, are proposed as numerical proxies for representing red
blood cells (RBCs). The dynamics of capsules are able to reproduce the main motions and shapes observed
in experiments with RBCs in both shear and parabolic flows. Hemorheological properties as the Fåhræus
and Fåhræus-Lindqvist e ects are captured in our simulations. In order to obtain the aforementioned results,
it is essential to adequately satisfy the incompressibility constraint close to the fluid-solid interface, which
is an arduous task in immersed approaches for fluid-structure interaction. Finally, compound capsules are
presented as numerical proxies for cells with nucleus such as, e.g., white blood cells (WBCs) and circulating tumor cells (CTCs). The dynamics of hyperelastic compound capsules in shear flow are studied in both
two- and three-dimensional settings. Moreover, we simulate how CTCs manage to pass through channel
narrowings, which is an interesting characteristic of CTCs since it is used in experiments to sort CTCs from
blood samples.
Keywords
Interacción fluido-estructura
Splines, Teoría de los
Splines, Teoría de los
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