A computational approach to modeling flow-induced large deformation of thin-walled compliant vessels

We present a computational method capable of modeling 3D flow-induced deformation of thin, highly compliant, hyperelastic vessels conveying viscous, inertial fluid. The method can uniformly consider vessel extension and collapse. Very large inflation, transient deformation, complex flow features as well as highly complex buckling shapes are well resolved by this method. The methodology combines finite volume and spectral methods for fluid motion, finite element method for structural mechanics of the vessel wall, and the immersed boundary method for two-way coupling between the wall and fluid. A hybrid of the continuous forcing and the ghost node methodologies capitalizing on the strengths of each is developed. The method avoids the surface instability encountered with the continuous forcing methods, as well as the need for domain remeshing as required in the iterative and partitioned approaches. The vessel wall can follow linear or nonlinear (strain softening and hardening) material models, and the fluid inertia can vary over a wide range. We demonstrate the versatility of the method by considering vessel inflation and collapse with large, complex, and transient deformation. Remarkable differences in vessel inflation at low versus moderate inertia are observed; this includes steady versus oscillatory motion, emergence of flow recirculation and pressure wave reflection which are well resolved. For the collapsing vessels, well-defined shapes with different buckling modes as well as highly complex buckling with fine surface folds are predicted. Additionally, a second-order correction to the well-known law of Laplace is developed and used to validate our computational results for vessel inflation.