1,646 research outputs found
Stabilized lowest order finite element approximation for linear three-field poroelasticity
A stabilized conforming mixed finite element method for the three-field
(displacement, fluid flux and pressure) poroelasticity problem is developed and
analyzed. We use the lowest possible approximation order, namely piecewise
constant approximation for the pressure and piecewise linear continuous
elements for the displacements and fluid flux. By applying a local pressure
jump stabilization term to the mass conservation equation we ensure stability
and avoid pressure oscillations. Importantly, the discretization leads to a
symmetric linear system. For the fully discretized problem we prove existence
and uniqueness, an energy estimate and an optimal a-priori error estimate,
including an error estimate for the divergence of the fluid flux. Numerical
experiments in 2D and 3D illustrate the convergence of the method, show the
effectiveness of the method to overcome spurious pressure oscillations, and
evaluate the added mass effect of the stabilization term.Comment: 25 page
A poroelastic model coupled to a fluid network with applications in lung modelling
Here we develop a lung ventilation model, based a continuum poroelastic
representation of lung parenchyma and a 0D airway tree flow model. For the
poroelastic approximation we design and implement a lowest order stabilised
finite element method. This component is strongly coupled to the 0D airway tree
model. The framework is applied to a realistic lung anatomical model derived
from computed tomography data and an artificially generated airway tree to
model the conducting airway region. Numerical simulations produce
physiologically realistic solutions, and demonstrate the effect of airway
constriction and reduced tissue elasticity on ventilation, tissue stress and
alveolar pressure distribution. The key advantage of the model is the ability
to provide insight into the mutual dependence between ventilation and
deformation. This is essential when studying lung diseases, such as chronic
obstructive pulmonary disease and pulmonary fibrosis. Thus the model can be
used to form a better understanding of integrated lung mechanics in both the
healthy and diseased states
Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity
A recent unsymmetric 4ânode, 8âDOF plane finite element USâATFQ4 is generalized to hyperelastic finite deformation analysis. Since the trial functions of USâATFQ4 contain the homogenous closed analytical solutions of governing equations for linear elasticity, the key of the proposed strategy is how to deal with these linear analytical trial functions (ATFs) during the hyperelastic finite deformation analysis. Assuming that the ATFs can properly work in each increment, an algorithm for updating the deformation gradient interpolated by ATFs is designed. Furthermore, the update of the corresponding ATFs referred to current configuration is discussed with regard to the hyperelastic material model, and a specified model, neoâHookean model, is employed to verify the present formulation of USâATFQ4 for hyperelastic finite deformation analysis. Various examples show that the present formulation not only remain the high accuracy and mesh distortion tolerance in the geometrically nonlinear problems, but also possess excellent performance in the compressible or quasiâincompressible hyperelastic finite deformation problems where the strain is large
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