A mixed virtual element method for Biot's consolidation model.

In this paper, we shall present a weak virtual element method for the standard three field poroelasticity problem on polytopal meshes. The flux velocity and pressure are approximated by the low order virtual element and the piecewise constant, while the elastic displacement is discretized by the virtual element with some tangential polynomials on element boundaries. A fully discrete scheme is then given by choosing the backward Euler for the time discretization.

DECOUPLING PDE COMPUTATION WITH INTRINSIC OR INERTIAL ROBIN INTERFACE CONDITION.

We study decoupled numerical methods for multi-domain, multi-physics applications. By investigating various stages of numerical approximation and decoupling and tracking how the information is transmitted across the interface for a typical multi-modeling model problem, we derive an approximate intrinsic or inertial type Robin condition for its semi-discrete model. This new interface condition is justified both mathematically and physically in contrast to the classical Robin interface condition conventionally introduced for decoupling multi-modeling problems.

Normal mode analysis of 3D incompressible viscous fluid flow models.

In this paper, we study the normal mode solutions of 3D incompressible viscous fluid flow models. The obtained theoretical results are then applied to analyze several time-stepping schemes for the numerical solutions of the 3D incompressible fluid flow models.

Parameter-robust multiphysics algorithms for Biot model with application in brain edema simulation.

In this paper, we develop parameter-robust numerical algorithms for Biot model and apply the algorithms in brain edema simulations. By introducing an intermediate variable, we derive a multiphysics reformulation of the Biot model. Based on the reformulation, the Biot model is viewed as a generalized Stokes subproblem combining with a reaction-diffusion subproblem.

An H(div)-conforming Finite Element Method for Biot's Consolidation Model.

In this paper, we develop an H(div)-conforming finite element method for Biot's consolidation model in poroelasticity. In our method, the flow variables are discretized by an H(div)-conforming mixed finite elements. For relaxing the -conformity of the displacement, we approximate the displacement by using an H(div)-conforming finite element method, in which the tangential components are discretized in the interior penalty discontinuous Galerkin framework.

A 3D OPENFOAM BASED FINITE VOLUME SOLVER FOR INCOMPRESSIBLE OLDROYD-B MODEL WITH INFINITY RELAXATION TIME.

In this paper, we develop a Finite Volume solver for a 3D incompressible Oldroyd-B model with infinity relaxation time. The Finite Volume solver is implemented by using a leading open-source computational mechanics software OpenFOAM. We have imposed the divergence free condition as a constraint on the momentum equation to derive a pressure equation and a predictor-corrector procedure is applied when solving the velocity field.

Comparisons of Some Iterative Algorithms for Biot Equations.

In this paper, we aim at solving the Biot model under stabilized finite element discretizations. To solve the resulting generalized saddle point linear systems, some iterative methods are proposed and compared. In the first method, we apply the GM-RES algorithm as the outer iteration.

IVUS-based computational modeling and planar biaxial artery material properties for human coronary plaque vulnerability assessment.

Image-based computational modeling has been introduced for vulnerable atherosclerotic plaques to identify critical mechanical conditions which may be used for better plaque assessment and rupture predictions. In vivo patient-specific coronary plaque models are lagging due to limitations on non-invasive image resolution, flow data, and vessel material properties. A framework is proposed to combine intravascular ultrasound (IVUS) imaging, biaxial mechanical testing and computational modeling with fluid-structure interactions and anisotropic material properties to acquire better and more complete plaque data and make more accurate plaque vulnerability assessment and predictions.

Planar biaxial characterization of diseased human coronary and carotid arteries for computational modeling.

Computational models have the potential to provide precise estimates of stresses and strains associated with sites of coronary plaque rupture. However, lack of adequate mathematical description of diseased human vessel wall mechanical properties is hindering computational accuracy. The goal of this study is to characterize the behavior of diseased human coronary and carotid arteries using planar biaxial testing.