Abstract : Fluid-structure interaction problems arise in many applications. In biomedicine, such models are used to describe the interaction between blood and arterial walls. Such models have also been used to describe the interaction between blood flow and biodegradable stents, blood flow in patient-specific models of abdominal aortas containing aneurysms, and blood flow and oxygen transport in a bioartifical pancreas. Other applications include geomechanics and aerodynamics. When a deformable structure is porous and allows flow through it, poroelastic models are commonly used to describe its behavior. The numerical simulation of fluid-elastic/poroelastic structure interaction problems has received considerable attention, but still remains a significant challenge in the mathematical and computational sciences. Main difficulties stem from the the intricate multiphysics nature of the problem, and strong nonlinearities. This minisymposium focuses on numerical methods for fluid-elastic or poroelastic structure interaction problems and applications. Possible topics include but are not limited to: 1) partitioned and monolithic numerical methods, 2) porous and poroelastic medium flow, 3) mathematical and numerical analysis, and 4) validation and verification of numerical solvers.
[03958] Space-time domain decomposition approach for Stoke flow coupled with poroelasticity
Format : Talk at Waseda University
Author(s) :
Hyesuk Lee (Clemson University)
Hemanta Kunwar (Clemson University)
Abstract : We consider decoupling iterative algorithms based on domain decomposition for the time-dependent Stokes-Biot model, in which different time steps can be used in the flow region and the poroelastic medium. The coupled system is formulated as a space-time interface problem based on interface conditions. The interface problem is then solved by an iterative method which involves the parallel solution of time-dependent homogeneous Stokes and Biot problems. Consequently, local discretization in both space and time can be used to handle multiphysics systems efficiently. Numerical results with nonconforming time grids are presented to illustrate the performance of the proposed methods.
[04129] Two-field any-order finite element solvers for poroelasticity problems
Format : Talk at Waseda University
Author(s) :
Jiangguo James Liu (Colorado State University )
Abstract : In this talk, we present a family of 2-field finite element solvers for poroelasticity problems based on weak Galerkin (WG) spatial discretizations and the backward differentiation formulas (BDF) temporal discretization. In particular, both primal variables (fluid pressure and solid displacement) are approximated by WG degree k>=0 (scalar or vector) polynomial shape functions defined separately in element interiors and on edges of a quadrilateral mesh. The discrete weak gradients of WG basis functions are constructed in certain broken Arbogast-Correa spaces (of vectors or matrices). The discrete weak gradients, strains, and divergences will be utilized to approximate their continuous counterparts in the variational formulations. Degree-k WG polynomials and BDF(k+1) are combined to develop time-marching schemes for linear poroelasticity. This combination results in a good balance of spatial and temporal discretizations. Numerical experiments on benchmarks will be presented to demonstrate the efficiency and flexibility of these new solvers. Extension to nonlinear poroelasticity problems will be discussed also. This is a joint work with Simon Tavener (Colorado State University, USA), Ruishu Wang (Jilin University, China), and Zhuoran Wang (Sun Yat-sen University, China).
[04672] A mathematical framework for poro-viso-elastic models
Format : Talk at Waseda University
Author(s) :
Justin Thomas Webster (University of Maryland, Baltimore County)
Abstract : Recent works in poroelasticity have included viscous structural effects. Here, we clarify mathematical properties of linear, quasi-static Biot systems with the addition of Kelvin-Voigt viscoelasticity. We demonstrate time-regularization and dissipative effects of viscoelasticity through a priori estimates. We use the full system, as well as the framework of implicit, degenerate evolutions. Precise statements of admissible initial conditions in each scenario are given.
[04316] An energy stable second-order method for three-phase flows
Format : Talk at Waseda University
Author(s) :
Catalin Trenchea (University of Pittsburgh)
Giselle Sosa Jones (Oakland University)
Abstract : We present a time-stepping scheme for the numerical approximation of a thermodynamically consistent model of incompressible and immiscible three-phase flow in porous media, with an intrinsic free energy dissipation law.
The model consists of three nonlinear degenerate parabolic equations for the saturations of each phase.
We prove that the proposed scheme is second-order accurate, and preserves the discrete free energy dissipation.
[04829] Cell-Based Numerical Approach to Evaluate CTC Binding Behavior in Microfluidic Device
Format : Talk at Waseda University
Author(s) :
YIFAN Wang (Texas Tech University)
Abstract : Circulating tumor cells (CTCs) are malignant cells that break free from the primary tumor and enter the bloodstream. Early detection of CTCs is crucial for diagnosis, but challenging because they are infrequent in blood samples. Microfluidic devices offer a promising detection technique, either actively enriching CTCs through external fields or passively separating them from other cells based on physical properties. A microfluidic device has been proposed by our collaborator at Texas Tech University to isolate CTCs from blood samples, with different micro-post sizes and layouts tested to optimize capture efficiency. However, the complex transport and adhesion behaviors of CTCs in blood cell suspensions remain incompletely understood. Here, we present a cell-based numerical approach based on the Lattice Boltzmann method to evaluate the binding behavior and trajectories of CTCs under different flow conditions, including cell size and coating density, microfluidic design, and cell collisions. Our validated results are used to improve the device design.
[02971] A Banach spaces-based fully-mixed formulation for the Navier–Stokes/Darcy coupled problem
Format : Talk at Waseda University
Author(s) :
Segundo Villa Fuentes (Monash University)
Ricardo Oyarzúa (Universidad del Bío-Bío)
Sergio Caucao (Universidad Católica de la Santísima Concepción)
Abstract : In this work we present and analyze a fully-mixed formulation for the coupling Navier–Stokes/Darcy equations.
Our approach is based on the introduction of a modified pseudostress tensor in the Navier–Stokes equations for the fluid, whereas the standard dual-mixed formulation for the Darcy model is considered. With this, we obtain a Banach spaces-based mixed variational formulation and a twofold saddle point structure.
Fixed-point strategy, together with the Banach–Nečas–Babuška and Banach’s fixed point theorems, are employed to prove the well-posedness of the continuous and discrete formulations.
[03829] Numerical simulation of the time-fractional Navier-Stokes-Fokker-Planck (tfNSFP) equation
Format : Talk at Waseda University
Author(s) :
Jonas Beddrich (Technical University of Munich)
Endre Süli (University of Oxford)
Barbara Wohlmuth (Technical University of Munich)
Abstract : The tfNSFP system describes the flow of dilute polymeric fluids. It is attractive as it enhances standard models for the viscoelasticity of polymer molecules by accounting for memory effects. The problem is challenging since it is non-local in time and defined on the Cartesian product of two d-dimensional spaces. We present a numerical method that combines a rational approximation approach, a space-splitting approach, and the Hermite spectral method to solve the tfNSFP equation.
