A new enrichment space for the treatment of discontinuous pressures in multi‐fluid flows

In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 1019–1031, 2010) in several problems involving jumps in the viscosity and/or the presence of singular forces at interfaces not conforming with the element edges. The combination of this enrichment space with another enrichment that accommodates discontinuities in the pressure gradient has also been explored, exhibiting excellent results in problems involving jumps in the density or the volume forces

A two-component fluid-solid finite element model of the red blood cell

The state of the art models for the red blood cell consist of two components: A solid network of fibers (worm-like chains) that correspond to the cytoskeleton, and a fluid surface with bending stiffness that corresponds to the lipid bilayer (X. Li et.al., Phil. Trans. R. Soc. A, 372:20130389 (2014)). The fluid and solid components are connected at the junctions of the network, where trans-membrane proteins anchor the bilayer to the cytoskeleton, but this connection is not rigid and under large deformations it is possible that cytoskeleton and bilayer detach from one another. It is well know that the interactions between the lipid bilayer membrane and the skeletal network (fluid-solid interactions) are responsible for the physical properties of red blood cell. However, quantifying these interactions and studying the related dynamics is still a topic discussed and full of open questions (S. Lux, Blood, 127:187–199 (2016)). In this work we will report on our first advances towards the development of a finite element method for this strongly coupled system. It leads to a fluid-structure interaction problem, with the salient feature that both the fluid and the structure are in fact two-dimensional bodies evolving in three-dimensional space.Publicado en: Mecánica Computacional vol. XXXV, no. 9.Facultad de Ingenierí

A two-component fluid-solid finite element model of the red blood cell

The state of the art models for the red blood cell consist of two components: A solid network of fibers (worm-like chains) that correspond to the cytoskeleton, and a fluid surface with bending stiffness that corresponds to the lipid bilayer (X. Li et.al., Phil. Trans. R. Soc. A, 372:20130389 (2014)). The fluid and solid components are connected at the junctions of the network, where trans-membrane proteins anchor the bilayer to the cytoskeleton, but this connection is not rigid and under large deformations it is possible that cytoskeleton and bilayer detach from one another. It is well know that the interactions between the lipid bilayer membrane and the skeletal network (fluid-solid interactions) are responsible for the physical properties of red blood cell. However, quantifying these interactions and studying the related dynamics is still a topic discussed and full of open questions (S. Lux, Blood, 127:187–199 (2016)). In this work we will report on our first advances towards the development of a finite element method for this strongly coupled system. It leads to a fluid-structure interaction problem, with the salient feature that both the fluid and the structure are in fact two-dimensional bodies evolving in three-dimensional space.Publicado en: Mecánica Computacional vol. XXXV, no. 9.Facultad de Ingenierí

A two-component fluid-solid finite element model of the red blood cell

The state of the art models for the red blood cell consist of two components: A solid network of fibers (worm-like chains) that correspond to the cytoskeleton, and a fluid surface with bending stiffness that corresponds to the lipid bilayer (X. Li et.al., Phil. Trans. R. Soc. A, 372:20130389 (2014)). The fluid and solid components are connected at the junctions of the network, where trans-membrane proteins anchor the bilayer to the cytoskeleton, but this connection is not rigid and under large deformations it is possible that cytoskeleton and bilayer detach from one another. It is well know that the interactions between the lipid bilayer membrane and the skeletal network (fluid-solid interactions) are responsible for the physical properties of red blood cell. However, quantifying these interactions and studying the related dynamics is still a topic discussed and full of open questions (S. Lux, Blood, 127:187–199 (2016)). In this work we will report on our first advances towards the development of a finite element method for this strongly coupled system. It leads to a fluid-structure interaction problem, with the salient feature that both the fluid and the structure are in fact two-dimensional bodies evolving in three-dimensional space.Publicado en: Mecánica Computacional vol. XXXV, no. 9.Facultad de Ingenierí

A finite element method for simulating soft active non-shearable rods immersed in generalized Newtonian fluids

We propose a finite element method for simulating one-dimensional solid models with finite thickness and finite length that move and experience large deformations while immersed in generalized Newtonian fluids. The method is oriented towards applications involving microscopic devices or organisms in the soft-bio-matter realm. By considering that the strain energy of the solid may explicitly depend on time, we incorporate a mechanism for active response. The solids are modeled as Cosserat rods, a detailed formulation being provided for the planar non-shearable case. The discretization adopts one-dimensional Hermite elements for the rod and two-dimensional low-order Lagrange elements for the fluid’s velocity and pressure. The fluid mesh is boundary-fitted, with remeshing at each time step. Several time marching schemes are studied, of which a semi-implicit scheme emerges as most effective. The method is demonstrated in very challenging examples: the roll-up of a rod to circular shape and later sudden release, the interaction of a soft rod with a fluid jet and the active self-locomotion of a sperm-like rod. The article includes a detailed description of a code that implements the method in the Firedrake library.publishedVersio

A domain decomposition multiscale mixed method for flow in porous media based on Robin boundary conditions

In this work we propose a domain decomposition method based on Robin type boundary con- ditions that is suitable to solve the porous media equations on very large reservoirs. In order to reduce the algebraic systems to be solved to affordable sizes, a multiscale formulation is considered in which the coupling variables between subdomains, namely, pressures and normal fluxes, are seek in low dimen- sional spaces on the skeleton of the decomposition, while considering the permeability heterogeneities in the original fine grid for the local problems. In the new formulation, a non-dimensional parameter in the Robin condition is introduced such that we may transit smoothly from two well known formulations, namely, the Multiscale Mortar Mixed and the Multiscale Hybrid Mixed finite element methods. In the proposed formulation the interface spaces for pressure and fluxes can be selected independently. This has the potential to produce more accurate results by better accommodating local features of the exact solution near subdomain boundaries. Several numerical examples which exhibit highly heterogeneous permeability fields and channelized regions are solved with the new formulation and results compared to the aforementioned multiscale methods.Publicado en: Mecánica Computacional vol. XXXV, no. 17Facultad de Ingenierí

A domain decomposition multiscale mixed method for flow in porous media based on Robin boundary conditions

In this work we propose a domain decomposition method based on Robin type boundary con- ditions that is suitable to solve the porous media equations on very large reservoirs. In order to reduce the algebraic systems to be solved to affordable sizes, a multiscale formulation is considered in which the coupling variables between subdomains, namely, pressures and normal fluxes, are seek in low dimen- sional spaces on the skeleton of the decomposition, while considering the permeability heterogeneities in the original fine grid for the local problems. In the new formulation, a non-dimensional parameter in the Robin condition is introduced such that we may transit smoothly from two well known formulations, namely, the Multiscale Mortar Mixed and the Multiscale Hybrid Mixed finite element methods. In the proposed formulation the interface spaces for pressure and fluxes can be selected independently. This has the potential to produce more accurate results by better accommodating local features of the exact solution near subdomain boundaries. Several numerical examples which exhibit highly heterogeneous permeability fields and channelized regions are solved with the new formulation and results compared to the aforementioned multiscale methods.Publicado en: Mecánica Computacional vol. XXXV, no. 17Facultad de Ingenierí

Multifluid flows with weak and strong discontinuous interfaces using an elemental enriched space

In a previous paper, the authors presented an elemental enriched space to be used in a finite-element framework (EFEM) capable of reproducing kinks and jumps in an unknown function using a fixed mesh in which the jumps and kinks do not coincide with the interelement boundaries. In this previous publication, only scalar transport problems were solved (thermal problems). In the present work, these ideas are generalized to vectorial unknowns, in particular, the incompressible Navier-Stokes equations for multifluid flows presenting internal moving interfaces. The advantage of the EFEM compared with global enrichment is the significant reduction in computing time when the internal interface is moving. In the EFEM, the matrix to be solved at each time step has not only the same amount of degrees of freedom (DOFs) but also the same connectivity between the DOFs. This frozen matrix graph enormously improves the efficiency of the solver. Another characteristic of the elemental enriched space presented here is that it allows a linear variation of the jump, thus improving the convergence rate, compared with other enriched spaces that have a constant variation of the jump. Furthermore, the implementation in any existing finite-element code is extremely easy with the version presented here because the new shape functions are based on the usual finite-element method shape functions for triangles or tetrahedrals, and once the internal DOFs are statically condensed, the resulting elements have exactly the same number of unknowns as the nonenriched finite elements.Peer ReviewedPreprin