In this work, we are interested in efficiently solving the quasi-static, linear Biot model for poroelasticity. We consider the fixed-stress splitting scheme, which is a popular method for iterative ...

https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6130

On the optimization of the fixed‑stress splitting for Biot's equations

http://ieeexplore.ieee.org/iel5/5/31337/01457178.pdf

Lectures in applied mathematics (vol. 19): Lectures on mathematical aspects of physiology

A boundary integral method for the simulation of the time-dependent deformation of Newtonian or non-Newtonian drops suspended in a Newtonian fluid is developed. The boundary integral formulation for Stokes flow is used and the non-Newtonian stress is treated as a source term which yields an extra integral over the domain of the drop. The implementation of the boundary conditions is facilitated by rewriting the domain integral by means of the Gauss divergence theorem. To apply the divergence theorem smoothness assumptions are made concerning the non-Newtonian stress tensor. The correctness of these assumptions in actual simulations is checked with a numerical validation procedure. The method appears mathematically correct and the numerical algorithm is second order accurate. Besides this validation we present simulation results for a Newtonian drop and a drop consisting of an Oldroyd-B fluid. The results for Newtonian and non-Newtonian drops in two dimensions indicate that the steady state deformation is quite independent of the drop-fluid. The deformation process, however, appears to be strongly dependent on the drop-fluid. For the non-Newtonian drop a mechanical model is developed to describe the time-dependent deformation of the cylinder for small capillary numbers.

A boundary integral method for two-dimensional non-Newtonian drops in slow viscous flow

An immersed finite element method for elliptic interface problems in three dimensions

In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well-known that the convergence of the method is strongly dependent on the applied stabilization/tuning parameter. In this work, we propose a new approach to optimize this parameter. We show theoretically that it depends also on the fluid flow properties and not only on the mechanics properties and the coupling coefficient. The type of analysis presented in this paper is not restricted to a particular spatial discretization. We only require it to be inf-sup stable. The convergence proof applies also to low-compressible or incompressible fluids and low-permeable porous media. Illustrative numerical examples, including random initial data, random boundary conditions or random source terms and a well-known benchmark problem, i.e. Mandel's problem are performed. The results are in good agreement with the theoretical findings. Furthermore, we show numerically that there is a connection between the inf-sup stability of discretizations and the performance of the fixed-stress splitting scheme.

On the optimization of the fixed-stress splitting for Biot's equations

An immersed discontinuous finite element method for Stokes interface problems

Immersed and Discontinuous Finite Element Methods

An improved superconvergence error estimate for the LDG method

Interferometric Synthetic Aperture Radar (InSAR) measurements are often biased due to atmospheric effects. Especially, the tropospheric water vapor engenders a delay of SAR signal propagation. In this paper, we propose a specific methodology for atmospheric effects correction on SAR interferograms. It is based on ancillary data collected from NOAA-AVHRR sensor. The specificity of the approach consists in its applicability where no ground truth GPS measurements are available neither for calibration nor for result validation. An adaptive validation demarche is also proposed.

/pdf/a-specific-methodology-for-atmospheric-effect-reduction-on-2pi6nrunwx.pdf

A specific methodology for atmospheric effect reduction on SAR interferograms

An immersed discontinuous finite element method for the Stokes problem with a moving interface

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