Residual drilling mud during conditioning of uneven boreholes in primary cementing. Part 1: Rheology and geometry effects in non-inertial flows

Augmented Lagrangian simulations study of yield-stress fluid flows in expansion-contraction and comparisons with physical experiments

“…Of note, inside this pseudo-plug zone, one can also see four little "square" plugs which are also exhibited in [29,27]. These four plugs are confirmed under mesh refinement (see below).…”

“…The discretization in space is done with finite-differences on rectangular grids. As such, present work is complementary to [28,29] since it allows to compare the results between structured and non-structured grids discretizations. For completeness and reproducibility of the paper, we give in Appendix A the algorithms we implemented with Fortran 90 and MPI.…”

“…fig. 6, 7 [29], taking into account the fact that the geometry is here fully symmetric in x and y, while [29] is only symmetric w.r.t. y.…”

“…Note that, following the details of section 2.2, we decide to take a pressure cut on a horizontal line which is defined at aỹ which is in the middle of the fluid part of the entrance/exit channels. This choice can be discussed (for instance Roustaei et al [29] take the averaged pressure alongỹ) but our point here is to say that the pressure has only a meaning in the fluid part (and not in the rigid zone). As a consequence, we do not want to compute averaged pressure alongỹ.…”

“…Let us mention the work of de Souza et al [7] which seems to be the first work close to the present study: they present experiments with Carbopol and compare with numerical solutions obtained with a regularization method. In addition, similar configurations are simulated in [28] and [29] using an AL method on unstructured meshes. Their code is implemented with the excellent Rheolef library [30] of Saramito and coworkers (see e.g.…”