On the elliptic mesh generation in domains containing multiple inclusions and undergoing large deformations

Viscous effects on the oscillations of two equal and deformable bubbles under a step change in pressure

“…Details of this method applied in the present problem are given in Chatzidai et al (2009), where a number of convergence tests have also been reported to determine (i) the number of elements required on the bubble surfaces in particular, to resolve the boundary layers that may arise in this problem and (ii) the radial distance, R ∞ , of the far-field boundary condition. Through numerous tests, it was determined that setting R ∞ = 30 was more than sufficient to guarantee that the outflow boundary did not affect our results in any measurable way.…”

On the transient coating of a straight tube with a viscoelastic material

“…To increase the solution accuracy in regions of particular interest or in regions with sharp variations of the solution vector such as those along the bubble surface and the advancing front, the element refinement method reported in [47] has been applied here as well. Fig.…”

An efficient parallel and fully implicit algorithm for the simulation of transient free-surface flows of multimode viscoelastic liquids

“…For the reduction of the effect of the length of the geometry on the solution, open inflow/outflow boundary conditions are adopted along the corresponding boundaries (Dimakopoulos and Tsamopoulos [11]). There are three basic approaches for the description of freesurface flows and the generation of the computational mesh (Dimakopoulos and Tsamopoulos [12], Chatzidai et al [26], Zacharioudaki et al [27]: Eulerian, Lagrangian and Arbitrary Lagrangian-Eulerian methods. The distinction between them depends on the time evolution of the grid points of the control volume: If the grid points follow the local velocity field, the method is called Lagrangian.…”

“…For reasons related with the required accuracy and the stability of such calculations (Chatzidai et al [26]), an arbitrary Langrangian-Eulerian technique is adopted here, which is based on solving a quasi-elliptic set of equations. In Cartesian geometries this set is:…”

“…Due to the large deformation of free-surfaces and, consequently, of the discretized control volume, triangular elements are used because they can follow closely these deformations and the large changes of the dependent variables without any numerically induced singularities. For improvement of the accuracy of our calculations, a hierarchical local refinement technique can be selectively applied along free-surfaces and/or the solid walls to resolve more accurately the stress boundary layers that may arise there (Chatzidai et al [26]). However, in the current study, we will focus on the evaluation of the performance of our parallel algorithms without making use of such an option.…”