The extended finite element method for two-phase and free-surface flows: A systematic study

A locally extended finite element method for the simulation of multi-fluid flows using the Particle Level Set method

“…At each time step, first the interface is moved and then one step of the predictor multi-corrector fluid solver is performed. This is in contrast to some more sophisticated coupling strategies such as those presented in [33] and [19].…”

“…Similarly for the weak discontinuities (kink in pressure fields) Moës et al [28] and Hansbo & Hansbo [23] separately proposed an abs-enrichment shape function that is defined as: Remark. Numerical results in [19] suggest that even when no surface tension is considered, sign-enrichment provides better results than abs-enrichment although the latter seems sufficient. Using the sign-enrichment, a larger approximation space for the pressure is provided which also allows capturing strong discontinuities in pressure.…”

“…Therefore, an improvement of the pressure approximation is more beneficial than modifying the velocity approximation. Numerical studies performed in [19] suggest that it is not advisable to enrich the velocity approximation space as it does not improve the results significantly. Severe convergence problems and an increase in the required number of iterations have been also reported as the consequences of the velocity enrichment.…”

“…The enrichments do not affect explicitly the nodal approximation of pressure as they are zero at the nodes of the mesh. These basis are known as the XFEM shifted basis [19] in the literature.…”

“…Similar to [15], these enrichments are condensed before assembly. Beside local enrichment, global one, and in particular the XFEM have been also widely used to model multi-fluid flow [17][18][19][20]. Except for the intrinsic XFEM [21], all versions of the XFEM add enrichments to the global system and therefore the graph of the system needs to be updated as the interface moves.…”