Determine the best bulk-equation formulation for general multi-material interface-capturing simulations

Determine which system of bulk equations best handles arbitrary configurations of sharp-interface multi-material flows in interface-capturing methods.

Background

The paper surveys interface-capturing approaches that evolve all materials simultaneously through a single system of bulk equations. Because different formulations are used to represent heterogeneous fluid-solid continua with discontinuous material properties, the authors identify the absence of a generally preferred formulation for correctly handling arbitrary configurations.

This problem concerns the comparative mathematical and physical adequacy of bulk models, rather than the particular viscoelastic system developed in the paper.

References

However, various systems of bulk equations % that resolve ``all'' materials interfaces (at all scales) have been used by interface-capturing methods to simulate multi-material motions on times $t \in (0,T)$ given a force field $f(t,x)$ in the ambiant physical space $x\inR3$, see e.g. , and it is not clear yet what is best to handle correctly a given configuration in general.

— Multi-material flow with a new viscoelastic model  (2609.35172 - Boyaval, 28 Sep 2026) in Section 1, Introduction