Chris Rycroft, Department of Mathematics, University of Wisconsin

The reference map technique for simulating complex materials and multi-body interactions

Conventional computational methods often create a dilemma for fluid–structure interaction problems. Typically, solids are simulated using a Lagrangian approach with grid that moves with the material, whereas fluids are simulated using an Eulerian approach with a fixed spatial grid, requiring some type of interfacial coupling between the two different perspectives. Here, a fully Eulerian method for simulating structures immersed in a fluid will be presented [1]. By introducing a reference map variable to model finite-deformation constitutive relations in the structures on the same grid as the fluid, the interfacial coupling problem is highly simplified. The method is particularly well suited for simulating soft, highly-deformable materials and many-body contact problems [2], and several examples in two and three dimensions [3] will be presented.

[1] K. Kamrin, C. H. Rycroft, and J.-C. Nave, J. Mech. Phys. Solids 60, 1952–1969 (2012).
[2] C. H. Rycroft et al., J. Fluid Mech. 898, A9 (2020).
[3] Y. L. Lin, N. J. Derr, and C. H. Rycroft, Proc. Natl. Acad. Sci. 119, e2105338118 (2022).