An arbitrary Lagrangian-Eulerian method for simulating interfacial dynamics between a hydrogel and a fluid

• Boundary conditions on the hydrogel surface are naturally embedded in weak form. With proper test functions, form recovers dissipative energy law. The displacement extension algorithm captures interfacial accurately. ALE method tracks moving interface as well deforming solid skeleton. numerical results show excellent agreement with available analytical solutions. Hydrogels crosslinked polymer networks swollen an aqueous solvent, and play central roles biomicrofluidic devices. In such applications, gel is often contact a flowing fluid, thus setting up fluid-hydrogel two-phase system. Using recently proposed model (Young et al. [41] 2019), we treat poroelastic material consisting of Saint Venant-Kirchhoff network Newtonian viscous develop finite-element for computing flows involving interface. tracked by using fixed-mesh arbitrary Lagrangian-Eulerian that maps to reference configuration. deformation coupled fluid governing equations into monolithic library deal.II. code validated against solutions several non-trivial flow problems: one-dimensional compression layer uniform flow, two-layer shear Darcy particle planar extensional flow. all cases, Numerical tests second-order convergence respect mesh refinement, first-order time-step refinement.