We propose a novel method to implicitly two-way couple Eulerian compressible flow to volumetric Lagrangian solids. The method works for both deformable and rigid solids and for arbitrary equations of state. The method exploits the formulation of  which solves compressible fluid in a semi-implicit manner, solving for the advection part explicitly and then correcting the intermediate state to time tn+1 using an implicit pressure, obtained by solving a modified Poisson system. Similar to previous fluid-structure interaction methods, we apply pressure forces to the solid and enforce a velocity boundary condition on the fluid in order to satisfy a no-slip constraint. Unlike previous methods, however, we apply these coupled interactions implicitly by adding the constraint to the pressure system and combining it with any implicit solid forces in order to obtain a strongly coupled, symmetric indefinite system (similar to , which only handles incompressible flow). We also show that, under a few reasonable assumptions, this system can be made symmetric positive-definite by following the methodology of . Because our method handles the fluid-structure interactions implicitly, we avoid introducing any new time step restrictions and obtain stable results even for high density-to-mass ratios, where explicit methods struggle or fail. We exactly conserve momentum and kinetic energy (thermal fluid-structure interactions are not considered) at the fluid-structure interface, and hence naturally handle highly non-linear phenomenon such as shocks, contacts and rarefactions. © 2011 Elsevier Inc.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): 42959
Acknowledgements: Research supported in part by a Packard Foundation Fellowship, an Okawa Foundation Research Grant, ONR N0014-06-1-0393, ONR N00014-06-1-0505, ONR N00014-09-1-0101, ONR N00014-05-1-0479 for a computing cluster, NIH U54-GM072970, NSF ACI-0323866, NSF IIS-0326388, and King Abdullah University of Science and Technology (KAUST) 42959. J.G. was supported in part by, and computational resources were provided in part by ONR N00014-06-1-0505 and ONR N00014-09-C-015.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.