A fixed-mesh method for incompressible flow-structure systems with finite solid deformations

Hong Zhao, Jonathan B. Freund, Robert D. Moser

Research output: Contribution to journalArticlepeer-review


A fixed-mesh algorithm is proposed for simulating flow-structure interactions such as those occurring in biological systems, in which both the fluid and solid are incompressible and the solid deformations are large. Several of the well-known difficulties in simulating such flow-structure interactions are avoided by formulating a single set of equations of motion on a fixed Eulerian mesh. The solid's deformation is tracked to compute elastic stresses by an overlapping Lagrangian mesh. In this way, the flow-structure interaction is formulated as a distributed body force and singular surface force acting on an otherwise purely fluid system. These forces, which depend on the solid elastic stress distribution, are computed on the Lagrangian mesh by a standard finite-element method and then transferred to the fixed Eulerian mesh, where the joint momentum and continuity equations are solved by a finite-difference method. The constitutive model for the solid can be quite general. For the force transfer, standard immersed-boundary and immersed-interface methods can be used and are demonstrated. We have also developed and demonstrated a new projection method that unifies the transfer of the surface and body forces in a way that exactly conserves momentum; the interface is still effectively sharp for this approach. The spatial convergence of the method is observed to be between first- and second-order, as in most immersed-boundary methods for membrane flows. The algorithm is demonstrated by the simulations of an advected elastic disk, a flexible leaflet in an oscillating flow, and a model of a swimming jellyfish.

Original languageEnglish (US)
Pages (from-to)3114-3140
Number of pages27
JournalJournal of Computational Physics
Issue number6
StatePublished - Mar 1 2008

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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