A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
Invertible finite elements for robust simulation of large deformation
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Coupling water and smoke to thin deformable and rigid shells
ACM SIGGRAPH 2005 Papers
A DLM/FD method for fluid/flexible-body interactions
Journal of Computational Physics
Journal of Computational Physics
An adaptive, formally second order accurate version of the immersed boundary method
Journal of Computational Physics
A fast variational framework for accurate solid-fluid coupling
ACM SIGGRAPH 2007 papers
A LBM-DLM/FD method for 3D fluid-structure interactions
Journal of Computational Physics
A fixed-mesh method for incompressible flow-structure systems with finite solid deformations
Journal of Computational Physics
Two-way coupling of fluids to rigid and deformable solids and shells
ACM SIGGRAPH 2008 papers
An Unconditionally Stable MacCormack Method
Journal of Scientific Computing
Journal of Computational Physics
Accurate tangential velocities for solid fluid coupling
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
An efficient fluid-solid coupling algorithm for single-phase flows
Journal of Computational Physics
Two-way coupling of rigid and deformable bodies
Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Numerically stable fluid-structure interactions between compressible flow and solid structures
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Chimera grids for water simulation
Proceedings of the 12th ACM SIGGRAPH/Eurographics Symposium on Computer Animation
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
Journal of Computational Physics
Hi-index | 31.47 |
In this paper we consider a strongly coupled (monolithic) fluid structure interaction framework for incompressible flow, as opposed to a loosely coupled (partitioned) method. This requires solving a single linear system that combines the unknown velocities of the structure with the unknown pressures of the fluid. In our previous work, we were able to obtain a symmetric formulation of this coupled system; however, it was also indefinite, making it more difficult to solve. In fact in practice there have been cases where we have been unable to invert the system. In this paper we take a novel approach that consists of factoring the damping matrix of deformable structures and show that this can be used to obtain a symmetric positive definite system, at least to the extent that the uncoupled systems were symmetric positive definite. We use a traditional MAC grid discretization of the fluid and a fully Lagrangian discretization of the structures for the sake of exposition, noting that our procedure can be generalized to other scenarios. For the special case of rigid bodies, where there are no internal damping forces, we exactly recover the system of Batty et al. (2007) [4].