Results

**1 - 5**of**5**### A stable FSI algorithm for light rigid bodies in compressible flow

"... In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies with zero mass and zero moments of inertia. The approach is b ..."

Abstract
- Add to MetaCart

(Show Context)
In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies with zero mass and zero moments of inertia. The approach is based on a local characteristic projection of the force on the rigid body and is a natural extension of the recently developed algorithm for coupling compressible flow and deformable bodies [1, 2, 3]. Normal mode analysis is used to prove the stability of the approximation for a one-dimensional model problem and numerical computations confirm these results. In multiple space dimensions the approach naturally reveals the form of the added mass tensors in the equations governing the motion of the rigid body. These tensors, which depend on certain surface integrals of the fluid impedance, couple the translational and angular velocities of the body. Numerical results in two space dimensions, based on the use of moving overlapping grids and adaptive mesh refinement, demonstrate the behavior and efficacy of the new scheme. These results include the simulation of the difficult problem of a shock impacting an ellipse of zero mass.

### Deforming Composite Grids for Solving Fluid Structure Problems

"... We describe a mixed Eulerian-Lagrangian approach for solving fluid-structure interaction (FSI) problems. The technique, which uses deforming composite grids (DCG), is applied to FSI problems that couple high speed compressible flow with elastic solids. The fluid and solid domains are discretized wit ..."

Abstract
- Add to MetaCart

(Show Context)
We describe a mixed Eulerian-Lagrangian approach for solving fluid-structure interaction (FSI) problems. The technique, which uses deforming composite grids (DCG), is applied to FSI problems that couple high speed compressible flow with elastic solids. The fluid and solid domains are discretized with composite overlapping grids. Curvilinear grids are aligned with each interface and these grids deform as the interface evolves. The majority of grid points in the fluid domain generally belong to background Cartesian grids which do not move during a simulation. The FSI-DCG approach allows large displacements of the interfaces while retaining high quality grids. Efficiency is obtained through the use of structured grids and Cartesian grids. The governing equations in the fluid and solid domains are evolved in a partitioned approach. We solve the compressible Euler equations in the fluid domains using a high-order Godunov finite-volume scheme. We solve the linear elastodynamic equations in the solid domains using a second-order upwind scheme. We develop interface approximations based on the solution of a fluid-solid Riemann problem that results in a stable scheme even for the difficult case of light solids coupled to heavy fluids. The FSI-DCG approach is verified for three problems with known solutions, an elastic-piston problem, the superseismic shock problem and a deforming diffuser. In addition, a self convergence study is performed for an elastic shock hitting

### On Explicit/Implicit and Incompressible/Compressible Issues of Immersed Boundary/Continuum Methods by

"... In addition to an overview of the immersed boundary/continuum methods and their finite ele-ment formulations, explicit vs. implicit and incompressible vs. compressible issues are discussed. The recent finite element formulations retain the same strategies employed in the original immersed boundary m ..."

Abstract
- Add to MetaCart

(Show Context)
In addition to an overview of the immersed boundary/continuum methods and their finite ele-ment formulations, explicit vs. implicit and incompressible vs. compressible issues are discussed. The recent finite element formulations retain the same strategies employed in the original immersed boundary method, namely, the independent Lagrangian solid mesh moves on top of a fixed or pre-scribed background Eulerian fluid mesh. The added features in recent finite element formulations are the generality of the immersed solid which can occupy a finite volume in the fluid and be imper-meable, compressible, and highly deformable. Furthermore, a matrix-free Newton-Krylov iterative solution technique also resolves the time step limitation issues related to stiff spring supports from the boundary and the high elasticity moduli of the immersed solid. This implicit iterative approach enables the application of immersed methods to many engineering problems some of which are documented here for illustrative purposes.

### A stable partitioned FSI algorithm for incompressible flow and elastic solids

"... A stable partitioned algorithm for coupling incompressible flows with compressible elastic solids is de-scribed. This added-mass partitioned (AMP) scheme requires no sub-iterations, can be made fully second-or higher-order accurate, and remains stable even in the presence of strong added-mass effect ..."

Abstract
- Add to MetaCart

A stable partitioned algorithm for coupling incompressible flows with compressible elastic solids is de-scribed. This added-mass partitioned (AMP) scheme requires no sub-iterations, can be made fully second-or higher-order accurate, and remains stable even in the presence of strong added-mass effects. The ap-proach extends the scheme of Banks et al. [1, 2] for compressible flow, and uses Robin (mixed) boundary conditions with the fluid and solid solvers at the interface. The AMP Robin conditions are derived from a local characteristic decomposition in the solid at the interface. Two forms of the Robin conditions are derived depending on whether the fluid equations are advanced with a fractional-step method or not. A normal mode analysis for a discretization of an FSI model problem is performed to show that the new AMP algorithm is stable for any ratio of the solid and fluid densities, including the case of very light solids when the added-mass effects are large. In contrast, it is shown that a traditional partitioned algorithm involving a Dirichlet-Neumann coupling for the same FSI problem is formally unconditionally unstable for any ratio of densities. Exact traveling wave solutions are derived for three FSI model problems of increasing complex-ity, and these solutions are used to verify the stability and accuracy of the corresponding numerical results

### unknown title

"... A stable partitioned FSI algorithm for incompressible flow and structural shells ..."

Abstract
- Add to MetaCart

A stable partitioned FSI algorithm for incompressible flow and structural shells