Numerical simulation of a pulsatile flow through a flexible channel

IFIP Advances in Information and Communication Technology

2014

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Section: Algorithm 2 By the Bfgs Methodsmentioning

confidence: 99%

Steady Fluid-Structure Interaction Using Fictitious Domain

Halanay

IFIP Advances in Information and Communication Technology

2014

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“…The governing equations for fluid-structure interaction problem are (1)- (16). The above fluid and structure models could be considered unbalanced: on the one hand, the structure is governed by a linear elastic constitutive law adapted for small displacements and, on the other hand, the fluid equations are written in a moving domain.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…This technique was successfully employed in [16,17], where implicit algorithms are presented. We will use the same least square method based on the BFGS method in order to impose the continuity of the stress at the interface.…”

Section: Implicit and Semi-implicit Time Integration Schemesmentioning

confidence: 99%

“…We can use the same strategy for the unsteady fluid-structure interaction problems and at each time step, we have to solve an optimization problem. The gradient of the cost function is approached by finite differences in [16] where it is proved the superiority of the Broyden, Fletcher, Goldforb, Shano (BFGS) method in comparison with the modified Newton method (Newton with line search), when moderate time step is used. The analytic formula of the gradient of the cost function is presented in [17].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A fast method for solving fluid–structure interaction problems numerically

Numerical Methods in Fluids

2008

SUMMARYThe paper presents a semi-implicit algorithm for solving an unsteady fluid-structure interaction problem. The algorithm for solving numerically the fluid-structure interaction problems was obtained by combining the backward Euler scheme with a semi-implicit treatment of the convection term for the Navier-Stokes equations and an implicit centered scheme for the structure equations. The structure is governed either by the linear elasticity or by the non-linear St Venant-Kirchhoff elasticity models. At each time step, the position of the interface is predicted in an explicit way. Then, an optimization problem must be solved, such that the continuity of the velocity as well as the continuity of the stress hold at the interface. During the Broyden, Fletcher, Goldforb, Shano (BFGS) iterations for solving the optimization problem, the fluid mesh does not move, which reduces the computational effort. The term 'semi-implicit' used for the fully algorithm means that the interface position is computed explicitly, while the displacement of the structure, velocity and the pressure of the fluid are computed implicitly. Numerical results are presented.

“…There exists a rich literature on solving numerically fluid-structure interaction problems. Some methods are based on partitioned procedures, the fluid and structure sub-problems are solved separately using iterative process: fixed point iterations [1][2][3], Newton-like methods [4][5][6] or optimization techniques [7][8][9]. Monolithic methods solve the fluid-structure interaction problem as a single system of equations, [10][11][12][13], or more recently [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Simulation of Fluid–Structure Interaction Problems Using Monolithic Semi-Implicit Algorithm

2019

Fluids

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A monolithic semi-implicit method is presented for three-dimensional simulation of fluid–structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier–Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. We use a global mesh for the fluid–structure domain where the fluid–structure interface is an interior boundary. The continuity of velocity at the interface is automatically satisfied by using globally continuous finite element for the velocity in the fluid–structure mesh. The method is fast because we solve only a linear system at each time step. Three-dimensional numerical tests are presented.