Shape Optimization of Fluid-Structure Interaction Problems Using Two-Equation Turbulence Models

In this paper, continuum-based sizing and configuration design sensitivity analysis (DSA) and optimization methods using the established transient dynamic analysis code DYNA3D are developed. For transient dynamic analysis, the explicit central difference method is used. For the structural domain, the updated Lagrangian formulation is used since it is appropriate for the path dependent problem. The first-order variations of the kinetic energy form, strain energy form, load form, and kinematic and structural responses with respect to the sizing and configuration design variables are derived. For the updated Lagrangian formulation, the design velocity field that defines the mapping between the initial and perturbed designs is updated at each updated configuration. The direct differentiation method is used in this paper for DSA. Numerical implementation of sizing DSA, configuration DSA, and optimization of a vehicle frame and A-pillar models has been carried out using the nonlinear finite element analysis (FEA) code DYNA3D.

Numerical Simulation of Oil Tank Behavior Under Seismic Excitation. Fluid – Structure Interaction Problem Solution

Modeling concept and numerical simulation of ultrasonic wave propagation in a moving fluid-structure domain based on a monolithic approach

The 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. Copyright © 2008 John Wiley & Sons, Ltd.

Design sensitivity analysis of sheet metal forming processes with a direct differentiation method

The objective of this study is to examine two analytical methods for the design sensitivity analysis of optimal control problems and to develop the analyses necessary for the application of the methods to thermal systems. The two methods are the direct differentiation method and the adjoint variable method. Results for these methods are compared with those obtained using central finite difference approximations for design sensitivity analysis. The adjoint variable method has the potential to reduce significantly computational times for design sensitivity analysis while sacrificing only a small amount of accuracy. As the number of functional requiring design sensitivity analysis increases, however, the adjoint variable method becomes less attractive and the direct differentiation method becomes more attractive.

In the paper, high performance implementation of an existing Arbitrary Lagrangian and Eulerian (ALE) moving mesh generation technique for shared memory systems using OpenMP is discussed. Currently, there are various existing techniques for moving mesh, but in Fluid Structure Interaction (FSI) problems, adaptive techniques using ALE method of r-type are more applicable. A conjugate gradient method with preconditioned matrix has been used for constraint optimization of the non-linear problem. In the parallel algorithm first mesh is ordered using divide and conquer approach for the processors with small cache memory. Then it is solved using OpenMP. Experiments are carried out using four AMD Opteron processors and 98% efficiency of the code in term of speed up is achieved. Quality of mesh is also verified by using Jacobian (for area) and angles of triangle.

A multi-resolution smoothed particle hydrodynamics with multi-GPUs acceleration for three-dimensional fluid-structure interaction problems

A wavelet immersed boundary method for two-variable coupled fluid-structure interactions

An adaptive mesh rezoning scheme for moving boundary flows and fluid–structure interaction

Explicit and implicit methods for design sensitivity analysis of nonlinear structures subjected to transient dynamic loads are described. The direct differentiation method is used to calculate the sensitivities. Elastic and elasto-plastic problems undergoing large deformation are treated in the formulation. The explicit method is quite straightforward to implement for analysis as well as design sensitivity analysis: knowing all the quantities at time t, one updates the quantities for the next time point without solution of any linear system of equations, or any iterations. For the implicit method, the effective stiffness matrix for the sensitivity equation is different from that for the analysis phase due to inclusion of large deformation in the formulation. A numerical procedure to integrate the equation is proposed which uses the symmetric effective stiffness matrix from the analysis phase. Although the sensitivity analysis problem is linear, the procedure requires iterations for sensitivity calculations at each time step, as for the analysis phase. The implicit method is implemented using the pre-conditioned conjugate gradient iterative solution scheme. Numerical results for sensitivities indicate the implicit method to be more accurate than the explicit method for transient elastoplastic problems. However, the explicit method is substantially more efficient than the implicit method.

Design sensitivity analysis of dynamic response of nonviscously damped systems

Using the direct differentiation method, a design sensitivity analysis method for time-dependent incompressible fluids is developed. The fluid behavior is described as the motion of particles involved by the SPH method. In the SPH projection method, instead of changing the fluid density, incompressibility is enforced by the pressure Poisson equation derived from pressure projection, which enable to use larger time steps. In spite of the additional pressure Poisson equation, the computational cost for the design sensitivity is not expensive since the factorized system matrix of pressure Poisson equation can be utilized. Aforementioned computational efficiency is very beneficial for the design sensitivity computation required for every time step in explicit time integration and updated Lagrangian schemes, for which an update scheme of design velocity field is developed using the velocity sensitivity. Through demonstrative numerical examples, the developed DSA method turns out to be efficient and shows excellent agreement with finite differencing.

Abstract. In this paper we investigate the finite-time and asymptotic behaviour of algebraic turbulent mixing-layer models by numerical simulation. We compare the performances given by three different settings of the eddy viscosity. We consider Richardson number-based vertical eddy viscosity models. Two of these are classical algebraic turbulence models usually used in numerical simulations of global oceanic circulation, i.e. the Pacanowski–Philander and the Gent models, while the other one is a more recent model (Bennis et al., 2010) proposed to prevent numerical instabilities generated by physically unstable configurations. The numerical schemes are based on the standard finite element method. We perform some numerical tests for relatively large deviations of realistic initial conditions provided by the Tropical Atmosphere Ocean (TAO) array. These initial conditions correspond to states close to mixing-layer profiles, measured on the Equatorial Pacific region called the West-Pacific Warm Pool. We conclude that mixing-layer profiles could be considered as kinds of "absorbing configurations" in finite time that asymptotically evolve to steady states under the application of negative surface energy fluxes.

An efficient partitioned framework to couple Arbitrary Lagrangian-Eulerian and meshless vector form intrinsic finite element methods for fluid-structure interaction problems with deformable structures