No Arabic abstract
We present a novel formulation based on an immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluid-structure interaction (FSI) phenomena for air blast. We aim to develop a practical computational framework that is capable of capturing the mechanics of air blast coupled to solids and structures that undergo large, inelastic deformations with extreme damage and fragmentation. An immersed technique is used, which involves an a priori monolithic FSI formulation with the implicit detection of the fluid-structure interface and without limitations on the solid domain motion. The coupled weak forms of the fluid and structural mechanics equations are solved on the background mesh. Correspondence-based PD is used to model the meshfree solid in the foreground domain. We employ the Non-Uniform Rational B-Splines (NURBS) IGA functions in the background and the Reproducing Kernel Particle Method (RKPM) functions for the PD solid in the foreground. We feel that the combination of these numerical tools is particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of IGA and RKPM, the benefits of using immersed methodology in handling the fluid-structure coupling, and the capabilities of PD in simulating fracture and fragmentation scenarios. Numerical examples are provided to illustrate the performance of the proposed air-blast FSI framework.
Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large-scale fluid-structure interaction systems characterized by large structural deformations. Numerical methods to solve these problems, including embedded/immersed boundary methods, are typically not differentiable and lack smoothness. We propose a framework that is built on unscented Kalman filter/inversion to efficiently calibrate and provide uncertainty estimations of such complicated models with noisy observation data. The approach is derivative-free and non-intrusive, and is of particular value for the forward model that is computationally expensive and provided as a black box which is impractical to differentiate. The framework is demonstrated and validated by successfully calibrating the model parameters of a piston problem and identifying the damage field of an airfoil under transonic buffeting.
We present novel coupling schemes for partitioned multi-physics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative coupling, support for multi-rate time stepping, and higher-order convergence in time. To achieve this, we combine waveform relaxation -- a known method to achieve higher order in applications with split time stepping based on continuous representations of coupling variables in time -- with interface quasi-Newton coupling, which has been developed throughout the last decade and is generally accepted as a very robust iterative coupling method even for gluing together black-box simulation codes. We show convergence results (in terms of convergence of the iterative solver and in terms of approximation order in time) for two academic test cases -- a heat transfer scenario and a fluid-structure interaction simulation. We show that we achieve the expected approximation order and that our iterative method is competitive in terms of iteration counts with those designed for simpler first-order-in-time coupling.
We investigate a multirate time step approach applied to decoupled methods in fluid and structure interaction(FSI) computation, where two different time steps are used for fluid and structure respectively. For illustration, the multirate technique is tested by the decoupled beta-scheme. Numerical experiments show that the proposed approach is stable and retains the same order accuracy as the original single time step schemes, while with much less computational expense.
We consider a fully discrete loosely coupled scheme for incompressible fluid-structure interaction based on the time semi-discrete splitting method introduced in {emph{[Burman, Durst & Guzman, arXiv:1911.06760]}}. The splittling method uses a Robin-Robin type coupling that allows for a segregated solution of the solid and the fluid systems, without inner iterations. For the discretisation in space we consider piecewise affine continuous finite elements for all the fields and ensure the inf-sup condition by using a Brezzi-Pitkaranta type pressure stabilization. The interfacial fluid-stresses are evaluated in a variationally consistent fashion, that is shown to admit an equivalent Lagrange multiplier formulation. We prove that the method is unconditionally stable and robust with respect to the amount of added-mass in the system. Furthermore, we provide an error estimate that shows the error in the natural energy norm for the system is $mathcal Obig(sqrt{T}(sqrt{Delta t} + h)big)$ where $T$ is the final time, $Delta t$ the time-step length and $h$ the space discretization parameter.
We present a novel preconditioning technique for Krylov subspace algorithms to solve fluid-structure interaction (FSI) linearized systems arising from finite element discretizations. An outer Krylov subspace solver preconditioned with a geometric multigrid (GMG) algorithm is used, where for the multigrid level sub-solvers, a field-split (FS) preconditioner is proposed. The block structure of the FS preconditioner is derived using the physical variables as splitting strategy. To solve the subsystems originated by the FS preconditioning, an additive Schwarz (AS) block strategy is employed. The proposed field-split preconditioner is tested on biomedical FSI applications. Both 2D and 3D simulations are carried out considering aneurysm and venous valve geometries. The performance of the FS preconditioner is compared with that of a second preconditioner of pure domain decomposition type.