arXiv subjects

Charbel Farhat

Publications and source records attributed to Charbel Farhat.

27 records · Page 2Linked to original sources

arXiv2019

An Embedded Boundary Approach for Resolving the Contribution of Cable Subsystems to Fully Coupled Fluid-Structure Interaction

Cable subsystems characterized by long, slender, and flexible structural elements are featured in numerous engineering systems. In each of them, interaction between an individual cable and the surrounding fluid is inevitable. Such a Fluid-Structure Interaction (FSI) has received little attention in the literature, possibly due to the inherent complexity associated with fluid and structural semi-discretizations of disparate spatial dimensions. This paper proposes an embedded boundary approach for filling this gap, where the dynamics of the cable are captured by a standard finite element representation $\mathcal C$ of its centerline, while its geometry is represented by a discrete surface $Σ_h$ that is embedded in the fluid mesh. The proposed approach is built on master-slave kinematics between $\mathcal C$ and $Σ_h$, a simple algorithm for computing the motion/deformation of $Σ_h$ based on the dynamic state of $\mathcal C$, and an energy-conserving method for transferring to $\mathcal C$ the loads computed on $Σ_h$. Its effectiveness is demonstrated for two highly nonlinear applications featuring large deformations and/or motions of a cable subsystem and turbulent flows: an aerial refueling model problem, and a challenging supersonic parachute inflation problem. The proposed approach is verified using numerical data, and validated using real flight data.

cs.CE↗

arXiv2015

Real-time solution of computational problems using databases of parametric linear reduced-order models with arbitrary underlying meshes

A comprehensive approach for real-time computations using a database of parameterized linear reduced-order models (ROMs) is proposed. The method proceeds by sampling offline ROMs for specific values of the parameters and interpolating online the associated reduced operators. In the offline phase, a pre-processing step transforms the reduced operators into consistent sets of generalized coordinates prior to their interpolation. The present paper also introduces a consistency enforcement approach for models defined on arbitrary underlying meshes. In the online phase, the operators are interpolated on matrix manifolds. The proposed framework is illustrated on two realistic multi-physics problems: an inverse acoustic scattering problem around a submarine and flutter predictions for a wing-tank system. The second application is implemented on a mobile device, illustrating the capability of the proposed framework to operate in real-time.

math.NA↗

arXiv2015

Linearized Aeroelastic Computations in the Frequency Domain Based on Computational Fluid Dynamics

An iterative, CFD-based approach for aeroelastic computations in the frequency domain is presented. The method relies on a linearized formulation of the aeroelastic problem and a fixed-point iteration approach and enables the computation of the eigenproperties of each of the wet aeroelastic eigenmodes. Numerical experiments on the aeroelastic analysis and design optimization of two wing configurations illustrate the capability of the method for the fast and accurate aeroelastic analysis of aircraft configurations and its advantage over classical time-domain approaches.

physics.flu-dyn↗

arXiv2015

Projection-based model reduction for contact problems

To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that tend to dramatically increase computational complexity. Although significant progress has been achieved in the development of computational approaches for the reduction of nonlinear computational mechanics models, addressing the issue of contact remains a major hurdle. To this effect, this paper introduces a projection-based model reduction approach for both static and dynamic contact problems. It features the application of a non-negative matrix factorization scheme to the construction of a positive reduced-order basis for the contact forces, and a greedy sampling algorithm coupled with an error indicator for achieving robustness with respect to model parameter variations. The proposed approach is successfully demonstrated for the reduction of several two-dimensional, simple, but representative contact and self contact computational models.

physics.comp-ph↗

arXiv2014

Progressive construction of a parametric reduced-order model for PDE-constrained optimization

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by a given Reduced-Order Model (ROM) is defined with the goal of converging to the solution of a given PDE-constrained optimization problem. For each reduced optimization problem, the constraining ROM is trained from sampling the High-Dimensional Model (HDM) at the solution of some of the previous problems in the sequence. The reduced optimization problems are equipped with a nonlinear trust-region based on a residual error indicator to keep the optimization trajectory in a region of the parameter space where the ROM is accurate. A technique for incorporating sensitivities into a Reduced-Order Basis (ROB) is also presented, along with a methodology for computing sensitivities of the reduced-order model that minimizes the distance to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced optimization framework is applied to subsonic aerodynamic shape optimization and shown to reduce the number of queries to the HDM by a factor of 4-5, compared to the optimization problem solved using only the HDM, with errors in the optimal solution far less than 0.1%.

math.OC↗

arXiv2014

Reduction of Nonlinear Embedded Boundary Models for Problems with Evolving Interfaces

Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfaces. Developing model reduction methods for computational frameworks based on such methods seems however to be challenging. Indeed, most popular model reduction techniques are projection-based, and rely on basis functions obtained from the compression of simulation snapshots. In a traditional interface-fitted computational framework, the computation of such basis functions is straightforward, primarily because the computational domain does not contain in this case a fictitious region. This is not the case however for an embedded computational framework because the computational domain typically contains in this case both real and ghost regions whose definitions complicate the collection and compression of simulation snapshots. The problem is exacerbated when the interface separating both regions evolves in time. This paper addresses this issue by formulating the snapshot compression problem as a weighted low-rank approximation problem where the binary weighting identifies the evolving component of the individual simulation snapshots. The proposed approach is application independent and therefore comprehensive. It is successfully demonstrated for the model reduction of several two-dimensional, vortex-dominated, fluid-structure interaction problems.

physics.comp-ph↗

arXiv2013

A practical factorization of a Schur complement for PDE-constrained Distributed Optimal Control

A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution of which is crucial. A new factorization of the Schur complement for such a system is proposed and its characteristics discussed. The factorization introduces two complex factors that are complex conjugate to each other. The proposed solution methodology involves the application of a parallel linear domain decomposition solver---FETI-DPH---for the solution of the subproblems with the complex factors. Numerical properties of FETI-DPH in this context are demonstrated, including numerical and parallel scalability and regularization dependence. The new factorization can be used to solve Schur complement systems arising in both range-space and full-space formulations. In both cases, numerical results indicate that the complex factorization is promising.

math.NA↗

arXiv2013

On the stability of projection-based linear reduced-order models: Descriptor vs non-descriptor forms

Two comprehensive approaches are considered for constructing projection-based reduced-order computational models for linear dynamical systems. The first one reduces the governing equations written in the descriptor form, using a Galerkin or Petrov-Galerkin projection onto a reduced-order basis or pair of them, respectively. These bases can be constructed by any preferred method such as the Proper Orthogonal Decomposition, Balanced Proper Orthogonal Decomposition, or Moment Matching method. The second approach transforms first the governing equations into their non-descriptor form before applying the same projection-based model order reduction method. For several structural and coupled fluid-structure dynamical systems, it is observed that the first reduction approach leads to reduced-order models that exhibit significantly better numerical stability and accuracy properties than those resulting from the second one. These observations are reinforced by theoretical results that anticipate and confirm the better stability properties obtained in general when reducing the descriptor rather than non-descriptor form of the equations governing a linear dynamical system.

math.DS↗

arXiv2012

The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows

The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear model reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with residual minimization; it delivers computational efficency by a hyper-reduction procedure based on the `gappy POD' technique. Originally presented in Ref. [1], where it was applied to implicit nonlinear structural-dynamics models, this method is further developed here and applied to the solution of a benchmark turbulent viscous flow problem. To begin, this paper develops global state-space error bounds that justify the method's design and highlight its advantages in terms of minimizing components of these error bounds. Next, the paper introduces a `sample mesh' concept that enables a distributed, computationally efficient implementation of the GNAT method in finite-volume-based computational-fluid-dynamics (CFD) codes. The suitability of GNAT for parameterized problems is highlighted with the solution of an academic problem featuring moving discontinuities. Finally, the capability of this method to reduce by orders of magnitude the core-hours required for large-scale CFD computations, while preserving accuracy, is demonstrated with the simulation of turbulent flow over the Ahmed body. For an instance of this benchmark problem with over 17 million degrees of freedom, GNAT outperforms several other nonlinear model-reduction methods, reduces the required computational resources by more than two orders of magnitude, and delivers a solution that differs by less than 1% from its high-dimensional counterpart.

math.NA↗