The Discrete Geometric Conservation Law and the Nonlinear Stability of ALE Schemes for the Solution of Flow Problems on Moving Grids

Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline

doi:10.1006/jcph.2001.6932

Cited by 295 publications

(249 citation statements)

References 16 publications

Supporting

Mentioning

233

Contrasting

Order By: Relevance

“…This has led to the so-called discrete geometric conservation law (DGCL), as advocated in [32][33][34], which governs the geometric parameters of the numerical scheme, such as grid positions and velocities, so that the corresponding numerical scheme exactly reproduces a constant solution.…”

Section: Treatment Of the Ale Fluxesmentioning

confidence: 99%

“…The task of finding ALE coefficients that render the scheme geometrically conservative is not trivial and has been treated by a number of authors [31][32][33][34][35]. Here the approach of [35] is followed.…”

Section: Treatment Of the Ale Fluxesmentioning

confidence: 99%

“…Following the approach of Farhat et al [32], a conventional serial staggered solution procedure with full subiteration at each time level, shown schematically in Figure 3, is applied. The four steps of the scheme are outlined as follows:…”

Section: Partitioned Fluid-structure Interface Couplingmentioning

confidence: 99%

See 2 more Smart Citations

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Wood

Gil

Hassan

et al. 2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYThis paper presents a fully coupled three-dimensional solver for the analysis of time-dependent fluidstructure interaction. A partitioned time-marching algorithm is employed for the solution to the timedependent coupled discretized problem, thus enabling the use of highly developed, robust and well-tested solvers for each field. Coupling of the fields is achieved through a conservative transfer of information at the fluid-structure interface. An implicit coupling is achieved when the solutions to the fluid and structure subproblems are cycled at each time step until convergence is reached. The three-dimensional unsteady incompressible fluid is solved using a powerful implicit dual time-stepping technique with an explicit multistage Runga-Kutta time stepping in pseudo-time and arbitrary Lagrangian-Eulerian formulation for the moving boundaries. A finite element dynamic analysis of the highly deformable structure is carried out with a numerical strategy combining the implicit Newmark time integration algorithm with a NewtonRaphson second-order optimization method. Various test cases are presented for benchmarking and to demonstrate the potential applications of this method.

show abstract

Section: Treatment Of the Ale Fluxesmentioning

confidence: 99%

Section: Treatment Of the Ale Fluxesmentioning

confidence: 99%

See 1 more Smart Citation

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Wood

Gil

Hassan

et al. 2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…First introduced by Thomas and Lombard [19], it has been shown mathematically and through numerical experiment [20][21][22] that satisfying the GCL can improve the accuracy and stability of the chosen scheme. A straightforward technique for the numerical implementation of the GCL [23,24] has been included as part of the dual-time stepping approach.…”

Section: Numerical Implementationmentioning

confidence: 99%

Assessment of the Fluid-Structure Interaction Capabilities for Aeronautical Applications of the Open-Source Solver Su2.

Sánchez¹,

Kline²,

Thomas³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

View full text Add to dashboard Cite

Abstract. We report on an international effort to develop an open-source computational environment for high-fidelity fluid-structure interaction analysis. In particular, we will focus on verification of the implementation for application in computational aeroelasticity. The capabilities of the SU2 code for aeroelastic analysis have been further enhanced both by developing natively embedded tools for the study of largely deformable solids, and by wrapping it using Python tools for an improved communication with external solvers. Both capabilities will be demonstrated on relevant test cases, including rigid-airfoil solutions with indicial functions, the Isogai Wing Section, test cases from the AIAA 2nd Aeroelastic Prediction Workshop, and the vortex-induced vibrations of a flexible cantilever in the wake of a square cylinder. Results show very good performance both in terms of accuracy and computational efficiency. The modularity and versatility of the baseline suite allows for a flexible framework for multidisciplinary computational analysis. The software libraries have been freely shared with the community to encourage further engagement in the improvement, validation and further development of this open-source project.

show abstract

“…The flow is modelled as a one-dimensional, isentropic, inviscid flow. Usually, the governing equation for the flow are written in the arbitrary LagrangianEulerian (ALE) to cope with the moving and deforming mesh [4,6]. In this paper, however, we only consider the fluid on a non-moving mesh.…”

Section: Fluid-structure Interaction Model Problemmentioning

confidence: 99%

Implicit and Explicit Higher Order Time Integration Schemes for Fluid-Structure Interaction Computations

Zuijlen

Bijl

2004

Computational Science - ICCS 2004

View full text Add to dashboard Cite

Abstract. In this paper higher order time integration schemes are applied to fluid-structure interaction (FSI) simulations. For a given accuracy, we investigate the efficiency of higher order time integration schemes compared to lower order methods. In the partitioned FSI simulations on a one-dimensional piston problem, a mixed implicit/explicit (IMEX) time integration scheme is employed: the implicit scheme is used to integrate the fluid and structural dynamics, whereas an explicit Runge-Kutta scheme integrates the coupling terms. The resulting IMEX scheme retains the order of the implicit and explicit schemes. In the IMEX scheme considered, the implicit scheme consists of an explicit first stage, singly diagonally implicit Runge-Kutta (ESDIRK) scheme, which is a multistage, L-stable scheme.

show abstract

The Discrete Geometric Conservation Law and the Nonlinear Stability of ALE Schemes for the Solution of Flow Problems on Moving Grids

Cited by 295 publications

References 16 publications

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Assessment of the Fluid-Structure Interaction Capabilities for Aeronautical Applications of the Open-Source Solver Su2.

Implicit and Explicit Higher Order Time Integration Schemes for Fluid-Structure Interaction Computations

Contact Info

Product

Resources

About