On stabilization of the CBS algorithm: Internal and external time steps

Nithiarasu, Perumal; Zienkiewicz, O. C.

doi:10.1002/(sici)1097-0207(20000630)48:6<875::aid-nme907>3.0.co;2-u

Cited by 33 publications

(36 citation statements)

References 7 publications

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“…The use of the stabilisation technique via dual time steps is inspired by Nithiarasu and Zienkiewicz (2000). The effect of this technique shall be discussed later.…”

Section: Characteristic-based Split (Cbs) Schemementioning

confidence: 99%

“…In the CBS scheme, dual time-step sizes can be referred back to the pioneering work of for seeking the optimal steady-state solution of the compressible fluid flows. To enhance the pressure stabilisation, dual time-step sizes were then introduced into two Stokes problems by Nithiarasu and Zienkiewicz (Nithiarasu and Zienkiewicz 2000;Nithiarasu 2006). In…”

Section: Boxmentioning

confidence: 99%

“…This stabilisation technique seldom works in the elastic solid problem (Nithiarasu 2006), but has favourable effect on the Stokes flow in a lid-driven cavity (Nithiarasu and Zienkiewicz 2000). As γ > 1.0 may be profitable for the deformable mesh problems (Nithiarasu and Zienkiewicz 2000), the present study adopts dual time-step sizes as follows. γ = 1.0 is employed for the elements in A1 and A3, while variable values of γ , ranging from 1.0 to 3.0, are adopted for the elements in A2.…”

Section: Boxmentioning

confidence: 99%

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Partitioned subiterative coupling schemes for aeroelasticity using combined interface boundary condition method

Zhou

Han

et al. 2014

International Journal of Computational Fluid Dynamics

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The combined interface boundary condition (CIBC) method has been recently proposed for fluid-structure interaction. The CIBC method employs a Gauss-Seidel-like procedure to transform traditional interface conditions into velocity and traction corrections whose effect is controlled by a dimensional parameter. However, the original CIBC method has to invoke the uncorrected traction when forming the traction correction. This process limits its application to fluid-rigid body interaction. To repair this drawback, a new formulation of the CIBC method has been developed by using a new coupling parameter. The reconstruction is simple and the structural traction is removed completely. Two partitioned subiterative coupling versions of the CIBC method are developed. The first scheme is an implicit strategy while the second one is a semi-implicit strategy. Iterative loops are actualised by the fixed-point algorithm with Aitken accelerator. The obtained results agree with the well-documented data, and some famous flow phenomena have been successfully detected.Keywords: fluid-structure interaction; aeroelasticity; partitioned subiterative coupling scheme; finite element method; combined interface boundary condition method IntroductionIn real life, fluid-structure interaction (FSI) contains the sophisticated principles of mathematics and the abundant essences of physics. Today, FSI has become one of the most challenging topics in computational fluid dynamics and has received a great deal of attention. It is a frequent issue in a rich variety of engineering realms such as civil engineering, ocean engineering, aerospace engineering, mechanical engineering and biomedical engineering. A major paradigm of FSI concerns the aeroelasticity, of which a typical application is the interplay of natural wind with a high-rise building or a suspension bridge in civil engineering. In this case, a catastrophe is likely to occur if failing to consider the FSI effect. The old Tacoma Narrows Bridge in the 1940s is the most well-known example. As a consequence, FSI is a significant consideration for the design of some practical structures.Except for the most simplified cases, FSI is too complicated (i.e. high nonlinearity and uncertainty) to be solved analytically. Instead, it has to be analysed by means of physical or numerical experiments. For numerical researches, FSI comprises three ingredients: computational fluid dynamics, computational structural dynamics and computational mesh dynamics (Wall and Ramm 1998); or, in other words, it is dominated by a three-field nonlinear formulation (Farhat, Lesoinne, and Maman 1995). Of these fields, the scientific

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“…The use of the stabilisation technique via dual time steps is inspired by Nithiarasu and Zienkiewicz (2000). The effect of this technique shall be discussed later.…”

Section: Characteristic-based Split (Cbs) Schemementioning

confidence: 99%

Section: Boxmentioning

confidence: 99%

Section: Boxmentioning

confidence: 99%

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Partitioned subiterative coupling schemes for aeroelasticity using combined interface boundary condition method

Zhou

Han

et al. 2014

International Journal of Computational Fluid Dynamics

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“…Taking shape functions as the weighting functions, the weak form of Eqs. (28), (29) and (30) can be obtained as…”

Section: Spatial Discretizationmentioning

confidence: 99%

Characteristic-Based Split (CBS) Finite Element Method for Incompressible Viscous Flow with Moving Boundaries

Sun

Zhang

Ren

2012

Engineering Applications of Computational Fluid Mechanics

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This paper gives an insight into the existing ALE (arbitrary Lagrangian Eulerian)-CBS (characteristic-based split) method and proposes an alternative CBS scheme for incompressible viscous flow with moving boundaries. First, the existing CBS scheme in ALE framework is reformulated from the Navier-Stokes (NS) equations in Eulerian description, and its advantages and drawbacks are discussed. Then, the classical semi-implicit CBS scheme is combined with the segment spring analogy method, and a new CBS solution procedure in Eulerian framework is developed for moving mesh. By the proposed CBS scheme, the influence of the mesh velocity in the existing ALE-CBS method is circumvented, and the extension of the existing CBS schemes and programs for fixed boundary problems to moving boundary problems seems to be more convenient. Finally, two moving boundary problems, namely the broken dam problem and the flow around an oscillating circular cylinder are presented. Numerical results from the proposed CBS scheme agree very well with available results in literature and show a slightly higher accuracy than those from the existing ALE-CBS method. Combined with other classical CBS schemes involving compressibility, turbulence, viscoelasticity, etc. and suitable moving mesh techniques, the proposed CBS solution procedure could be applied widely to the moving boundary problems in engineering.

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“…The reader is referred to Appendix for more details. Hence, one arrives at the justification for adjustable internal time-steps [27], to be judged as acting on each fractional-stage solution variable and indeed, expressing dependency upon the mesh selected (fraction of the Courant number).…”

Section: C-under-relaxation Procedures (Incompressible Flow)mentioning

confidence: 99%

Numerical simulation of compressible viscoelastic liquids

Keshtiban

Belblidia

Webster

2004

Journal of Non-Newtonian Fluid Mechanics

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A stable and accurate time-marching pressure-correction/Taylor-Galerkin finite element algorithm is presented to accommodate low Mach number compressible and incompressible viscoelastic liquid flows. The algorithm is based on an operator splitting constructive process that discloses three fractional stages. For the compressible regime, a piecewise-constant density interpolation with gradient recovery is employed, for which the background theory and consistency of approach are discussed. The scheme is applied to contraction flows for Oldroyd model fluids, covering entry-exit flows and high pressure-drop situations. Stability and performance characteristics of the new algorithmic implementation are highlighted. Solutions are provided for a range of compressible settings, tending to the incompressible limit at vanishing Mach number.

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On stabilization of the CBS algorithm: Internal and external time steps

Cited by 33 publications

References 7 publications

Partitioned subiterative coupling schemes for aeroelasticity using combined interface boundary condition method

Partitioned subiterative coupling schemes for aeroelasticity using combined interface boundary condition method

Characteristic-Based Split (CBS) Finite Element Method for Incompressible Viscous Flow with Moving Boundaries

Numerical simulation of compressible viscoelastic liquids

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