hp-Adaptive time integration based on the BDF for viscous flows

Hay, Alexander; Étienne, Stéphane; Pelletier, Dominique; Garon, André

doi:10.1016/j.jcp.2015.03.022

Cited by 38 publications

(34 citation statements)

References 22 publications

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“…This section reviews the BDF definition and their stability properties. The interested reader should refer to (Hay et al , 2015; Muller et al , 2018) for further details.…”

Section: Numerical Procedures and Methodsmentioning

confidence: 99%

“…In former studies (Hetu and Pelletier, 1992; Ilinca et al , 1997b), the gradients recovery methodology of (Zhu and Zienkiewicz, 1987) proved very effective to design a robust mesh adaptation technique for steady laminar and turbulent flows. We also showed in recent papers that hp -adaptive backward differentiation formulas (BDF)-based time-integrators combined with a monolithic solver is a very efficient way to solve viscous flows (Hay et al , 2015) and FSI problems (Hay et al , 2014). By computing the local temporal error estimates and assessing the stability condition for each dependent variables separately, our previous work successfully extended the methodology to turbulent flows.…”

Section: Introductionmentioning

confidence: 97%

“…Additional efficiency can be achieved by using a time-integrator with an adaptive order. Such a feature is really useful if a time-integrator proven not to be A-stable is used (Hay et al , 2015). Indeed, increasing the time-integrator order can drastically improve the time-integration precision, which enables to increase the time-step size even more.…”

Section: Introductionmentioning

confidence: 99%

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Interactions between adaptive time-integrators and adaptive meshing in a monolithic FEM solver

Muller

Pelletier

Garon

2019

HFF

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Purpose This paper aims to focus on characterization of interactions between hp-adaptive time-integrators based on backward differentiation formulas (BDF) and adaptive meshing based on Zhu and Zienkiewicz error estimation approach. If mesh adaptation only occurs at user-supplied times and results in a completely new mesh, it is necessary to stop the time-integration at these same times. In these conditions, one challenge is to find an efficient and reliable way to restart the time-integration. The authors investigate what impact grid-to-grid interpolation errors have on the relaunch of the computation. Design/methodology/approach Two restart strategies of the time-integrator were used: one based on resetting the time-step size h and time-integrator order p to default values (used in the initial startup phase), and another designed to restart with the time-step size h and order p used by the solver prior to remeshing. The authors also investigate the benefits of quadratically interpolate the solution on the new mesh. Both restart strategies were used to solve laminar incompressible Navier–Stokes and the Unsteady Reynolds Averaged Naviers-Stokes (URANS) equations. Findings The adaptive features of our time-integrators are excellent tools to quantify errors arising from the data transfer between two grids. The second restart strategy proved to be advantageous only if a quadratic grid-to-grid interpolation is used. Results for turbulent flows also proved that some precautions must be taken to ensure grid convergence at any time of the simulation. Mesh adaptation, if poorly performed, can indeed lead to losing grid convergence in critical regions of the flow. Originality/value This study exhibits the benefits and difficulty of assessing both spatial error estimates and local error estimates to enhance the efficiency of unsteady computations.

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“…This section reviews the BDF definition and their stability properties. The interested reader should refer to (Hay et al , 2015; Muller et al , 2018) for further details.…”

Section: Numerical Procedures and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Interactions between adaptive time-integrators and adaptive meshing in a monolithic FEM solver

Muller

Pelletier

Garon

2019

HFF

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“…Also at the initial time, the cylinder stood at the positionX cyl = 0. CADYF integrated the coupled system of equations (3.4) using hp-adaptive backward differential formula (BDF) methods (Hay et al 2015b). The order and time step adjusted automatically so that the local truncation error remained smaller than a constant absolute tolerance equal to 10 −5 .…”

Section: Coral Branch As a Circular Spring-mounted Cylinder In Flowmentioning

confidence: 99%

Vortex-induced vibrations: a soft coral feeding strategy?

2021

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“…It performs both stepsize (h-adaptivity) and order selection (p-adaptivity) to control respectively the solution accuracy and the computational efficiency of the time integration procedure. 11 The algorithm selects the most appropriate method within the formulas of order 1 to 6 (referred to as BDF-1 to BDF-6 respectively in what follows) according to the preset solution accuracy and equation stiffness.…”

Section: Introductionmentioning

confidence: 99%

An ALE/FE formulation for high precision interface tracking in separated multiphase flows

Hay

Étienne

Pelletier

2015

22nd AIAA Computational Fluid Dynamics Conference

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We present an Arbitrary Lagrangian Eulerian/Finite Element (ALE/FE) formulation to simulate flows with sharp interfaces between several fluids or phases. The proposed numerical approach relies on the explicit representation of interfaces as a collection of inner mesh edges and the direct tracking of the time evolution of these interfaces. The ALE/FE formulation allows for the use of high-order time integrators within a hp-adaptive time integration procedure already developed for single phase flows. The kinematic and dynamic conditions across interfaces are enforced with the use of zero-thickness interfacial finiteelement along interfaces. We consider both linear (P1) and quadratic (P2) finite element discretization. The simulation of very large deformation of interfaces is rendered possible by the use of an adaptive remeshing algorithm. The method is applied to the prediction of the propagation of solitary waves in basins with constant and variable bathymetry as well as the simulation of the Rayleigh-Taylor instability.

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hp-Adaptive time integration based on the BDF for viscous flows

Cited by 38 publications

References 22 publications

Interactions between adaptive time-integrators and adaptive meshing in a monolithic FEM solver

Interactions between adaptive time-integrators and adaptive meshing in a monolithic FEM solver

Vortex-induced vibrations: a soft coral feeding strategy?

An ALE/FE formulation for high precision interface tracking in separated multiphase flows

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