An ALE Formulation for Explicit Runge–Kutta Residual Distribution

Arpaia, Luca; Ricchiuto, Mario; Abgrall, Rémi

doi:10.1007/s10915-014-9910-5

Cited by 13 publications

(24 citation statements)

References 32 publications

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“…This contribution is a first step to evaluate the unsteady fitting method when schemes with different properties are used. We evaluate the results obtained with explicit residual distribution schemes in Arbitrary Lagrangian Eulerian (ALE) form, developed in [16,5].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Shock-Fitting and Predictor-Corrector Explicit ALE Residual Distribution

Campoli

Quemar

Bonfiglioli

et al. 2017

Shock Wave and High Pressure Phenomena

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Shock-Fitting and Predictor-Corrector Explicit ALE Residual Distribution

Campoli

Quemar

Bonfiglioli

et al. 2017

Shock Wave and High Pressure Phenomena

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“…Simple algebraic manipulations show that this definition satisfies the integral DGCL (see [33] for details)…”

Section: Finite Volume Discrete Approximationmentioning

confidence: 99%

“…We compare the finite volume results to those of the two-step explicit Residual Distribution (RD) method developed in [40,33,14]. On a moving mesh, the evolution equation obtained with the RD method is derived from the weak form of the well balanced equation (17).…”

Section: Residual Distribution Discrete Approximationmentioning

confidence: 99%

“…where now the fluctuations˜ K i are a splitting of the following geometrically non-conservative average steady cell residual, see [33] X…”

Section: Residual Distribution Discrete Approximationmentioning

confidence: 99%

“…Note that, as for the FV scheme and as prescribed in the ALE formulation proposed in [33], most geometrical quantities necessary for the computation of the residuals (42) and (45) are evaluated on the mid-point averaged mesh T n+1/2 h which ensure…”

Section: Residual Distribution Discrete Approximationmentioning

confidence: 99%

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r−adaptation for Shallow Water flows: conservation, well balancedness, efficiency

Arpaia¹,

Ricchiuto²

2018

Computers & Fluids

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We investigate the potential of the so-called "relocation" mesh adaptation in terms of resolution and e ciency for the simulation of free surface flows in the near shore region. Our work is developed in three main steps. First, we consider several Arbitrary Lagrangian Eulerian (ALE) formulations of the shallow water equations on moving grids, and provide discrete analogs in the Finite Volume and Residual Distribution framework. The compliance to all the physical constraints, often in competition, is taken into account. We consider di↵erent formulations allowing to combine volume conservation (DGCL) and equilibrium (Well-Balancedness), and we clarify the relations between the so-called pre-balanced form of the equations (Rogers et al., J.Comput.Phys. 192, 2003), and the classical upwiniding of the bathymetry term gradients (Bermudez and Vazquez, Computers and Fluids 235, 1994). Moreover, we propose a simple remap of the bathymetry based on high accurate quadrature on the moving mesh which, while preserving an accurate representation of the initial data, also allows to retain mass conservation within an arbitrary accuracy. Second, the coupling of the resulting schemes with a mesh partial di↵erential equation is studied. Since the flow solver is based on genuinely explicit time stepping, we investigate the e ciency of three coupling strategies in terms of cost overhead w.r.t. the flow solver. We analyze the role of the solution remap necessary to evaluate the error monitor controlling the adaptation, and propose simplified formulations allowing a reduction in computational cost. The resulting ALE algorithm is compared with the rezoning Eulerian approach with interpolation proposed e.g. in (Tang and Tang, SINUM 41, 2003). An alternative cost e↵ective Eulerian approach, still allowing a full decoupling between adaptation and flow evolution steps is also proposed. Finally, a thorough numerical evaluation of the methods discussed is performed. Numerical results on propagation, and inundation problems shows that the best compromise between accuracy and CPU time is provided by a full ALE formulation. If a loose coupling with the mesh adaptation is sought, then the cheaper Eulerian approach proposed is shown to provide results quite close to the ALE.

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Residual Based Method for Sediment Transport

Poullet

Ramsamy

Ricchiuto

2021

SEMA SIMAI Springer Series

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This contribution deals with a high order Residual Distribution (RD) numerical scheme to simulate sediment transport. The morphodynamic model that has been used, couples shallow-water equations for the fluid flow and the Exner law for the sediment part. Thus, the choice of the approach by a non-conservative hyperbolic system has been made. Different schemes have already been applied to approximate the entropic solution for several test cases [10]. The one proposed in this paper resorts to RD-method, TVD Runge Kutta [27,31] and stabilisation upwind methods [13], with limiters. It can be viewed as an improvement of the generalized approximate Roe method [14,8,29] with some other good properties (Path-conservative, well-balanced...). Numerical results show the ability of the model in 1D to compute accurate solutions and to reproduce some classical test problems. The best results that we obtained, use MinMod flux limiters. This work is incorporated within the framework of the study of a sediment transport modelling. One aim of this contribution, is to provide first, an useful simulation tool, in the context of a 1D space-time problem. Considering the geophysical aspect,

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An ALE Formulation for Explicit Runge–Kutta Residual Distribution

Cited by 13 publications

References 32 publications

Shock-Fitting and Predictor-Corrector Explicit ALE Residual Distribution

Shock-Fitting and Predictor-Corrector Explicit ALE Residual Distribution

r−adaptation for Shallow Water flows: conservation, well balancedness, efficiency

Residual Based Method for Sediment Transport

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