Residual distribution for general time-dependent conservation laws

In this paper we consider the solution of hyperbolic conservation laws on moving meshes by means of an Arbitrary Lagrangian Eulerian (ALE) formulation of the Runge-Kutta Residual Distribution (RD) schemes of Ricchiuto and Abgrall (J Comput Phys 229(16):5653-5691, 2010). Up to the authors knowledge, the problem of recasting RD schemes into ALE framework has been solved with first order explicit schemes and with second order implicit schemes. Our resulting scheme is explicit and second order accurate when computing discontinuous solutions.

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“…This test case is contained in [17]. We use it to test the shock-capturing capabilities of the schemes.…”

Section: A 2d Riemann Problemmentioning

confidence: 99%

An ALE Formulation for Explicit Runge-Kutta Residual Distribution

Abgrall

Arpaia

Ricchiuto

2014

Springer Proceedings in Mathematics &Amp; Statistics

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“…In the RD approach, this has been done by [11,17,34] to give a few examples. This leads to implicit schemes with possibly stability constraints.…”

Section: Unsteady Problemsmentioning

confidence: 99%

“…This leads to implicit schemes with possibly stability constraints. These stability constraints can be removed by a "two-layers" technique, see [34] and then [11] for details. A simpler method is described in [17], it uses discontinuous in time finite elements.…”

Section: Unsteady Problemsmentioning

confidence: 99%

A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art

Abgrall

2012

Commun. comput. phys.

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Abstract. We describe and review non oscillatory residual distribution schemes that are rather natural extension of high order finite volume schemes when a special emphasis is put on the structure of the computational stencil. We provide their connections with standard stabilized finite element and discontinuous Galerkin schemes, show that their are really non oscillatory. We also discuss the extension to these methods to parabolic problems. We also draw some research perspectives.

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“…Regardless of the temporal scheme used, the original RDS formulation cannot be more than first order accurate in timedependent computations due to the inconsistency of the spatial discretization (Ferrante and Deconinck [8]). Various solutions have been proposed to overeóme this difficulty; see, e.g., Ferrante and Deconinck [8] and Caraeni [2], who made use of a finite-element like mass-matrix that were consistent with the spatial discretization, and Ricchiuto et al [16] and Csik and Deconinck [4], who introduce space-time residual distribution schemes. But, all of these papers are focused on inviscid unsteady solutions, with non-steady viscous computation not conclusive (Caraeni et al [3]) and putting more emphasis on the numerical aspect of the method than in its real predictive capabilities for complex viscous flows.…”

Section: Introductionmentioning

confidence: 99%

Unsteady residual distribution schemes for transition prediction

Meseguer

Valero

Martel

et al. 2010

Aerospace Science and Technology

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ARTICLE INFO ABSTRACTIn this work, the unsteady simulation of the Navier-Stokes equations is carried out by using a Residual Distribution Schemes (RDS) methodology. This algorithm has a compact stencil (cell-based computations) and uses a finite element like method to compute the residual over the cell. The RDS method has been successfully proven in steady Navier-Stokes computation but its application to fully unsteady configurations is still not closed, because some of the properties of the steady counterpart can be lost. Kevwords-Here, we proposed a numerical solution for unsteady problems that is fully compatible with the original Unsteady numerical simulation approach. In order to check the method, we chose a very demanding test case, namely the numerical Finite element methods simulation of a Tollmien-Schlichting (TS) wave in a 2D boundary layer. The evolution of this numerical Boundary layer transition perturbation is accurately computed and checked against theoretical results.

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Residual distribution for general time-dependent conservation laws

Cited by 58 publications

References 44 publications

An ALE Formulation for Explicit Runge-Kutta Residual Distribution

An ALE Formulation for Explicit Runge-Kutta Residual Distribution

A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art

Unsteady residual distribution schemes for transition prediction

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