Space-time residual distribution schemes for hyperbolic conservation laws

Csı́k, Árpád; Ricchiuto, Mario; Deconinck, H.; Poedts, Stefaan

doi:10.2514/6.2001-2617

Cited by 21 publications

(35 citation statements)

References 4 publications

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“…When a continuous representation of the solution is assumed the past-shield condition can be relaxed by the use of a pair of time layers [5]. If a second layer is introduced (see the diagram in the middle of Figure 1) and solved for at the same time as the first layer then it is only necessary to enforce upwinding in time in the first layer.…”

Section: Two-layer Schemesmentioning

confidence: 99%

“…Assume now that u is continuous and has a piecewise linear variation in space and in time, and that its discrete values are stored at the nodes of the space-time mesh. The discrete fluctuation φ j,n is evaluated by combining the midpoint rule in time with exact integration in space (which can be carried out using an appropriate, conservative, linearisation) [5]. This gives a second order accurate representation of the fluctuation which can be written as…”

Section: Space-time Fluctuation Distributionmentioning

confidence: 99%

“…The k i and k i are the space-time "inflow" parameters, i.e. for an upwind scheme in space-time a node is only updated if the corresponding k i > 0 [5].…”

Section: Space-time Fluctuation Distributionmentioning

confidence: 99%

“…Those schemes, however, reduce to first order accuracy away from the steady state, so much recent research has aimed to impose the same combination of properties on time-dependent simulations, leading to the space-time formulation [5] described briefly in Section 2.…”

Section: Introductionmentioning

confidence: 99%

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Discontinuous fluctuation distribution

Hubbard

2008

Journal of Computational Physics

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This paper proposes an approach to the approximation of timedependent hyperbolic conservation laws which is both second order accurate in space and time (for any sufficiently smooth solution profile, even one containing turning points) and free of spurious oscillations for any time-step. The numerical algorithm is based on the concept of fluctuation distribution, applied on a space-time mesh of triangular prisms, for which second order accurate schemes already exist which are oscillation-free if the time-step satisfies a CFL-type constraint. This restriction is lifted here by combining the concept of a two-layer scheme with a representation of the solution which is allowed to be discontinuous in time. Numerical results are presented in two space dimensions, using unstructured meshes of space-time triangular prisms, for the scalar advection equation, Burgers' equation and the Euler equations of gasdynamics.Key-words: conservation laws, positivity, stability, large time steps, residual distribution, second order accuracy * University of Leeds † INRIA Bordeaux -Sud-Ouest Discontinuous residual distribution : A route to unconditional positivity and high order accuracyRésumé : This paper proposes an approach to the approximation of timedependent hyperbolic conservation laws which is both second order accurate in space and time (for any sufficiently smooth solution profile, even one containing turning points) and free of spurious oscillations for any time-step. The numerical algorithm is based on the concept of fluctuation distribution, applied on a space-time mesh of triangular prisms, for which second order accurate schemes already exist which are oscillation-free if the time-step satisfies a CFL-type constraint. This restriction is lifted here by combining the concept of a two-layer scheme with a representation of the solution which is allowed to be discontinuous in time. Numerical results are presented in two space dimensions, using unstructured meshes of space-time triangular prisms, for the scalar advection equation, Burgers' equation and the Euler equations of gasdynamics.

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Section: Two-layer Schemesmentioning

confidence: 99%

Section: Space-time Fluctuation Distributionmentioning

confidence: 99%

“…The k i and k i are the space-time "inflow" parameters, i.e. for an upwind scheme in space-time a node is only updated if the corresponding k i > 0 [5].…”

Section: Space-time Fluctuation Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discontinuous fluctuation distribution

Hubbard

2008

Journal of Computational Physics

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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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