Oh no, not the wiggles again! A revisit of an old problem and a new approach

Russell, Thomas F.; Binning, Philip John

doi:10.1016/s0167-5648(04)80075-3

Cited by 6 publications

(14 citation statements)

References 8 publications

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“…Since the right-hand term of (4) is computed with numerical integration, the mass-lumping procedure is only used at the new time level and is obtained by choosing = 1 6 in (5). Full lumping can be seen as the addition of an artificial diffusion [8] which makes the mass matrix an M-matrix (a non-singular matrix with m ii >0, m i j 0). The M-matrix property guaranties the respect of the discrete maximum principle, i.e.…”

Section: Numerical Diffusion With Ellammentioning

confidence: 99%

“…local maxima or minima (and therefore non-physical oscillation) will not appear in the solution. However, full lumping is known to add excessive numerical diffusion when several time steps are used [8]. To avoid this problem, one-dimensional ELLAM scheme with a selective lumping has been developed in [8].…”

Section: Numerical Diffusion With Ellammentioning

confidence: 99%

“…However, full lumping is known to add excessive numerical diffusion when several time steps are used [8]. To avoid this problem, one-dimensional ELLAM scheme with a selective lumping has been developed in [8]. The basic idea of this scheme is to add the minimal numerical diffusion required to avoid oscillations.…”

Section: Numerical Diffusion With Ellammentioning

confidence: 99%

“…Moreover, mass-lumping is often used to avoid oscillations with numerical methods and is known to add numerical diffusion with Eulerian-Lagrangian methods [8]. To reduce this problem, one-dimensional ELLAM scheme with a selective lumping has been developed in [8].…”

Section: Introductionmentioning

confidence: 99%

“…To reduce this problem, one-dimensional ELLAM scheme with a selective lumping has been developed in [8]. With this scheme, artificial diffusion is not added uniformly to the solution but only where it is required.…”

Section: Introductionmentioning

confidence: 99%

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A new approach to avoid excessive numerical diffusion in Eulerian–Lagrangian methods

Younès

Fahs

Ackerer

2007

Commun. Numer. Meth. Engng.

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SUMMARYLumping is often used to avoid non-physical oscillations for advection-dispersion equations but is known to add numerical diffusion. A new approach is detailed in order to avoid excessive numerical diffusion in Eulerian-Lagrangian methods when several time steps are used. The basic idea of this approach is to keep the same characteristics during all time steps and to interpolate only the concentration variations due to the dispersion process. In this way, numerical diffusion due to the lumping is removed at the end of each time step. The method is combined with the Eulerian-Lagrangian localized adjoint method (ELLAM) which is a mass conservative characteristic method for solving the advection-dispersion equation.Two test problems are modelled to compare the proposed method to the consistent, the full and the selective lumping approaches for linear and non-linear transport equations.

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Section: Numerical Diffusion With Ellammentioning

confidence: 99%

Section: Numerical Diffusion With Ellammentioning

confidence: 99%

Section: Numerical Diffusion With Ellammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A new approach to avoid excessive numerical diffusion in Eulerian–Lagrangian methods

Younès

Fahs

Ackerer

2007

Commun. Numer. Meth. Engng.

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On the use of large time steps with ELLAM for transport with kinetic reactions over heterogeneous domains

2009

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An Eulerian Lagrangian localized adjoint method (ELLAM) is considered for the resolution of advection‐dominated transport problems in porous media. Contrary to standard Eulerian methods, ELLAM can use large time steps because the advection term is approximated accurately without any CFL restriction. However, it is shown in this article that special care must be taken for the approximation of the dispersive and reactive terms when large time steps are used over heterogeneous domains. An alternative procedure is proposed. It is based on an equivalent dispersion coefficient or an equivalent reaction rate when different zones are encountered during the tracking. Numerical experiments are performed with variable dispersion or variable reaction rates over space (including nonlinearity). When classical ELLAM require numerous time steps to handle heterogeneity, the alternative procedure is shown to perform with the same accuracy in a single time step. © 2009 American Institute of Chemical Engineers AIChE J, 2009

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Semidiscrete formulations for transient transport at small time steps

Harari

Hauke

2007

Numerical Methods in Fluids

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SUMMARYSolutions of direct time-integration schemes for transient advection-diffusion-reaction problems that converge in time to conventional semidiscrete formulations may be polluted at small time steps by spurious spatial oscillations. This degradation is not an artifact of the time-marching scheme, but rather a property of the solution of the semidiscrete Galerkin approximation itself. An analogy to steady advectiondiffusion-reaction problems with a modified reaction coefficient by the Rothe method of discretizing in time prior to spatial discretization provides an upper bound on the time step for the onset of spatial instability. Spatial stabilization removes this pathology, leading to stabilized implicit time-integration schemes that are free of spurious oscillations at small time steps.

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Oh no, not the wiggles again! A revisit of an old problem and a new approach

Cited by 6 publications

References 8 publications

A new approach to avoid excessive numerical diffusion in Eulerian–Lagrangian methods

A new approach to avoid excessive numerical diffusion in Eulerian–Lagrangian methods

On the use of large time steps with ELLAM for transport with kinetic reactions over heterogeneous domains

Semidiscrete formulations for transient transport at small time steps

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