On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part II – Analysis for and finite elements

John, Volker; Knobloch, Petr

doi:10.1016/j.cma.2007.12.019

Cited by 97 publications

(82 citation statements)

References 32 publications

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“…For transient problems, it can be considered in a semi-implicit way (taking the value from the previous time step without nonlinear iterations), but for the steady state case nonlinear iterations are needed. In order to improve convergence we have used the damping parameter ω ∈ [0.01, 1] proposed in [18]. In any case, for q = 10, the nonlinear error got stuck in values of order 10 −2 -10 −3 .…”

Section: Propagation Of Discontinuitiesmentioning

confidence: 99%

On discrete maximum principles for discontinuous Galerkin methods

Badia

Hierro

2015

Computer Methods in Applied Mechanics and Engineering

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The aim of this work is to propose a monotonicity-preserving method for discontinuous Galerkin (dG) approximations of convection-diffusion problems. To do so, a novel definition of discrete maximum principle (DMP) is proposed using the discrete variational setting of the problem, and we show that the fulfilment of this DMP implies that the minimum/maximum (depending on the sign of the forcing term) is on the boundary for multidimensional problems. Then, an artificial viscosity (AV) technique is designed for convection-dominant problems that satisfies the above mentioned DMP. The noncomplete stabilized interior penalty dG method is proved to fulfil the DMP property for the one-dimensional linear case when adding such AV with certain parameters. The benchmarks for the constant values to satisfy the DMP are calculated and tested in the numerical experiments section. Finally, the method is applied to different test problems in one and two dimensions to show its performance.

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Section: Propagation Of Discontinuitiesmentioning

confidence: 99%

On discrete maximum principles for discontinuous Galerkin methods

Badia

Hierro

2015

Computer Methods in Applied Mechanics and Engineering

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“…In order to avoid non-physical undershoots/overshoots of the approximations of k := k n+1 and ω := ω n+1 , the additional nonlinear crosswind diffusion method can be applied, cf. [19], [20], [21], but there is no guarantee of no undershoots/overshoots. Particularly for the solution of intermittency equation as well as equation for k and ω, these undershoots/overshoots can lead to incorrect results.…”

Section: Space Discretization Of the K-ω Turbulence Modelmentioning

confidence: 99%

On several aspects of finite element approximations of laminar/turbulent transition models

Sváček

2014

EPJ Web of Conferences

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“…Inspired by the bad experiences with the SUPG method and the upwind method, comprehensive numerical studies of stabilized finite element methods for scalar time-dependent convection-diffusion-reaction equations were performed in [17,18]. These studies included besides the SUPG method a number of Spurious Oscillations at Layers Diminishing (SOLD) schemes [11,12], a local projection stabilization (LPS) scheme [25] and two FiniteElement-Method Flux-Corrected-Transport (FEM-FCT) schemes [21,22,23]. All studies in [17,18] led to the consistent conclusion that the FEM-FCT schemes are far better than the other approaches.…”

Section: The Equations For the Chemical Reactionmentioning

confidence: 99%

On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems

John

Roland

2010

Numerical Meth Engineering

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Population balance systems are models for processes in nature and industry which lead to a coupled system of equations (Navier-Stokes equations, transport equations, . . .) where the equations are defined in domains with different dimensions. This paper will study the impact of using different schemes for solving the three-dimensional equation of a precipitation process in a two-dimensional flow domain. The numerical schemes for the three-dimensional equation are assessed with respect to the median of the volume fraction of the particle size distribution and the computational costs. It turns out that in the case of a structured flow field with small variations in time all schemes give qualitatively the same results. For a highly time-dependent flow field, the evolution of the median of the volume fraction differs considerably between first order and higher order schemes.

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On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part II – Analysis for and finite elements

Cited by 97 publications

References 32 publications

On discrete maximum principles for discontinuous Galerkin methods

On discrete maximum principles for discontinuous Galerkin methods

On several aspects of finite element approximations of laminar/turbulent transition models

On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems

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