A limiting approach for DG discretizations on mixed type meshes

Kontzialis, Konstantinos; Panourgias, Konstantinos; Ekaterinaris, John A.

doi:10.1016/j.cma.2014.11.004

Cited by 10 publications

(3 citation statements)

References 40 publications

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“…For plasma flows, discontinuities appear to the electromagnetic field variables as well. Therefore, a modified total variation banded (TVB) slope limiter proposed by Cockburn and Shu is used for both flow and electromagnetic field variables. The limiter is applied in the transformed canonical space of cubical elements, and then, the limited values are transferred back to the physical space elements using collapsed coordinates .…”

Section: Numerical Approachmentioning

confidence: 99%

A fully implicit scheme for simulating ionized gas flows using the gas dynamics electrodynamics coupled system

Panourgias

Ekaterinaris

2014

Numerical Methods in Fluids

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SUMMARY The flow of ionized gases under the influence of electromagnetic fields is governed by the coupled system of the compressible flow equations and the Maxwell equations. In this system, coupling of the flow with the electromagnetic field is obtained through nonlinear and stiff source terms, which may cause difficulties with the numerical solution of the coupled system. The discontinuous Galerkin finite element method is used for the numerical solution of this system. For the magnetic field vector, discontinuous Galerkin discretization is performed using a divergence‐free vector base for the magnetic field to preserve zero divergence in the element and retain the implicit constraint of a divergence‐free magnetic field vector down to very low level both globally and locally. To circumvent difficulties resulting from the presence of the stiff source terms, implicit time marching is used for the fully coupled system to avoid wrong wave shapes and propagation speeds that are obtained when the coupling source terms are lagged in time or by using splitting iterative schemes. Numerical solutions for benchmark problems computed on collocated meshes for the flow and electromagnetic field variables with this fully coupled monolithic approach showed good agreement with other numerical solutions and exact results. Copyright © 2014 John Wiley & Sons, Ltd.

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Section: Numerical Approachmentioning

confidence: 99%

A fully implicit scheme for simulating ionized gas flows using the gas dynamics electrodynamics coupled system

Panourgias

Ekaterinaris

2014

Numerical Methods in Fluids

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“…The TVB limiter is used to indicate the troubled cells in the application of special relativistic hydrodynamics [43]. Effort has also been made to provide guidance for an automated choice of the TVB constant M. A unified approach for the determination of this constant in mixed type meshes was studied and applied by Kontzialis et al [19] and by Panourgias et al [27], where M was chosen according to the variation of the derivatives of the numerical solution. In [39], Vuik and Ryan proposed an automatic parameter selection strategy for this TVB constant M based on Tukey's boxplot method of outlier-detection, and its application with compact-WENO finite element method is shown in [11].…”

Section: Introductionmentioning

confidence: 99%

Multi-layer Perceptron Estimator for the Total Variation Bounded Constant in Limiters for Discontinuous Galerkin Methods

Shu

2021

La Matematica

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“…A positivity-preserving limiter is used in [30] to enforce the minimum entropy principle. Positivity preserving limiting is also proposed in conjunction with 2D mixed element unstructured meshes in [31,32]. In general, limiters are less robust as compared to WENO reconstruction in their control of spurious oscillations in flows with strong shocks.…”

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confidence: 99%

Explicit discontinuous spectral element method with entropy generation based artificial viscosity for shocked viscous flows

Chaudhuri

Jacobs

Don

et al. 2017

Journal of Computational Physics

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A spatio-temporal adaptive artificial viscosity (AV) based shock-capturing scheme is proposed for the solution of both inviscid and viscous compressible flows using a high-order parallel Discontinuous Spectral Element Method (DSEM). The artificial viscosity and artificial thermal conduction coefficients are proportional to the viscous and thermal entropy generating terms, respectively, in the viscous entropy conservation law. The magnitude of AV is limited based on the explicit stable CFL criterion, so that the stable artificial viscous time step size is greater than the convective stable time step size. To further ensure the stability of this explicit approach, an adaptive variable order exponential filter is applied, if necessary, in elements where the AV has been limited. In viscous flow computations a modified Jameson's sensor (Ducros et al., JCP 152 (2)) limits the AV to small values in viscous shear regions, so as to maintain a high-order resolution in smooth regions and an essentially non-oscillatory behavior near sharp gradients/shocks regions. We have performed a systematic and extensive validation of the algorithm with one-dimensional problems (inviscid moving shock and viscous shock-structure interaction), two-dimensional problems (inviscid steady and unsteady shocked flows and viscous shock-boundary layer interaction), and a three-dimensional supersonic turbulent flow over a ramped cavity. These examples demonstrate that the explicit DSEM scheme with adaptive artificial

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A limiting approach for DG discretizations on mixed type meshes

Cited by 10 publications

References 40 publications

A fully implicit scheme for simulating ionized gas flows using the gas dynamics electrodynamics coupled system

A fully implicit scheme for simulating ionized gas flows using the gas dynamics electrodynamics coupled system

Multi-layer Perceptron Estimator for the Total Variation Bounded Constant in Limiters for Discontinuous Galerkin Methods

Explicit discontinuous spectral element method with entropy generation based artificial viscosity for shocked viscous flows

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