A discontinuous Galerkin approach for high-resolution simulations of three-dimensional flows

Panourgias, Konstantinos; Ekaterinaris, John A.

doi:10.1016/j.cma.2015.10.016

Cited by 13 publications

(7 citation statements)

References 56 publications

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“…The SU 2 code has adaptive mesh refinement capabilities. It was found that for simpler shock interactions, adaptive mesh refinement (h-refinement) can yield superior resolution [18]. The unsteady complex wave interactions of the present study (see Fig.…”

Section: Computational Approachmentioning

confidence: 66%

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Normal shock wave attenuation during propagation in ducts with grooves

2019

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Experimental investigations and numerical simulations of normal shock waves of different strengths propagating inside ducts with roughness are presented. The roughness is added in the form of grooves. Straight and branching ducts are considered in order to better explore the mechanisms causing attenuation of the shock and the physics behind the evolution of the complex wave patterns resulting from diffraction and reflection of the primary moving shock. A well-established finite volume numerical method is used and further validated for several test cases relevant to this study. The computed results are compared with experimental measurements in ducts with grooves. Good agreement between high-resolution simulations and the experiment is obtained for the shock speeds and complex wave patterns created by the grooves. High frequency response time histories of pressure at various locations were recorded in the experiments. The recorded pressure histories and shock strengths were found in fair agreement with the two-dimensional simulation results

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Section: Computational Approachmentioning

confidence: 66%

“…Previous numerical simulations of high-speed flows with shocks have employed high order methods, such as fifth-order accurate in space or higher Weighted Essentially Non-Oscillatory (WENO) schemes [10,17], or the Discontinuous Galerkin (DG) method [18]. High order methods for viscous flows however are computationally intensive.…”

Section: Computational Approachmentioning

confidence: 99%

Normal shock wave attenuation during propagation in ducts with grooves

2019

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“…We list below only a few examples over the past year (since 2015). Recent applications of DG methods can be found in the simulations of the Cahn-Hilliard-Brinkman system [85], compressible flow in the transonic axial compressor [190], computational astrophysics [197], computational geosciences [221], elastodynamics [53], flow instabilities [51], Fokker-Planck equations [152], fractional PDEs [111,243], front propagation with obstacles [17], functionalized Cahn-Hilliard equation [87], interfaces [278], magnetohy-drodynamics [265], moment closures for kinetic equations [2], multi-phase flow and phase transition [52,169], Navier-Stokes and Boussinesq equations [64,224], nonlinear Schrodinger equation [86,149,158], ocean waves [192], population models [112], porous media [84], rarefied gas [212], semiconductor device simulation [155], shallow water equations [73], thin film epitaxy problem [247], traffic flow and networks [21], three-dimensional flows [175], turbulent flows [246], underwater explosion [235], viscous surface wave [245], and wavefield modeling [95]. This very incomplete list over just one year period clearly demonstrates the wide-spread application of the DG method in computational science and engineering.…”

Section: Discontinuous Galerkin and Related Schemesmentioning

confidence: 99%

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

Shu

2016

Journal of Computational Physics

162

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For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, namely the weighted essentially non-oscillatory (WENO) finite difference and finite volume schemes and discontinuous Galerkin (DG) finite element methods, emphasizing several of their recent developments: bound-preserving limiters for DG, finite volume and finite difference schemes, which address issues in robustness and accuracy; WENO limiters for DG methods, which address issues in non-oscillatory performance when there are strong shocks, and inverse Lax-Wendroff type boundary treatments for finite difference schemes, which address issues in solving complex geometry problems using Cartesian meshes.

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“…Implementation of p‐refinement is performed in a parallel environment, and it is straightforward with the hierarchical Legendre polynomial bases; it is however more complicated for divergence‐free vector bases. Application of both h‐ and p‐adaptivity for the DG method requires information exchange only at the element faces and has been validated and demonstrated that it is conservative and for problems with smooth solutions converges to the design order of accuracy of the scheme . Numerical solutions with p‐adaptivity were also obtained for flows including discontinuities .…”

Section: P‐adaptivitymentioning

confidence: 99%

“…Application of both h-and p-adaptivity for the DG method requires information exchange only at the element faces and has been validated and demonstrated that it is conservative and for problems with smooth solutions converges to the design order of accuracy of the scheme. 52,53 Numerical solutions with p-adaptivity were also obtained for flows including discontinuities. 54 For large scale three-dimensional simulations, it is important to ensure that the parallel efficiency is high during the entire course of the computation.…”

Section: P-adaptivitymentioning

confidence: 99%

A p‐adaptive method for electromagnetic wave propagation

Panourgias

Ekaterinaris²

2017

Numerical Meth Engineering

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Summary The discontinuous Galerkin FEM is used for the numerical solution of the three‐dimensional Maxwell equations. Control of errors in the numerical level for the divergence‐free constraint of the magnetic field can be obtained through the use of divergence‐free vector bases. In this work, the so‐called perfectly hyperbolic formulation of the Maxwell equations is used to retain both divergence‐free magnetic field and in the presence of charges to satisfy the Gauss constraint for the electric field at the numerical level. For both approaches, it is found that higher‐order approximations have favorable effect on the preservation of the divergence constraints and that the perfectly hyperbolic formulations retains these errors to a lower level. It is shown that high‐order accuracy in space and time is achieved in unstructured meshes using implicit time marching. For nonuniform meshes, local resolution refinement is used using p‐type adaptivity to ensure accurate electromagnetic wave propagation. Thus, the potential of the method to reach the required higher resolution in anisotropic meshes and obtain accurate electromagnetic wave propagation with reduced computational effort is demonstrated.

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A discontinuous Galerkin approach for high-resolution simulations of three-dimensional flows

Cited by 13 publications

References 56 publications

Normal shock wave attenuation during propagation in ducts with grooves

Normal shock wave attenuation during propagation in ducts with grooves

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

A p‐adaptive method for electromagnetic wave propagation

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