Discontinuous Galerkin Method for Material Flow Problems

For the simulation of material flow problems based on two-dimensional hyperbolic partial differential equations different numerical methods can be applied. Compared to the widely used finite volume schemes we present an alternative approach, namely, the discontinuous Galerkin method, and explain how this method works within this framework. An extended numerical study is carried out comparing the finite volume and the discontinuous Galerkin approach concerning the quality of solutions.

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Numerical approximation of incompressible fluid flow problems by discontinuous Galerkin method

10.1063/5.0030874 ◽

2020 ◽

Author(s):

Ondřej Winter ◽

Petr Sváček

Keyword(s):

Fluid Flow ◽

Incompressible Fluid ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Numerical Approximation ◽

Incompressible Fluid Flow ◽

Flow Problems

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Assessment of a high-order discontinuous Galerkin method for internal flow problems. Part I: Benchmark results for quasi-1D, 2D waves propagation and axisymmetric turbulent flows

Computers & Fluids ◽

10.1016/j.compfluid.2016.05.013 ◽

2016 ◽

Vol 134-135 ◽

pp. 61-80

Author(s):

C. De Bartolo ◽

A. Nigro ◽

V. Covello ◽

F. Bassi

Keyword(s):

Galerkin Method ◽

Turbulent Flows ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Internal Flow ◽

High Order ◽

Flow Problems ◽

Waves Propagation

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A finite volume / discontinuous Galerkin method for the advective Cahn–Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging

Computational Geosciences ◽

10.1007/s10596-017-9709-1 ◽

2018 ◽

Vol 22 (2) ◽

pp. 543-563 ◽

Cited By ~ 13

Author(s):

Florian Frank ◽

Chen Liu ◽

Faruk O. Alpak ◽

Beatrice Riviere

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Finite Volume ◽

Discontinuous Galerkin Method ◽

Ct Imaging ◽

Micro Ct ◽

Hilliard Equation ◽

Degenerate Mobility ◽

Cahn Hilliard Equation

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Discontinuous Galerkin method for solving incompressible two-phase shallow granular flow model

Advances in Mechanical Engineering ◽

10.1177/1687814019874908 ◽

2019 ◽

Vol 11 (9) ◽

pp. 168781401987490

Author(s):

Muhammad Rehan Saleem ◽

Ubaid Ahmed Nisar ◽

Shamsul Qamar

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Numerical Scheme ◽

Flow Model ◽

Numerical Study ◽

Momentum Exchange ◽

Two Phase ◽

Runge Kutta ◽

Model Equations

This article deals with the numerical study of two-phase shallow flow model describing the mixture of fluid and solid granular particles. The model under investigation consists of coupled mass and momentum equations for solid granular material and fluid particles through non-conservative momentum exchange terms. The non-conservativity of model equations poses major challenges for any numerical scheme, such as well balancing, positivity preservation, accurate approximation of non-conservative terms, and achievement of steady-state conditions. Thus, in order to approximate the present model an accurate, well-balanced, robust, and efficient numerical scheme is required. For this purpose, in this article, Runge–Kutta discontinuous Galerkin method is applied successfully for the first time to solve the model equations. Several test problems are also carried out to check the performance and accuracy of our proposed numerical method. To compare the results, the same model is solved by staggered central Nessyahu–Tadmor scheme. A good comparison is found between two schemes, but the results obtained by Runge–Kutta discontinuous Galerkin scheme are found superior over the central Nessyahu–Tadmor scheme.

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An Application of Discontinuous Galerkin Method for Blast Wave Simulations

ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Volume 4 ◽

10.1115/esda2010-25072 ◽

2010 ◽

Author(s):

Emre Alpman

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Blast Wave ◽

Finite Volume ◽

Discontinuous Galerkin Method ◽

Numerical Solutions ◽

Blast Waves ◽

Strong Discontinuities ◽

Runge Kutta ◽

Volume Method

An implementation of Runge-Kutta Discontinuous Galerkin method to an in-house computational fluid dynamics code capable of simulating blast waves was performed. The resultant code was tested for two shock tube problems with moderately and extremely strong discontinuities. Numerical solutions were compared with predictions of a finite volume method and exact solutions. It was observed that when there are extreme discontinuities in the flowfield, as in the case of blast waves, the limiter adopted for solution clearly affects the overall quality of the predictions. An alternative limiting technique was proposed and tested to improve the results obtained. Blast wave predictions using Runge-Kutta Discontinuous Galerkin method with the alternative limiting technique yielded slightly stronger and faster moving shock waves compared to finite volume solutions.

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