A Runge–Kutta discontinuous Galerkin method for the Euler equations

AbstractIn this paper, we extend using the Runge-Kutta discontinuous Galerkin method together with the front tracking method to simulate the compressible two-medium flow on unstructured meshes. A Riemann problem is constructed in the normal direction in the material interfacial region, with the goal of obtaining a compact, robust and efficient procedure to track the explicit sharp interface precisely. Extensive numerical tests including the gas-gas and gas-liquid flows are provided to show the proposed methodologies possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow and the interfacial vicinities of the two-medium flow in many occasions.

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Convexity in Hyperbolic Problems. Application to a Discontinuous Galerkin Method for the Resolution of the Polydimensional Euler Equations

Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications ◽

10.1007/978-3-322-87869-4_4 ◽

1989 ◽

pp. 31-42 ◽

Cited By ~ 3

Author(s):

F. Bourdel ◽

Ph. Delorme ◽

P. A. Mazet

Keyword(s):

Galerkin Method ◽

Euler Equations ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Hyperbolic Problems

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Implementing a discontinuous Galerkin method for the compressible, inviscid Euler equations in the DUNE framework

PAMM ◽

10.1002/pamm.201410457 ◽

2014 ◽

Vol 14 (1) ◽

pp. 953-954 ◽

Cited By ~ 3

Author(s):

Juan Pablo Gallego-Valencia ◽

Johannes Löbbert ◽

Steffen Müthing ◽

Peter Bastian ◽

Christian Klingenberg ◽

...

Keyword(s):

Galerkin Method ◽

Euler Equations ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method

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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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