A numerical study for the performance of the Runge–Kutta discontinuous Galerkin method based on different numerical fluxes

2006 ◽  
Vol 212 (2) ◽  
pp. 540-565 ◽  
Author(s):  
Jianxian Qiu ◽  
Boo Cheong Khoo ◽  
Chi-Wang Shu
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Numerical Study ◽  
Numerical Fluxes ◽  
Runge Kutta

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

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.

Runge-Kutta Discontinuous Galerkin Method with Front Tracking Method for Solving the Compressible Two-Medium Flow on Unstructured Meshes

2016 ◽  
Vol 9 (1) ◽  
pp. 73-91 ◽  
Author(s):  
Haitian Lu ◽  
Jun Zhu ◽  
Chunwu Wang ◽  
Ning Zhao
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Front Tracking ◽  
Unstructured Meshes ◽  
Interfacial Region ◽  
Tracking Method ◽  
Front Tracking Method ◽  
Medium Flow ◽  
Runge Kutta

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.

An Application of Discontinuous Galerkin Method for Blast Wave Simulations

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.

scholarly journals A numerical study of superconvergence of the discontinuous Galerkin method by patch reconstruction

2020 ◽  
Vol 28 (4) ◽  
pp. 1487-1501
Author(s):  
Zexuan Liu ◽  
◽  
Zhiyuan Sun ◽  
Jerry Zhijian Yang ◽  
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Numerical Study
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