Numerical study of the unsteady 2D coupled magneto-hydrodynamic equations on regular/irregular pipe using direct meshless local Petrov–Galerkin method

2022 ◽  
Vol 417 ◽  
pp. 126769
Author(s):  
Erfan Bahmani ◽  
Ali Shokri
2019 ◽  
Vol 11 (9) ◽  
pp. 168781401987490
Author(s):  
Muhammad Rehan Saleem ◽  
Ubaid Ahmed Nisar ◽  
Shamsul Qamar

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.


Author(s):  
Ruslan V. Zhalnin ◽  
Nikita A. Kuzmin ◽  
Victor F. Masyagin

The paper presents a numerical parallel algorithm based on an implicit scheme for the Galerkin method with discontinuous basis functions for solving diffusion-type equations on triangular grids. To apply the Galerkin method with discontinuous basis functions, the initial equation of parabolic type is transformed to a system of partial differential equations of the first order. To do this, auxiliary variables are introduced, which are the components of the gradient of the desired function. To store sparse matrices and vectors, the CSR format is used in this study. The resulting system is solved numerically using a parallel algorithm based on the Nvidia AmgX library. A numerical study is carried out on the example of solving two-dimensional test parabolic initial-boundary value problems. The presented numerical results show the effectiveness of the proposed algorithm for solving parabolic problems.


2020 ◽  
Vol 28 (4) ◽  
pp. 1487-1501
Author(s):  
Zexuan Liu ◽  
◽  
Zhiyuan Sun ◽  
Jerry Zhijian Yang ◽  

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Simone Göttlich ◽  
Patrick Schindler

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.


Sign in / Sign up

Export Citation Format

Share Document