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

2018 ◽  
Vol 22 (2) ◽  
pp. 543-563 ◽  
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

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 Discontinuous Galerkin Method for Material Flow Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Simone Göttlich ◽  
Patrick Schindler
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Finite Volume ◽  
Discontinuous Galerkin Method ◽  
Material Flow ◽  
Numerical Study ◽  
Hyperbolic Partial Differential Equations ◽  
Finite Volume Schemes ◽  
Flow Problems ◽  
Alternative Approach

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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