2202 CIP/multi-moment finite volume method and Discontinuous Galerkin 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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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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Numerical Solution of Multidimensional Compressible Flow by High Order Nodal Discontinuous Galerkin Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.392.100 ◽

2013 ◽

Vol 392 ◽

pp. 100-104 ◽

Cited By ~ 1

Author(s):

Fareed Ahmed ◽

Faheem Ahmed ◽

Yong Yang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Numerical Solution ◽

Finite Volume Method ◽

Discontinuous Galerkin ◽

Finite Volume ◽

High Order ◽

Numerical Predictions ◽

Volume Method ◽

Element Method

In this paper we present a robust, high order method for numerical solution of multidimensional compressible inviscid flow equations. Our scheme is based on Nodal Discontinuous Galerkin Finite Element Method (NDG-FEM). This method utilizes the favorable features of Finite Volume Method (FVM) and Finite Element Method (FEM). In this method, space discretization is carried out by finite element discontinuous approximations. The resulting semi discrete differential equations were solved using explicit Runge-Kutta (ERK) method. In order to compute fluxes at element interfaces, we have used Roe Approximate scheme. In this article, we demonstrate the use of exponential filter to remove Gibbs oscillations near the shock waves. Numerical predictions for two dimensional compressible fluid flows are presented here. The solution was obtained with overall order of accuracy of 3. The numerical results obtained are compared with experimental and finite volume method results.

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Discontinuous Galerkin Method for Material Flow Problems

Mathematical Problems in Engineering ◽

10.1155/2015/341893 ◽

2015 ◽

Vol 2015 ◽

pp. 1-15 ◽

Cited By ~ 1

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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