An efficient geometric approach to solve the slope limiting problem with the Discontinuous Galerkin method on unstructured triangles

2009 ◽  
Vol 26 (12) ◽  
pp. 1824-1835 ◽  
Author(s):  
Anis Younes ◽  
Marwan Fahs ◽  
Philippe Ackerer
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Geometric Approach ◽  
Slope Limiting

Application of a Discontinuous Galerkin Method to 1-D Liquid Sloshing

2003 ◽  
Author(s):  
Martin J. Guillot
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Shallow Water Equations ◽  
Godunov Method ◽  
First Order ◽  
Slope Limiter ◽  
Dg Method ◽  
Slope Limiting ◽  
Dam Breaking

A discontinuous Galerkin method is applied to the shallow water equations written in a rotating frame of reference. Linear approximating functions are employed on each element. A minmod slope limiter is incorporated to ensure non-linear total variation bounded (TVB) stability. The method is first applied to the dam breaking problem with zero rotation to validate the numerical implementation. A rotating tank is then investigated with sinusoidal rotation. Results are computed with and without slope limiting to investigate the effect of slope limiting on the solution. The DG method is also compared to a first order Godunov method and to experimental data.

scholarly journals FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, Part II: Advection operator and slope limiting

2016 ◽  
Vol 72 (7) ◽  
pp. 1896-1925 ◽  
Author(s):  
Balthasar Reuter ◽  
Vadym Aizinger ◽  
Manuel Wieland ◽  
Florian Frank ◽  
Peter Knabner
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Slope Limiting

scholarly journals A Problem-Independent Slope Limiting Algorithm for the Runge-Kutta Discontinuous Galerkin Method

2010 ◽  
Vol 10 (3) ◽  
pp. 326-342 ◽  
Author(s):  
S.A. Tokareva
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Intermediate Step ◽  
Standard Formulation ◽  
Third Order ◽  
Slope Limiting ◽  
Runge Kutta ◽  
Definition Of ◽  
Special Parameter

AbstractThis paper deals with the new algorithm of slope limiting in the Runge- Kutta discontinuous Galerkin (RKDG) method. The slope limiting is applied at each intermediate step of the Runge-Kutta process to guarantee the monotonicity of the resulting RKDG scheme. The standard formulation of the RKDG method assumes a manual prescription of the special parameter used in the limiting procedure. Such definition of the limiter makes the method problem-dependent, which is disadvantageous for practical computations. A new problem-independent way of estimating the limiting parameter is proposed and its performance in the second- and third-order RKDG methods is studied in this paper.

SELECTION OF VISCOUS TERMS APPROXIMATION IN DISCONTINUOUS GALERKIN METHOD

2013 ◽  
Vol 44 (3) ◽  
pp. 327-354
Author(s):  
Aleksey Igorevich Troshin ◽  
Vladimir Viktorovich Vlasenko ◽  
Andrey Viktorovich Wolkov
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Selection Of
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