scholarly journals Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations

2016 ◽  
Vol 327 ◽  
pp. 39-66 ◽  
Author(s):  
Gregor J. Gassner ◽  
Andrew R. Winters ◽  
David A. Kopriva
Keyword(s):  
Euler Equations ◽  
Discontinuous Galerkin ◽  
Compressible Euler Equations ◽  
Summation By Parts ◽  
Compressible Euler ◽  
Split Form

Numerical Solution of Compressible Euler Equations by High Order Nodal Discontinuous Galerkin Method

2013 ◽  
Vol 392 ◽  
pp. 165-169 ◽  
Author(s):  
Fareed Ahmed ◽  
Faheem Ahmed ◽  
Yong Yang
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Euler Equations ◽  
Discontinuous Galerkin ◽  
Gas Dynamics ◽  
High Order ◽  
Compressible Euler Equations ◽  
Element Space ◽  
Numerical Predictions ◽  
Compressible Euler

In this paper we present a robust, high order method for numerical solution of compressible Euler Equations of the gas dynamics. Euler equations are hyperbolic in nature. Our scheme is based on Nodal Discontinuous Galerkin Finite Element Method (NDG-FEM). This method combines mainly two key ideas which are based on the finite volume and finite element methods. In this method, we employ Discontinuous Galerkin (DG) technique for finite element space discretization by discontinuous approximations. Whereas, for temporal discretization, we used explicit Runge-Kutta (ERK) method. In order to compute fluxes at element interfaces, we have used Roe Approximate scheme. We used filter to remove spurious oscillations near the shock waves. Numerical predictions for Shock tube problem (SOD) are presented and compared with exact solution at different polynomial order and mesh sizes. Results show the suitability of DG method for modeling gas dynamics equations and effectiveness of high order approximations.

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