A New Technique for the Numerical Solution of the Compressible Euler Equations with Arbitrary Mach Numbers

2008 ◽  
pp. 523-531 ◽  
Author(s):  
M. Feistauer ◽  
V. Kučcera
Keyword(s):  
Numerical Solution ◽  
Euler Equations ◽  
New Technique ◽  
Compressible Euler Equations ◽  
Compressible Euler ◽  
Mach Numbers ◽  
A New Technique

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.

scholarly journals Efficient Solution of the Compressible Euler Equations for Low Mach Numbers

PAMM ◽  
2004 ◽  
Vol 4 (1) ◽  
pp. 420-421
Author(s):  
Frank Bramkamp ◽  
Saurya Ray ◽  
Josef Ballmann
Keyword(s):  
Euler Equations ◽  
Efficient Solution ◽  
Compressible Euler Equations ◽  
Compressible Euler ◽  
Mach Numbers

scholarly journals Singularity Formation for the Compressible Euler Equations

2017 ◽  
Vol 49 (4) ◽  
pp. 2591-2614 ◽  
Author(s):  
Geng Chen ◽  
Ronghua Pan ◽  
Shengguo Zhu
Keyword(s):  
Euler Equations ◽  
Compressible Euler Equations ◽  
Singularity Formation ◽  
Compressible Euler
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