Numerical solution of the linearized Euler equations with high‐order centered schemes

1998 ◽  
Vol 103 (5) ◽  
pp. 3073-3073
Author(s):  
John A. Ekaterinaris
Keyword(s):  
Numerical Solution ◽  
Euler Equations ◽  
High Order ◽  
Linearized Euler Equations

Implicit High-Order Time Marching Schemes for the Linearized Euler Equations

AIAA Journal ◽  
2007 ◽  
Vol 45 (8) ◽  
pp. 1819-1826 ◽  
Author(s):  
George Arabatzis ◽  
Panagiotis Vavilis ◽  
Ioannis Toulopoulos ◽  
John A. Ekaterinaris
Keyword(s):  
Euler Equations ◽  
High Order ◽  
Linearized Euler Equations ◽  
Time Marching ◽  
High Order Time

The Simulation of the Linearized Euler Equations by a Second Order Scheme is Possible

2005 ◽  
Vol 4 (1-2) ◽  
pp. 49-68
Author(s):  
R. Abgrall ◽  
M. Ravachol ◽  
S. Marret
Keyword(s):  
Numerical Simulation ◽  
Euler Equations ◽  
Finite Volume ◽  
Unstructured Meshes ◽  
High Order ◽  
Complex Geometries ◽  
Residual Distribution ◽  
Linearized Euler Equations ◽  
Order Scheme ◽  
The One

We are interested in the numerical simulation of acoustic perturbations via the linearized Euler equations using triangle unstructured meshes in complex geometries such as the one around a complete aircraft. It is known that the classical schemes using a finite volume formulation with high order extrapolation of the variables can be very disappointing. In this paper, we show that using an upwind residual distribution formulation, it is possible to simulate such problems, even on truly unstructured meshes. The main focus of the paper is on the propagative properties of the scheme.

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.

Numerical Solution of the Linearized Euler Equations Using Compact Schemes

2009 ◽  
pp. 837-842
Author(s):  
Kris Van den Abeele ◽  
Jan Ramboer ◽  
Ghader Ghorbaniasl ◽  
Chris Lacor
Keyword(s):  
Numerical Solution ◽  
Euler Equations ◽  
Compact Schemes ◽  
Linearized Euler Equations
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