Finite Volume Solvers and Moving Least Square Approximations for the Linearized Euler Equations on Unstructured Grids

2008 ◽  
Vol 123 (5) ◽  
pp. 3381-3381 ◽  
Author(s):  
Sofiane Khelladi ◽  
Xesús Nogueira ◽  
Farid Bakir ◽  
Luis Cueto‐Felgueroso ◽  
Ignasi Colominas
Keyword(s):  
Euler Equations ◽  
Finite Volume ◽  
Unstructured Grids ◽  
Least Square ◽  
Linearized Euler Equations ◽  
Moving Least Square

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.

A Robust WENO Type Finite Volume Solver for Steady Euler Equations on Unstructured Grids

2011 ◽  
Vol 9 (3) ◽  
pp. 627-648 ◽  
Author(s):  
Guanghui Hu ◽  
Ruo Li ◽  
Tao Tang
Keyword(s):  
Euler Equations ◽  
Finite Volume ◽  
Numerical Experiments ◽  
Unstructured Grids ◽  
Numerical Accuracy ◽  
Shock Region ◽  
Smooth Region ◽  
Type Reconstruction ◽  
Numer Math ◽  
Numerical Strategy

AbstractA recent work of Li et al. [Numer. Math. Theor. Meth. Appl., 1(2008), pp. 92-112] proposed a finite volume solver to solve 2D steady Euler equations. Although the Venkatakrishnan limiter is used to prevent the non-physical oscillations nearby the shock region, the overshoot or undershoot phenomenon can still be observed. Moreover, the numerical accuracy is degraded by using Venkatakrishnan limiter. To fix the problems, in this paper the WENO type reconstruction is employed to gain both the accurate approximations in smooth region and non-oscillatory sharp profiles near the shock discontinuity. The numerical experiments will demonstrate the efficiency and robustness of the proposed numerical strategy.

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