An efficient upwind relaxation-sweeping algorithm for three-dimensional Euler equations

1990 ◽  
Author(s):  
GE-CHENG ZHA ◽  
DAO-ZHI LIU
Keyword(s):  
Euler Equations ◽  
Three Dimensional

Analysis of three-dimensional aerospace configurations using the Euler equations

1989 ◽  
Author(s):  
N. KROLL ◽  
C. ROSSOW ◽  
S. SCHERR ◽  
J. SCHOENE ◽  
G. WICHMANN
Keyword(s):  
Euler Equations ◽  
Three Dimensional

scholarly journals The three-dimensional Euler equations: singular or non-singular?

Nonlinearity ◽  
2008 ◽  
Vol 21 (8) ◽  
pp. T123-T129 ◽  
Author(s):  
J D Gibbon ◽  
M Bustamante ◽  
R M Kerr
Keyword(s):  
Euler Equations ◽  
Three Dimensional

Advances in the Numerical Integration of the Three-Dimensional Euler Equations in Vibrating Cascades

1993 ◽  
Vol 115 (4) ◽  
pp. 781-790 ◽  
Author(s):  
G. A. Gerolymos
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Euler Equations ◽  
Finite Volume ◽  
Three Dimensional ◽  
Computational Results ◽  
Grid Refinement ◽  
Mobile Grid ◽  
Transonic Compressor ◽  
Runge Kutta

In the present work an algorithm for the numerical integration of the three-dimensional unsteady Euler equations in vibrating transonic compressor cascades is described. The equations are discretized in finite-volume formulation in a mobile grid using isoparametric brick elements. They are integrated in time using Runge-Kutta schemes. A thorough discussion of the boundary conditions used and of their influence on results is undertaken. The influence of grid refinement on computational results is examined. Unsteady convergence of results is discussed.

scholarly journals Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Yuma Fukushima ◽  
Daisuke Sasaki ◽  
Kazuhiro Nakahashi
Keyword(s):  
Euler Equations ◽  
Complex Geometry ◽  
Time Integration ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Shielding Effect ◽  
Immersed Boundary ◽  
Noise Propagation ◽  
Linearized Euler Equations ◽  
Cartesian Mesh

The linearized Euler equations (LEEs) solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN) configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.

A FULLY IMPLICIT SOLVER OF 3-D EULER EQUATIONS ON MULTIBLOCK CURVILINEAR GRIDS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1483-1486 ◽  
Author(s):  
HAI-QING SI ◽  
TONG-GUANG WANG ◽  
XIAO-YUN LUO
Keyword(s):  
Euler Equations ◽  
Three Dimensional ◽  
Implicit Time ◽  
Tvd Scheme ◽  
Time Step ◽  
Vector Operation ◽  
Fully Implicit ◽  
Curvilinear Grids ◽  
The Matrix ◽  
Implicit Solver

A fully implicit unfactored algorithm for three-dimensional Euler equations is developed and tested on multi-block curvilinear meshes. The convective terms are discretized using an upwind TVD scheme. The large sparse linear system generated at each implicit time step is solved by GMRES* method combined with the block incomplete lower-upper preconditioner. In order to reduce the memory requirements and the matrix-vector operation counts, an approximate method is used to derive the Jacobian matrix, which only costs half of the computational efforts of the exact Jacobian calculation. The comparison between the numerical results and the experimental data shows good agreement, which demonstrates that the implicit algorithm presented is effective and efficient.

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