Jacobian-free Newton-Krylov method for implicit time-spectral solution of the compressible Navier-Stokes equations

2015 ◽  
Vol 79 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Peter J. Attar
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Krylov Method ◽  
Spectral Solution

scholarly journals Navier-Stokes Analysis of Unsteady Transonic Flows Through Gas Turbine Cascades With and Without Coolant Ejection

1997 ◽  
Author(s):  
T. Tanuma ◽  
N. Shibukawa ◽  
S. Yamamoto
Keyword(s):  
Gas Turbine ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Implicit Time ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Turbine Cascades ◽  
Annular Cascade

An implicit time-marching higher-order accurate finite-difference method for solving the two-dimensional compressible Navier-Stokes equations was applied to the numerical analyses of steady and unsteady, subsonic and transonic viscous flows through gas turbine cascades with trailing edge coolant ejection. Annular cascade tests were carried out to verify the accuracy of the present analysis. The unsteady aerodynamic mechanisms associated with the interaction between the trailing edge vortices and shock waves and the effect of coolant ejection were evaluated with the present analysis.

Simulation of Flow Around Circular Cylinder Using a Collocation Spectral Method

2005 ◽  
Author(s):  
Johnny J. M. Rizales ◽  
Paulo T. T. Esperanc¸a ◽  
Andre´ Belfort Bueno
Keyword(s):  
Velocity Field ◽  
Circular Cylinder ◽  
Spectral Method ◽  
Stokes Equations ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Implicit Time ◽  
Integration Scheme ◽  
Navier Stokes Equations ◽  
Collocation Spectral Method

The purpose of this paper is to develop a Fourier-Chebyshev collocation spectral method for computing unsteady two-dimensional viscous incompressible flow past a circular cylinder for low Reynolds numbers. The incompressible Navier-Stokes equations (INSE) are formulated in terms of the primitive variables, velocity and pressure. The incompressible Navier-Stokes equations in curvilinear coordinates are spectrally discretized and time integrated by a second-order mixed explicit/implicit time integration scheme. This scheme is a combination of the Crank-Nicolson scheme operating on the diffusive term and Adams-Bashforth scheme acting on the convective term. The projection method is used to split the solution of the INSE to the solution of two decoupled problems: the diffusion-convection equation (Burgers equation) to predict an intermediate velocity field and the Poisson equation for the pressure, it is used to correct the velocity field and satisfy the continuity equation. Finally, the numerical results obtained for the drag and lift coefficients around the circular cylinder are compared with results previously published.

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