scholarly journals A Parallel Adaptive Newton-Krylov-Schwarz Method for 3D Compressible Inviscid Flow Simulations

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Marzio Sala ◽  
Pénélope Leyland ◽  
Angelo Casagrande
Keyword(s):  
Compressible Flows ◽  
Time Derivative ◽  
Inviscid Flow ◽  
Implicit Time ◽  
Residual Distribution ◽  
Preconditioning Techniques ◽  
Flow Simulations ◽  
Efficient Data ◽  
Time Marching ◽  
2D And 3D

A parallel adaptive pseudo transient Newton-Krylov-Schwarz (αΨNKS) method for the solution of compressible flows is presented. Multidimensional upwind residual distribution schemes are used for space discretisation, while an implicit time-marching scheme is employed for the discretisation of the (pseudo)time derivative. The linear system arising from the Newton method applied to the resulting nonlinear system is solved by the means of Krylov iterations with Schwarz-type preconditioners. A scalable and efficient data structure for theαΨNKS procedure is presented. The main computational kernels are considered, and an extensive analysis is reported to compare the Krylov accelerators, the preconditioning techniques. Results, obtained on a distributed memory computer, are presented for 2D and 3D problems of aeronautical interest on unstructured grids.

Computational Analysis of Pitch-Width Effects on the Losses of Turbine Blades

2001 ◽  
Author(s):  
C. Xu ◽  
R. S. Amano
Keyword(s):  
Secondary Flow ◽  
Compressible Flows ◽  
Turbine Blades ◽  
Time Derivative ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Width Ratio ◽  
Computational Code ◽  
Time Marching ◽  
Flow Effects

Abstract A three-dimensional computational code was developed for solving a time-averaged flow within a turbine blade-to-blade region using a novel time-marching method. A new concept of incorporating dissipation terms into the time derivative terms was proposed to allow the code to have the capability of handling both incompressible and compressible flows. The computational code was validated through comparisons with experiments in a turbine stator and was used to investigate the influence of secondary flow depending on different pitch-width ratios of the turbine blades. Detailed secondary flows as well as loss profiles in different sizes of root pitch-width ratio were presented. The results of this study provide useful information for evaluation of the secondary flow effects due to pitch-width ratio influence for the future turbine designs.

Time-Derivative Preconditioning Methods for Multicomponent Flows—Part I: Riemann Problems

2009 ◽  
Vol 76 (2) ◽  
Author(s):  
Jeffrey A. Housman ◽  
Cetin C. Kiris ◽  
Mohamed M. Hafez
Keyword(s):  
Numerical Methods ◽  
Time Derivative ◽  
Density Ratio ◽  
Stability And Convergence ◽  
Implicit Time ◽  
Fluid Interfaces ◽  
Incompressible Limit ◽  
Riemann Problems ◽  
Multicomponent Flows ◽  
Time Marching

A time-derivative preconditioned system of equations suitable for the numerical simulation of inviscid multicomponent and multiphase flows at all speeds is described. The system is shown to be hyperbolic in time and remains well conditioned in the incompressible limit, allowing time marching numerical methods to remain an efficient solution strategy. It is well known that the application of conservative numerical methods to multicomponent flows containing sharp fluid interfaces will generate nonphysical pressure and velocity oscillations across the component interface. These oscillations may lead to stability problems when the interface separates fluids with large density ratio, such as water and air. The effect of which may lead to the requirement of small physical time steps and slow subiteration convergence for implicit time marching numerical methods. At low speeds the use of nonconservative methods may be considered. In this paper a characteristic-based preconditioned nonconservative method is described. This method preserves pressure and velocity equilibrium across fluid interfaces, obtains density ratio independent stability and convergence, and remains well conditioned in the incompressible limit of the equations. To extend the method to transonic and supersonic flows containing shocks, a hybrid formulation is described, which combines a conservative preconditioned Roe method with the nonconservative preconditioned characteristic-based method. The hybrid method retains the pressure and velocity equilibrium at component interfaces and converges to the physically correct weak solution. To demonstrate the effectiveness of the nonconservative and hybrid approaches, a series of one-dimensional multicomponent Riemann problems is solved with each of the methods. The solutions are compared with the exact solution to the Riemann problem, and stability of the numerical methods are discussed.

Time-Derivative Preconditioning Methods for Multicomponent Flows—Part II: Two-Dimensional Applications

2009 ◽  
Vol 76 (3) ◽  
Author(s):  
Jeffrey A. Housman ◽  
Cetin C. Kiris ◽  
Mohamed M. Hafez
Keyword(s):  
Numerical Methods ◽  
Riemann Problem ◽  
Hybrid Method ◽  
Time Derivative ◽  
Hybrid Approach ◽  
Implicit Time ◽  
Two Dimensional ◽  
First Case ◽  
Multicomponent Flows ◽  
Time Marching

A time-derivative preconditioned system of equations suitable for the numerical simulation of multicomponent/multiphase inviscid flows at all speeds was described in Part I of this paper. The system was shown to be hyperbolic in time and remain well conditioned in the incompressible limit, allowing time marching numerical methods to remain an efficient solution strategy. Application of conservative numerical methods to multicomponent flows containing sharp fluid interfaces was shown to generate nonphysical pressure and velocity oscillations across the contact surface, which separates the fluid components. It was demonstrated using the one-dimensional Riemann problem that these oscillations may lead to stability problems when the interface separates fluids with large density ratios, such as water and air. The effect of which leads to the requirement of small physical time steps and slow subiteration convergence for the implicit time marching numerical method. Alternatively, the nonconservative and hybrid formulations developed by the present authors were shown to eliminate this nonphysical behavior. While the nonconservative method did not converge to the correct weak solution for flow containing shocks, the hybrid method was able to capture the physically correct entropy solution and converge to the exact solution of the Riemann problem as the grid is refined. In Part II of this paper, the conservative, nonconservative, and hybrid formulations described in Part I are implemented within a two-dimensional structured body-fitted overset grid solver, and a study of two unsteady flow applications is reported. In the first application, a multiphase cavitating flow around a NACA0015 hydrofoil contained in a channel is solved, and sensitivity to the cavitation number and the spatial order of accuracy of the discretization are discussed. Next, the interaction of a shock moving in air with a cylindrical bubble of another fluid is analyzed. In the first case, the cylindrical bubble is filled with helium gas, and both the conservative and hybrid approaches perform similarly. In the second case, the bubble is filled with water and the conservative method fails to maintain numerical stability. The performance of the hybrid method is shown to be unchanged when the gas is replaced with a liquid, demonstrating the robustness and accuracy of the hybrid approach.

Numerical Modeling of Radiative and Reactive Flow Field Around a Blunt Body at Hypersonic Regimes

2010 ◽  
Author(s):  
Morteza Rahmanpour ◽  
Reza Ebrahimi ◽  
Mehrzad Shams
Keyword(s):  
Flow Field ◽  
Differential Equations ◽  
Heat Fluxes ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Discrete Ordinates ◽  
Two Dimensional ◽  
Fully Implicit ◽  
Time Marching

A numerical method for calculation of strong radiation for two-dimensional reactive air flow field is developed. The governing equations are taken to be two dimensional, compressible Reynolds-average Navier-Stokes and species transport equations. Also, radiation heat flux in energy equation is evaluated using a model of discrete ordinate method. The model used S4 approximation to reduce the governing system of integro-differential equations to coupled set of partial differential equations. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method. The turbulent diffusion and heat fluxes are modeled by Baldwin and Lomax method. The flow solution is obtained with a fully implicit time marching method. A thermochemical nonequilibrium formulation appropriate to hypersonic transitional flow of air is presented. The method is compared with existing experimental results and good agreement is observed.

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.

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