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THE DEVELOPMENT OF A ONESTEP ACCURATE FLUX VECTORSPLITTING IMPLICIT ALGORITHM FOR EULER AND NAVIERSTOKES EQUATIONS

THE DEVELOPMENT OF A ONESTEP ACCURATE FLUX VECTORSPLITTING IMPLICIT ALGORITHM FOR EULER AND... This paper introduces a novel algorithm for solving the twodimensional Euler and NavierStokes compressible equations using a onestep effective flux vectorsplitting implicit method. The new approach makes a contribution by deriving a simple and yet effective implicit scheme which has the features of an exact factorization and avoids the solving of blockdiagonal system of equations. This results in a significant improvement in computational efficiency as compared to the standard BeamWarming and Steger implicit factored schemes. The current work has advantageous characteristics in the creation of higher order numerical implicit terms. The scheme is stable if we could select the correct values of the scalars and for the respective split fluxvectors F and G along the and directions. A simple solving procedure is suggested with the discussion of the implicit boundary conditions, stability analysis, timestep length and convergence criteria. This method is spatially secondorder accurate, fully conservative and implemented with general coordinate transformations for treating complex geometries. Also, the scheme shows a good convergence rate and acceptable accuracy in capturing the shock waves. Results calculated from the program developed include transonic flows through convergencedivergence nozzle and turbine cascade. Comparisons with other welldocumented experimental data are presented and their agreements are very promising. The extension of the algorithm to 3D simulation is straightforward and under way. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat and Fluid Flow Emerald Publishing

THE DEVELOPMENT OF A ONESTEP ACCURATE FLUX VECTORSPLITTING IMPLICIT ALGORITHM FOR EULER AND NAVIERSTOKES EQUATIONS

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References (9)

Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0961-5539
DOI
10.1108/eb017554
Publisher site
See Article on Publisher Site

Abstract

This paper introduces a novel algorithm for solving the twodimensional Euler and NavierStokes compressible equations using a onestep effective flux vectorsplitting implicit method. The new approach makes a contribution by deriving a simple and yet effective implicit scheme which has the features of an exact factorization and avoids the solving of blockdiagonal system of equations. This results in a significant improvement in computational efficiency as compared to the standard BeamWarming and Steger implicit factored schemes. The current work has advantageous characteristics in the creation of higher order numerical implicit terms. The scheme is stable if we could select the correct values of the scalars and for the respective split fluxvectors F and G along the and directions. A simple solving procedure is suggested with the discussion of the implicit boundary conditions, stability analysis, timestep length and convergence criteria. This method is spatially secondorder accurate, fully conservative and implemented with general coordinate transformations for treating complex geometries. Also, the scheme shows a good convergence rate and acceptable accuracy in capturing the shock waves. Results calculated from the program developed include transonic flows through convergencedivergence nozzle and turbine cascade. Comparisons with other welldocumented experimental data are presented and their agreements are very promising. The extension of the algorithm to 3D simulation is straightforward and under way.

Journal

International Journal of Numerical Methods for Heat and Fluid Flow – Emerald Publishing

Published: Aug 1, 1996

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