A finite-difference method of calculating a turbulent boundary layer of incompressible liquid

1974 ◽  
Vol 26 (2) ◽  
pp. 206-211 ◽  
Author(s):  
Yu. E. Karyakin ◽  
V. G. Sharov
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Turbulent Boundary Layer ◽  
Difference Method ◽  
Incompressible Liquid

A Finite-Difference Method for Calculating Compressible Laminar and Turbulent Boundary Layers

1970 ◽  
Vol 92 (3) ◽  
pp. 523-535 ◽  
Author(s):  
T. Cebeci ◽  
A. M. O. Smith
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Turbulent Boundary Layer ◽  
Turbulent Flows ◽  
Difference Method ◽  
Eddy Viscosity ◽  
Energy Equation ◽  
Composite Layer ◽  
Computation Time

This paper presents a finite-difference method for solving laminar and turbulent-boundary-layer equations for incompressible and compressible flows about two-dimensional and axisymmetric bodies and contains a thorough evaluation of its accuracy and computation-time characteristics. The Reynolds shear-stress term is eliminated by an eddy-viscosity concept, and the time mean of the product of fluctuating velocity and temperature appearing in the energy equation is eliminated by an eddy-conductivity concept. The turbulent boundary layer is regarded as a composite layer consisting of inner and outer regions, for which separate expressions for eddy viscosity are used. The eddy-conductivity term is lumped into a “turbulent” Prandtl number that is currently assumed to be constant. The method has been programed on the IBM 360/65, and its accuracy has been investigated for a large number of flows by comparing the computed solutions with the solutions obtained by analytical methods, as well as with solutions obtained by other numerical methods. On the basis of these comparisons, it can be said that the present method is quite accurate and satisfactory for most laminar and turbulent flows. The computation time is also quite small. In general, a typical flow, either laminar or turbulent, consists of about twenty x-stations. The computation time per station is about one second for an incompressible laminar flow and about two to three seconds for an incompressible turbulent flow on the IBM 360/65. Solution of energy equation in either laminar or turbulent flows increases the computation time about one second per station.

On a Convergent Multi-Moment Method for the Laminar Boundary Layer Equations

1967 ◽  
Vol 18 (4) ◽  
pp. 332-353 ◽  
Author(s):  
Howard E. Bethel
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Laminar Boundary Layer ◽  
Difference Method ◽  
Moment Method ◽  
External Flow ◽  
Higher Moments ◽  
Type Method ◽  
Boundary Layer Equations

SummaryThis paper presents a summary of a multi-moment method for solving the laminar boundary layer equations. Results obtained with the method tend to converge to the exact values as higher moments are used. Both similar and non-similar external flow fields are considered. The present results are compared with those obtained by another multi-moment method, a finite-difference method and a refined Pohlhausen-type method.

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