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Demirdžić, I.; Lilek, Ž.; Perić, M.
doi: 10.1002/fld.1650161202pmid: N/A
An existing two‐dimensional method for the prediction of steady‐state incompressible flows in complex geometry is extended to treat also compressible flows at all speeds. The primary variables are the Cartesian velocity components, pressure and temperature. Density is linked to pressure via an equation of state. The influence of pressure on density in the case of compressible flows is implicitly incorporated into the extended SIMPLE algorithm, which in the limit of incompressible flow reduces to its well‐known form. Special attention is paid to the numerical treatment of boundary conditions. The method is verified on a number of test cases (inviscid and viscous flows), and both the results and convergence properties compare favourably with other numerical results available in the literature.
Rutledge, Jeffrey; Sleicher, Charles A.
doi: 10.1002/fld.1650161203pmid: N/A
Interest in the use of supercomputers for the direct numerical calculation of turbulence prompts the development of efficient numerical techniques so that calculation at higher Reynolds numbers might be made. This paper presents an efficient pseudo‐spectral technique, similar to but different from others that have recently appeared, for the calculation of momentum and heat transfer to a constant‐property, turbulent fluid in a two‐dimensional channel with walls at different, uniform temperature. The code uses no empiricism, although periodic boundary conditions are used for fluctuating quantities in the streamwise and spanwise directions. Calculations were made for a Prandtl number of 0·72 and Reynolds number based on friction velocity and channel half‐height of 180 or 2800 based on channel half‐height and average velocity. Calculations of mean velocity profile, turbulence intensities, skewness, flatness, Reynolds stress and eddy diffusivity of heat near a wall compare favourably with experimental results. Representative contour plots of the temperature field near the wall and of the spanwise and streamwise two‐point velocity correlations are given. Deficiencies are that the calculation requires many hours on a fast computer with a large high‐speed memory and that the grid size in each direction for appropriate resolution is approximately proportional to the square of the Reynolds number and to the Prandtl number raised to some power greater than one.
doi: 10.1002/fld.1650161204pmid: N/A
A scheme for the numerical solution of the two‐dimensional (2D) Euler equations on unstructured triangular meshes has been developed. The basic first‐order scheme is a cell‐centred upwind finite‐volume scheme utilizing Roe's approximate Riemann solver. To obtain second‐order accuracy, a new gradient based on the weighted average of Barth and Jespersen's three‐point support gradient model is used to reconstruct the cell interface values. Characteristic variables in the direction of local pressure gradient are used in the limiter to minimize the numerical oscillation around solution discontinuities. An Approximate LU (ALU) factorization scheme originally developed for structured grid methods is adopted for implicit time integration and shows good convergence characterisitics in the test. To eliminate the data dependency which prohibits vectorization in the inversion process, a black‐gray‐white colouring and numbering technique on unstructured triangular meshes is developed for the ALU factorization scheme. This results in a high degree of vectorization of the final code. Numerical experiments on transonic Ringleb flow, transonic channel flow with circular bump, supersonic shock reflection flow and subsonic flow over multielement aerofoils are calculated to validate the methodology.
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