By W.F. Jr. Ballhaus, M.Y. Hussaini
This specified quantity comprises the court cases of the Symposium hung on June 26, 1988 at Williamsburg, Virginia, in honor of Professor Maurice Holt at the social gathering of his 70th birthday. there have been greater than dozen contributors from 11 international locations. They have been both his prior scholars or his colleagues whose careers crossed his sooner or later. The twenty-one papers during this quantity are the written model of the displays at this Symposium; they're often within the region of computational fluid dynamics (CFD), a box within which Professor Holt is a pioneer. those papers disguise just about all points of CFD together with numerical research, symbolic research, and grid genera tion. They disguise various issues akin to complicated plume flows, surprise waves and surprise focussing, coronary flow, loose floor flows, direct containment warmth ing in nuclear reactors, and uranium enrichment. there's additionally an editorial at the development and destiny instructions in CFD by means of one of many precise specialists during this zone. as well as CFD papers, there's an experimental paper at the movement of round glass beads in airflow in a ninety° vertical-to-horizontal bend, in addition to a ancient paper on seventy years of fluid dynamic learn at Aerodynamisches Institut at Aachen. it's worthy mentioning that there's additionally an editorial at the uncomplicated fluid idea via a world-renowned authority on continuum mechanics.
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A schematic of the situation is shown in figure (1) where typical cell centers and volumes are shown, and this figure will be utilized to illustrate the problem and a solution. The general problem is that all the independent variables become coupled to the mesh singularity, and it is more difficult to form efficient implicit finite difference or finite volumes equations from the basic laws. Also, the use of the popular factored methods becomes very difficult, and one is forced to use explicit techniques which can be inefficient for the solution of the Navier-Stokes equations.
Figures 3 d, e, and f give the axial distributions of Mach number, density, and temperature. The results of calculations for the case 3 are given in Figure 4 in terms of pressure and density contours. Again the existence of strong and weak shocks is clearly visible. 4. Concluding Remarks Through these preliminary calculations, we have gained confidence on the use of the NND scheme suggested here. The scheme possesses good stability characteristics and converged accuracy and this is essential to any high shock resolution scheme.
00 'IIr rH . ll Oil> '100 t .. • O. j / . 00 4. 00 I . CO 1 . 00 IO ,(J;I 12' ,\10 (b) Axial density distribution (a) Axial pressure distribution 54 I ,.. 00 /l . ,: :"'-- (d) axial mach number distribution (c) axial temperature distribution Comparison between the present calculated results of axial pressure, density, temperature and Mach number distributions and those obtained in ref. M_ _ _ _ _ _ _ _ _ _r-_ _ no . ~ . 2 . r~f.