By M. B. Giles (auth.), V. Venkatakrishnan, Manuel D. Salas, Sukumar R. Chakravarthy (eds.)
In this quantity, designed for engineers and scientists operating within the sector of Computational Fluid Dynamics (CFD), specialists provide checks of the functions of CFD, spotlight a few primary matters and obstacles, and suggest novel techniques to beat those difficulties. in addition they supply new avenues for study in conventional and non-traditional disciplines. The scope of the papers levels from the scholarly to the sensible.
This e-book is exotic from previous surveys by means of its emphasis at the difficulties dealing with CFD and by means of its specialise in non-traditional purposes of CFD innovations. there were a number of major advancements in CFD because the final workshop held in 1990 and this publication brings jointly the main advancements in one unified volume.
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EXAMPLES OF ERROR PROPAGATION FROM DISCONTINUITIES 31 For the time discretization, a Runge-Kutta method is used. It is well known (Shu & Osher, 1988), that the second order method for the convective terms gives a good performance with respect to shocks. Here hj - 1/ 2 is the numerical flux function described above, and we use A = ~t/ ~x. The source term is added such that it does not impose any additional stability restrictions and such that the accuracy is the same as for the convective method (two).
7--;';-,,----'-:--~, Fig. 3. Exact ZND profile. Fig. 4. Twice the resolution of Fig. 2. It is known that the traveling wave oscillates around this ZND profile as it propagates, thus this profile can only be considered as an exact solution on the average. Next we shall investigate how well we can capture the behavior of the peak pressure at the ZND spike. It is possible to increase the pressure in the left hand state, and thereby give the detonation wave a so called overdrive. For a detonation moving with speed s, the overdrive, I, is defined as I = (s/sCJ)2 where SCJ is the speed of a Chapman-Joguet 36 ..
67-81. O. , "On the stability definition of difference approximations for the initial boundary value problem," Appl. Num. , Vol. 12, 1993, pp. 213-227. , 1986, pp. 281-297. Lubich, C. , "On resolvent conditions and stability estimates," BIT, Vol. 31, 1991, pp. 293-313. J. , "On the use of stability regions in the numerical analysis of initial value problems," Math. , Vol. 57, No. 195, 1991, pp. 221-237. G. , "A 3D time-domain flutter prediction method for turbomachinery blades," In Proc. Int. Forum on Aeroelasticity and Structural Dynamics, Royal Aeronautical Society, Manchester, 1995.
Barriers and Challenges in Computational Fluid Dynamics by M. B. Giles (auth.), V. Venkatakrishnan, Manuel D. Salas, Sukumar R. Chakravarthy (eds.)