By Carlo Cercignani (auth.), Prof. Dr. Vinicio Boffi, Prof. Dr. Helmut Neunzert (eds.)
Read or Download Proceedings of the Third German-Italian Symposium Applications of Mathematics in Industry and Technology: June 18–22, 1988 Siena (Under the auspices of the C.N.R. — D.F.G. agreement) PDF
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Extra info for Proceedings of the Third German-Italian Symposium Applications of Mathematics in Industry and Technology: June 18–22, 1988 Siena (Under the auspices of the C.N.R. — D.F.G. agreement)
And we denote by cI> the (0) (it is known that space of functions defined on r which are the traces of functions of Hd ao . . =1- Hd HI/2 ... ), see [LM]). 00 (~. 2) is equivalent to find U E HJ(n) so that", = ula;. i=l •... 5) Ui =0 on ri on 1 SiS M - 1 an n a~ 1 SiS M where lPi is any HI-extension of IP to ~ vanishing on an n a~. 8) where Vi is the outward unit vector to ~. 6). The approximation of such a sequence in the frame of a finite dimensional method (finite elements, spectral, ... 1).
19) -lluN + QOUN = I at each point of EN internal to O. 19) is the following. One looks for polynomials UN,i e PN(~), i=l, ... 8) hold. 8) need only be satisfied at the collocation points induced on the interface boundaries. Though the multidomain spectral solution fails to be equivalent to the single-domain one anymore (as apposite to the finite element case), it neverthless enjoyes the same properties of stability and asymptotic accuracy. 6), then the overall spectral multidomain method can be fonnally interpreted variationalwise (as for the finite element case).
Numerical Damping In computing flows with higher Reynolds-numbers a certain amount of numerical damping is necessary in order to suppress spurious oscillations in the solutions. Traditional techniques are the "(spatial) upwind discretization" of the transport terms or the use of "artificial viscosity". Both methods (in their original form) are only first order accurate and tend to smear out sharp boundary layers and interior "shocks". Below, two more sophisticated approaches are described which may prove to even manage the stable transition for Re ~ 00 • a) Backward characteristic method: This approach is also known as "transport-diffusion algorithm" (Pironneau ).
Proceedings of the Third German-Italian Symposium Applications of Mathematics in Industry and Technology: June 18–22, 1988 Siena (Under the auspices of the C.N.R. — D.F.G. agreement) by Carlo Cercignani (auth.), Prof. Dr. Vinicio Boffi, Prof. Dr. Helmut Neunzert (eds.)