BAIL 2006 Book of Abstracts - Institut für Numerische und ...
BAIL 2006 Book of Abstracts - Institut für Numerische und ... BAIL 2006 Book of Abstracts - Institut für Numerische und ...
L. SAVIĆ, H. STEINRÜCK: Asymptotic Analysis of the mixed convection flow past a horizontal plate near the trailing edge ✬ ✫ of the plate ∆A interacts not only via the potential flow in the upper deck but also via the hydrostatic pressure in the main deck with the pressure ∆p in the lower deck. The interaction law for the pressure difference between the upper and lower side can be written in the form ∆A ′ (x (3) ) + √ 3ash(x (3) � ) x (3)� 1/3 = � � 0 1 ∆ˆp(ξ) + 2as|ξ| − π −∞ 1/3 x (3) dξ − − ξ 1 � ∞ As(ξ) − ash(ξ)|ξ| π −∞ 1/3 x (3) � dξ − ξ Where As(x (3) ) is the displacement thickness obtained for the classical trailing edge problem [3, 1] and x (3) is the coordinate in the lower, main and upper deck parallel to the plate. Here as is a constant and h(.) the heayside function. It turns out that the difference pressure ∆p has a discontinuity at the trailing edge. Thus new sub-layers (in the main and lower deck) to resolve this discontinuity are introduced. In the following table we give an overview of the most important layers needed for the asymptotic analysis. We introduce the following notation according to the stretching factor as a power of the Reynolds number: x (α) = Re α/8 x and y (β) = Re β/8 y. α β flow region 0 0 potential flow region 0 4 boundary layer and wake 3 3 upper deck 3 4 main deck 3 5 lower deck 4 4 main deck - trailing edge 5 5 lower deck - trailing edge Table 1: Scales of the different flow regions The new results of the analysis will be the local behavior of the difference pressure at the trailing edge. For both of the newly introduced sub-layers elliptic equations for the local pressure variation can be derived and will be solved numerically. Thus on triple deck scales there will be a flow around the trailing edge. Thus the perturbation of the classical triple deck problem by small buoyancy effects behaves quite differently than by small angles of attack [3]. References [1] K. Stewartson, On the flow near the trailing edge of flat plate, Mathematika, 16, 106-121 (1969). [2] A.F. Messiter, Boundary layer flow near the trailing edge of flat plate, SIAM J. Appl. Math., 18, 241-257, (1970). [3] R. Chow and R. E. Melnik, Numerical Solutions of Triple-Deck Equations for Laminar Trailing Edge Stall, Grumman Research Dept., Report RE-526J (1976). [4] W. Schneider and M. G. Wasel, Breakdown of the boundary-layer approximation for mixed convection flow above a horizontal plate, Int. J. Heat Transfer, 28, 2307-2313 (1985). [5] Lj. Savić and H. Steinrück, Mixed convection flow past a horizontal plate, Theoretical and Applied Mechanics, 32, 1-19 (2005). Speaker: STEINRÜCK, H. 42 BAIL 2006 2 ✩ ✪
G.I. Shiskin, P. Hemker Robust Methods for Problems with Layer Phenomena and Additional Singularities Speaker: The minisymposium will be concerned with singularly perturbed multiscale problems having additional singularities. A complicated geometry or unboundedness of the domain and/or the lack of sufficient smoothness (or compatibility) of the problem data may result in singular solutions that have their own specific scales, besides boundary/interior layers. We intend to examine techniques for constructing numerical methods that converge parameter-uniformly (in the maximum norm). The following research aspects will be also considered: (i) As a rule, such parameter-uniformly convergent numerical methods have too low order of uniform convergence, which restricts their applicability in practice. With this respect, methods how to increase the accuracy of parameter-uniformly convergent numerical methods will be considered. (ii) When standard numerical methods, for example, domain decomposition methods are used to find solutions of parameter-uniformly convergent discrete approximations, the decomposition errors of the discrete solutions and the number of iterations required to solve the discrete problem depend on the perturbation parameter and grow when it tends to zero. We will consider decomposition methods preserving the property of parameter-uniform convergence. Domain decomposition and local defect correction techniques allows us to reduce the construction of robust numerical methods for multiscale problems to locally robust methods for monoscale problems on the specific subdomains. Other aspects and applications will be also under consideration. Problems for partial differential equations with different types of boundary and interior layers will be considered. To construct special numerical methods, fitted meshes, which are a priori and a posteriori condensing in the layer regions, are used. • Deirdre Branley: A Schwarz method for a convection-diffusion problem with a corner singularity • Thorsten Linss: Layer-adapted meshes for time-dependent reaction-diffusion • Grigory I. Shishkin: Grid Approximation of Parabolic Equations with Nonsmooth
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- Page 17 and 18: Contents Greetings . . . . . . . .
- Page 19 and 20: CONTENTS S. HEMAVATHI, S. VALARMATH
- Page 21 and 22: CONTENTS G. LUBE: A stabilized fini
- Page 23: Plenary Presentations
- Page 26 and 27: P. HOUSTON: Discontinuous Galerkin
- Page 28 and 29: M. STYNES: Convection-diffusion pro
- Page 30 and 31: V. GRAVEMEIER, S. LENZ, W.A. WALL:
- Page 33: Minisymposia
- Page 36 and 37: R.K. DUNNE, E. O’RIORDAN, M.M. TU
- Page 38 and 39: G.I. SHISHKIN: A posteriori adapted
- Page 40 and 41: W. LAYTON, I. STANCULESCU: Numerica
- Page 42 and 43: H. WANG: A Component-Based Eulerian
- Page 44 and 45: R. HARTMANN: Discontinuous Galerkin
- Page 46 and 47: V. HEUVELINE: On a new refinement s
- Page 48 and 49: J.A. MACKENZIE, A. NICOLA: A Discon
- Page 50 and 51: R. SCHNEIDER, P. JIMACK: Anisotropi
- Page 53 and 54: Speaker: Debopam Das, Tapan Sengupt
- Page 55 and 56: M.H. BUSCHMANN, M. GAD-EL-HAK: Turb
- Page 57 and 58: A. NAYAK, D. DAS: Three-dimesnional
- Page 59 and 60: J. HUSSONG, N. BLEIER, V.V. RAM: Th
- Page 61 and 62: T.K. SENGUPTA, A. KAMESWARA RAO: Sp
- Page 63: L. SAVIĆ, H. STEINRÜCK: Asymptoti
- Page 67 and 68: D. BRANLEY, A.F. HEGARTY, H. PURTIL
- Page 69 and 70: T. LINSS, N. MADDEN: Layer-adapted
- Page 71 and 72: L.P. SHISHKINA, G.I. SHISHKIN: A Di
- Page 73 and 74: I.V. TSELISHCHEVA, G.I. SHISHKIN: D
- Page 75 and 76: S. HEMAVATHI, S. VALARMATHI: A para
- Page 77 and 78: J. Maubach, I, Tselishcheva Robust
- Page 79 and 80: M. ANTHONISSEN, I. SEDYKH, J. MAUBA
- Page 81 and 82: S. LI, L.P. SHISHKINA, G.I. SHISHKI
- Page 83 and 84: A.I. ZADORIN: Numerical Method for
- Page 85 and 86: P. ZEGELING: An Adaptive Grid Metho
- Page 87: Contributed Presentations
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- Page 92 and 93: TH. ALRUTZ, T. KNOPP: Near-wall gri
- Page 94 and 95: M. BAUSE: Aspects of SUPG/PSPG and
- Page 96 and 97: L. BOGUSLAWSKI: Sheare Stress Distr
- Page 98 and 99: A.CANGIANI, E.H.GEORGOULIS, M. JENS
- Page 100 and 101: C. CLAVERO, J.L. GRACIA, F. LISBONA
- Page 102 and 103: B. EISFELD: Computation of complex
- Page 104 and 105: A. FIROOZ, M. GADAMI: Turbulence Fl
- Page 106 and 107: A. FIROOZ, M. GADAMI: Turbulence Fl
- Page 108 and 109: S.A. GAPONOV, G.V. PETROV, B.V. SMO
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G.I. Shiskin, P. Hemker<br />
Robust Methods for Problems with Layer Phenomena and Additional Singularities<br />
Speaker:<br />
The minisymposium will be concerned with singularly perturbed<br />
multiscale problems having additional singularities. A complicated<br />
geometry or unbo<strong>und</strong>edness <strong>of</strong> the domain and/or the lack <strong>of</strong> sufficient<br />
smoothness (or compatibility) <strong>of</strong> the problem data may result in<br />
singular solutions that have their own specific scales, besides bo<strong>und</strong>ary/interior<br />
layers. We intend to examine techniques for constructing<br />
numerical methods that converge parameter-uniformly (in the maximum<br />
norm).<br />
The following research aspects will be also considered: (i) As a rule,<br />
such parameter-uniformly convergent numerical methods have too low<br />
order <strong>of</strong> uniform convergence, which restricts their applicability in<br />
practice. With this respect, methods how to increase the accuracy <strong>of</strong><br />
parameter-uniformly convergent numerical methods will be considered.<br />
(ii) When standard numerical methods, for example, domain decomposition<br />
methods are used to find solutions <strong>of</strong> parameter-uniformly convergent<br />
discrete approximations, the decomposition errors <strong>of</strong> the discrete<br />
solutions and the number <strong>of</strong> iterations required to solve the discrete<br />
problem depend on the perturbation parameter and grow when it tends<br />
to zero. We will consider decomposition methods preserving the property<br />
<strong>of</strong> parameter-uniform convergence. Domain decomposition and<br />
local defect correction techniques allows us to reduce the construction<br />
<strong>of</strong> robust numerical methods for multiscale problems to locally robust<br />
methods for monoscale problems on the specific subdomains. Other aspects<br />
and applications will be also <strong>und</strong>er consideration. Problems for<br />
partial differential equations with different types <strong>of</strong> bo<strong>und</strong>ary and interior<br />
layers will be considered. To construct special numerical methods,<br />
fitted meshes, which are a priori and a posteriori condensing in the layer<br />
regions, are used.<br />
• Deirdre Branley: A Schwarz method for a convection-diffusion problem with a<br />
corner singularity<br />
• Thorsten Linss: Layer-adapted meshes for time-dependent reaction-diffusion<br />
• Grigory I. Shishkin: Grid Approximation <strong>of</strong> Parabolic Equations with Nonsmooth
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