BAIL 2006 Book of Abstracts - Institut für Numerische und ...

More documents

Recommendations

Info

Initial Condition in the Presence of Boundary Layers of Different Types • Lidia P. Shishkina: A Difference Scheme of Improved Accuracy for a Quasilinear Singularly Perturbed Elliptic Convection-Diffusion Equation in the Case of the Third-Kind Boundary Condition • Irina V. Tselishcheva: Domain Decomposition Method for a Semilinear Singularly Perturbed Elliptic Convection-Diffusion Equation with Concentrated Sources • S. Valarmathi: A parameter-uniform numerical method for a system of singularly perturbed ordinary differential equations
D. BRANLEY, A.F. HEGARTY, H. PURTILL, G.I. SHISHKIN: A Schwarz method for a convection-diffusion problem with a corner singularity ✬ ✫ A Schwarz method for a convection-diffusion problem with a corner singularity. ∗ Deirdre Branley 1 , Alan F. Hegarty 1 , Helen Purtill 1 and Grigory I. Shishkin 2 . 1 Department of Mathematics and Statistics, University of Limerick, Plassey, Limerick, Ireland. deirdre.branley@ul.ie, alan.hegarty@ul.ie, helen.purtill@ul.ie, 2 Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences 16 S. Kovalevskaya Street, Ekaterinburg 620219, Russia shishkin@imm.uran.ru We are concerned with two dimensional steady state convection-diffusion problems with singular outflow boundary conditions. It is well known that, where the boundary conditions are sufficiently smooth and compatible, such problems can be solved with uniform accuracy with respect to the small parameter ε using a standard finite difference operator on special piece-wise uniform meshes [1, 2]. Where the outflow boundary data are only weakly regular and compatible, parameter-uniform solutions may also be obtained by this method [2]. However, orders of convergence are relatively small and pointwise errors relatively large in this case. Numerical methods for singularly perturbed problems comprising domain decomposition and Schwarz iterative technique have been examined by a number of authors, for example in [1], [3], [4] and [5]. In particular, MacMullen et al. [5] constructed a parameter-uniform Schwarz method for singularly perturbed linear convection-diffusion problems in two dimensions with sufficiently smooth and compatible boundary data. We examine experimentally the performance of such methods extended to the class of singularly perturbed convection-diffusion problems with more general boundary conditions described below. We consider problems of the form Lu ≡ ε∆uε + a(x, y).∇u = f in a domain Ω, the unit square, with Dirichlet boundary conditions, where all components of a are strictly positive. Such problems exhibit regular layers along the outflow boundaries, as well as a corner boundary layer at the outflow boundary corner. We deal with outflow boundary conditions, where the first derivatives are not compatible at the outflow boundary corner. We implement domain decomposition methods to isolate the neighbourhood of the singularity, along with a Schwarz iterative technique, with the aim of developing a Schwarz method to produce parameter-uniformly accurate solutions on the whole domain in the oresence of such a singularity. References [1] J.J.H. Miller, E.O’Riordan, G.I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems, World Scientific, Singapore, 1996. [2] P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O’Riordan, G.I. Shishkin, Robust Computational Techniques for Boundary Layers, Chapman & Hall, CRC, Boca Raton, FL, 2000. [3] J.J.H. Miller, E. O’Riordan, G.I. Shishkin, S. Wang, A parameter-uniform Schwarz method for a singularly-perturbed reaction-diffusion problem with an interior layer, Appl. Num. Math., 35 (2000), 323-337. ∗ This research was supported in part by the Irish Research Council for Science, Engineering and Technology and by the Russian Foundation for Basic Research under grant No. 04-01-00578. 1 Speaker: BRANLEY, D. 45 BAIL 2006 ✩ ✪
Page 1:
BAIL 2006 International Conference
Page 5 and 6:
Plenary Session 1 Session 2 Session
Page 7 and 8:
Room School-Lab (SL) Room MPI Sessi
Page 9 and 10:
Room School-Lab (SL) Room MPI Tuesd
Page 11 and 12:
Page 13 and 14:
Page 15 and 16: Room School-Lab (SL) Room MPI Minis
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 and 64: L. SAVIĆ, H. STEINRÜCK: Asymptoti
Page 65: G.I. Shiskin, P. Hemker Robust Meth
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
Page 90 and 91: F. ALIZARD, J.-CH. ROBINET: Two-dim
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
Page 110 and 111: M. HAMOUDA, R. TEMAM: Boundary laye
Page 112 and 113: M. HAMOUDA, R. TEMAM: Boundary laye
Page 114 and 115: M. HÖLLING, H. HERWIG: Computation
Page 116 and 117:
A.-M. IL’IN, B.I. SULEIMANOV: The
Page 118 and 119:
W.S. ISLAM, V.R. RAGHAVAN: Numerica
Page 120 and 121:
D. KACHUMA, I. SOBEY: Fast waves du
Page 122 and 123:
A. KAUSHIK, K.K. SHARMA: A Robust N
Page 124 and 125:
P. KNOBLOCH: On methods diminishing
Page 126 and 127:
T. KNOPP: Model-consistent universa
Page 128 and 129:
J.-S. LEU, J.-Y. JANG, Y.-C. CHOU:
Page 130 and 131:
V.D. LISEYKIN, Y.V. LIKHANOVA, D.V.
Page 132 and 133:
G. LUBE: A stabilized finite elemen
Page 134 and 135:
H. LÜDEKE: Detached Eddy Simulatio
Page 136 and 137:
K. MANSOUR: Boundary Layer Solution
Page 138 and 139:
J. MAUSS, J. COUSTEIX: Global Inter
Page 140 and 141:
O. MIERKA, D. KUZMIN: On the implem
Page 142 and 143:
K. MORINISHI: Rarefied Gas Boundary
Page 144 and 145:
A. NASTASE: Qualitative Analysis of
Page 146 and 147:
F. NATAF, G. RAPIN: Application of
Page 148 and 149:
N. NEUSS: Numerical approximation o
Page 150 and 151:
M.A. OLSHANSKII: An Augmented Lagra
Page 152 and 153:
N. PARUMASUR, J. BANASIAK, J.M. KOZ
Page 154 and 155:
B. RASUO: On Boundary Layer Control
Page 156 and 157:
H.-G. ROOS: A Comparison of Stabili
Page 158 and 159:
B. SCHEICHL, A. KLUWICK: On Turbule
Page 160 and 161:
O. SHISHKINA, C. WAGNER: Boundary a
Page 162 and 163:
M. STYNES, L. TOBISKA: Using rectan
Page 164 and 165:
P. SVÁ ˘CEK: Numerical Approximat
Page 166 and 167:
N.V. TARASOVA: Full asymptotic anal
Page 168 and 169:
C.H. TAI, C.-Y. CHAO, J.-C. LEONG,
Page 170 and 171:
H. TIAN: Uniformly Convergent Numer
Page 172 and 173:
ABOUTUNSTEADYBOUNDARYLAYERONADIHEDR
Page 174 and 175:
A.E.P. VELDMANN: High-order symmetr
Page 176 and 177:
Z.-H. YANG, Y.-Z. LI, Y. ZHU: Appli
Page 178 and 179:
Q. YE: Numerical simulation of turb
Page 181:
Participants
Page 184 and 185:
Mrs.Maragatha Meenakshi Ponnusamy P
Page 186 and 187:
Authors Alizard, F., 67 Alrutz, Th,
show all

BAIL 2006 Book of Abstracts - Institut für Numerische und ...

Create successful ePaper yourself

Delete template?

Save as template?