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

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W. LAYTON, I. STANCULESCU: Numerical Analysis of Approximate Deconvolution Models of Turbulence ✬ ✫ Numerical Analysis of Approximate Deconvolution Models of Turbulence William Layton ∗ and Iuliana Stanculescu † Abstract If the NSE are averaged with a local, spacial, convolution type filter the resulting system is not closed due to the term g ∗ (uu). A deconvolution operator GN is one which satisfies: u = GN(g ∗ u) + O(δ 2N+2 ) (0.1) where δ is the filter width. This yields the closure method: g ∗ (uu) = g ∗ (GN(g ∗ u)GN(g ∗ u)) + O(δ 2N+2 ) (0.2) We will review several solutions to the ill-possed deconvolution problem, present an ”optimal” deconvolution procedure and present numerical analysis and numerical experiments with it. ∗ Department of Mathematics, University of Pittsburgh, Pittsburgh, PA,15260, U.S.A.; email: wjl@pitt.edu, www.math.pitt.edu/˜wjl † Department of Mathematics, University of Pittsburgh, Pittsburgh, PA,15260, U.S.A.; email: ius1@pitt.edu, www.math.pitt.edu/˜ius1 Speaker: STANCULESCU, I. 18 BAIL 2006 1 ✩ ✪
H. WANG: A Component-Based Eulerian-Lagrangian Formulation for Compositional Flow in Porous Media ✬ ✫ A Component-Based Eulerian-Lagrangian Formulation for Compositional Flow in Porous Media Hong Wang ∗ Introduction Compositional models describe the simultaneous transport of multiple components flowing in coexisting phases in porous media [1, 4]. Because each component can transfer between different phases, the mass of each phase or a component within a particular phase is no longer conserved. Instead, the total mass of each component among all the phases must be conserved, leading to strongly coupled systems of transient nonlinear advection-diffusion equations. These equations are closely coupled to a set of constraining equations, which are strongly nonlinear, implicit functions of phase pressure, temperature, and composition. These equations need to be solved in all spatial cells at each iterative step of each time step via thermodynamic flash calculation. In industrial applications, upwind methods have commonly been used to stabilize the numerical approximations [1, 4]. However, these methods often generate excessive numerical dispersion and serious spurious effects due to grid orientation. Eulerian-Lagrangian methods symmetrize the transport equations and generate accurate numerical solutions even if large time steps and coarse spatial grids are used. They have demonstrated excellent performance in the numerical simulations of single-phase flow [3, 5] and immiscible two phase flow [2]. However, there exist serious mathematical and numerical difficulties in the development of Eulerian-Lagrangian methods for multiphase multicomponent compositional flow. We present a component-based Eulerian-Lagrangian formulation for compositional flow, which can be used by many Eulerian-Lagrangian methods. Numerical experiments We simulate the transport of Methane, Propane, and n-Hexane, flowing in coexisting liquid and vapor phases in a horizontal porous medium reservoir Ω = (0, 1000) × (0, 1000) ft 2 with a thickness of 1 ft over a time period of 20 years. An injection well is located at the upper-right corner of Ω with a volumetric injection rate of Q =15ft 3 /day. A production well is located at the lower-left corner with a production rate of Q = −15 ft 3 /day. The porosity φ = 0.1. The permeability is 60 md. The effect of capillary pressure is neglected. The relative permeability k r,l =(s l ) 2 and k r,v =(1−s l ) 2 . The initial reservoir pressure is 2100 psia and the reservoir temperature is 350 o K. The composition of the resident fluid is cMethane = 0.5, cP ropane =0.2, and cn−Hexane =0.3, which is in liquid phase at the given temperature and pressure. The composition of the injected fluid is ¯cMethane = 0.8, ¯cP ropane =0.15, and ¯cn−Hexane =0.05, which is in vapor phase. We use a uniform coarse spatial grid of ∆x =∆y= 25 ft. We use a time step of ∆tel =1 year for the Eulerian-Lagrangian method, and of ∆tup = 2 days for the upwind method that is the largest possible. In Figure 1(a) we present the plots of the overall mole fraction cMethane generated by the Eulerian-Lagrangian method at t = 5 and 20 years. In Figure 1(b) we present the plots of the normalized molar amount n v Methane = ρv s v c v Methane /(ρ cMethane), where ρ v and sv are density and saturation of the vapor phase and ρ is bulk molar density of the fluid mixture. Note that nv i represents the fraction of ci in the vapor phase. Thus, nv i = 1 or 0 indicates that component i stays in the vapor phase or liquid phase completely. 0
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 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 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 and 66: G.I. Shiskin, P. Hemker Robust Meth
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
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,
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