Reduced-basis output bound methods for parabolic problems

In this paper, we extend reduced-basis output bound methods developed earlier for elliptic problems, to problems described by ‘parameterized parabolic’ partial differential equations. The essential new ingredient and the novelty of this paper consist in the presence of time in the formulation and solution of the problem. First, without assuming a time discretization, a reduced-basis procedure is presented to ‘efficiently’ compute accurate approximations to the solution of the parabolic problem and ‘relevant’ outputs of interest. In addition, we develop an error estimation procedure to ‘a posteriori validate’ the accuracy of our output predictions. Second, using the discontinuous Galerkin method for the temporal discretization, the reduced-basis method and the output bound procedure are analysed for the semi-discrete case. In both cases the reduced-basis is constructed by taking ‘snapshots’ of the solution both in time and in the parameters: in that sense the method is close to Proper Orthogonal Decomposition (POD)

On Predicting The Turbulence-induced Secondary Flows Using Nonlinear K-∈ Models

Low turbulent Reynolds number direct simulation data are used to calculate the invariants of the Reynolds stress and the turbulent dissipation rate in a square duct. The results show that, depending on the region where the analysis is carried out, the turbulent flow field comes close to one-, two-, and three-component states. Modeling such flows - even at higher Reynolds numbers - will require models that can approach all three states. A number of related nonlinear k-∈ models are tested a priori using the direct simulation data. The numerical simulation using Reynolds averaged Navier-Stokes equations with these models was performed. Their ability to predict the secondary flows, with a low-Reynolds k-∈ model, cannot be gauged from realizability. © 1996 American Institute of Physics.8718561868Speziale, C.G., Analytical methods for the developments of Reynoldsstress closures in turbulence (1991) Annu. Rev. Fluid Mech., 23, p. 107Speziale, C.G., On non-linear k-l and k-∈ models of turbulence (1987) J. Fluid Mech., 178, p. 459Joseph, D.D., (1984) Fluid Dynamics of Viscoelastic Liquids, , Springer-Verlag, New YorkShih, T., Zhu, J., Lumley, J.L., (1993) A Realizable Reynolds Stress Algerbraic Equation Model, , NASA Tech. Memo TM-105993Rubinstein, R., Barton, J.M., Nonlinear Reynolds stress models and the renormalization group (1990) Phys. Fluids A, 8, p. 1472Demuren, A.O., Rodi, W., Calculation of turbulence-driven secondary motion in non-circular ducts (1984) J. Fluid Mech., 140, p. 189Gatski, T.B., Speziale, C.G., On explicit algebraic stress models for complex turbulent flows (1993) J. Fluid Mech., 254, p. 59Pope, S.B., A more general effective-viscosity hypothesis (1975) J. Fluid Mech., 72, p. 331Huser, A., Biringen, S., Hatay, F.F., Direct simulation of turbulent flow in a square duct: Reynolds-stress budgets (1994) Phys. Fluids, 6, p. 3144Gibson, M.M., Launder, B.E., Ground effects on pressure fluctuations in the atmospheric boundary layer (1979) J. Fluid Mech., 86, p. 491Cheesewright, R., McGrath, G., Petty, D.G., (1990) LDA Measurements of Turbulent Flow in a Duct of Square Cross Section at Low Reynolds Number, , Aeronautical Engineering Department, University of London, Report No. ER 101Huser, A., Biringen, S., Direct numerical simulation of turbulent flow in a square duct (1993) J. Fluid Mech., 257, p. 65Gavrilakis, S., Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct (1992) J. Fluid Mech., 244, p. 101Gavrilakis, S., (1993) Turbulent Velocity Structures Derived from POD Analyses, , Institute de Machines Hydrauliques et de Mécanique des Fluides, École Polytechnique Fédérale de Lausanne, Report No. T-93-30Antonia, R.A., Kim, J., Browne, L.W.B., Some characteristics of small-scale turbulence in turbulent duct flow (1991) J. Fluid Mech., 233, p. 369Bradshaw, P., Blair Perot, J., A note on turbulent energy dissipation in viscous wall region (1993) Phys. Fluids, 5, p. 3305Kim, J., Moin, P., Moser, R., Turbulent statistics in fully developed channel flow at low Reynolds number (1987) J. Fluid Mech., 177, p. 133Tennekes, H., Lumley, J.L., (1972) A First Course in Turbulence, , MIT Press, Cambridge, MALumley, J.L., Computational Modeling of Turbulent Flows (1978) Advances in Applied Mechanics, 18, p. 123. , Academic Press. New YorkGavrilakis, S., Large-scale structures in the turbulent flow near a right-angled corner (1994) 1st ERCOFTAC Workshop on Direct and Large-Eddy Simulation, , SurreyGessner, F.B., The origin of secondary flow in turbulent flow along a corner (1973) J. Fluid Mech., 58, p. 1Speziale, C.G., The dissipation rate correlation and turbulent secondary flows in noncircular ducts (1986) Trans. Am. Soc. Mech. Eng. J. Fluid Eng., 108, p. 118Durbin, P.A., Near-wall turbulence closure modeling without damping functions (1991) Theor. Comput. Fluid Dyn., 3, p. 1Rodi, W., Mansour, N.N., Low Reynolds number k-∈ modeling with the aid of direct simulation (1993) J. Fluid Mech., 250, p. 509Mompean, G., Three-equation turbulence model for prediction of the mean square temperature variance in grid-generated flows and round jets (1994) Int. J. Heat Mass Transfer, 37, p. 1165Chien, K.Y., Prediction of channel and boundary-layer flows with a low-Reynolds-number turbulence model (1982) AIAA J., 20, p. 33Lam, C.K.G., Bremhorst, K., A modified form of the k-∈ model predicting wall turbulence (1981) Trans. Am. Soc. Mech. Eng. J. Fluid. Eng., 103, p. 456Reynolds, W.C., Computation of turbulent flows (1976) Annu. Rev. Fluid Mech., 8, p. 183Lindberg, P.A., (1994), private communicationNisizima, S., A numerical study of turbulent square-duct flow using an anisotropic k-∈ model (1990) Theor. Comput. Fluid Dyn., 2, p. 61Launder, B.E., Tselepidakis, D.P., Contribution to the modelling of near-wall turbulence (1993) Turbulent Shear Flows 8, p. 81. , edited by F. Durst, R. Friedrich, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw, MunichNaimi, N., Gessner, F.B., A calculation method for developing turbulent flow in rectangular ducts of arbitrary aspect ratio (1995) J. Fluid Eng., 117, p. 249Launder, B.E., Reece, G.J., Rodi, W., Progress in the development of a Reynolds-stress turbulence closure (1975) J. Fluid Mech., 68, p. 537Hanjalic, K., Launder, B.E., A Reynolds stress model of turbulence and its application to thin shear flows (1972) J. Fluid Mech., 52, p. 60

Reduced-basis Output Bound Methods for Parametrised Partial Differential Equations

An efficient and reliable method for the prediction of outputs of interest of partial differential equations with affine parameter dependence is presented. To achieve efficiency we employ the reduced-basis method: a weighted residual Galerkin-type method, where the solution is projected onto low-dimensional spaces with certain problem-specific approximation properties. Reliability is obtained by a posteriori error estimation methods - relaxations of the standard error-residual equation that provide inexpensive but sharp and rigorous bounds for the error in outputs of interest. Special affine parameter dependence of the differential operator is exploited to develop a two-stage off-line/on-line blackbox computational procedure. In the on-line stage, for every new parameter value, we calculate the output of interest and an associated error bound. The computational complexity of the on-line stage of the procedure scales only with the dimension of the reduced-basis space and the parametric complexity of the partial differential operator; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control. The theory and corroborating numerical results are presented for: symmetric coercive problems (e.g. problems in conduction heat transfer), parabolic problems (e.g. unsteady heat transfer), noncoercive problems (e.g. the reduced-wave, or Helmholtz, equation), the Stokes problem (e.g flow of highly viscous fluids), and certain nonlinear equations (e.g. eigenvalue problems)

Zeolite mineralogy of the Cayo formation in Guayaquil, Ecuador

This work shows the presence of zeolites in the Cretaceous Cayo formation in Coastal Ecuador. In the area of Guayaquil the Cayo formation consist of marine pyroclastic flow deposits, associated fallout tuffs and epiclastic rocks. The main zeolites are Ca-heulandite (mean Si/Al: 3.30) and Ca-clinoptilolite (mean Si/Al: 4.35). Less common are laumontite, mordenite and analcime. Zeolites compose 10–60% of the rocks. The deposit is of great importance for Ecuador, considering its enormous zeolitised outcrop area (more than 10,000 km2

Study protocol for THINK : a multinational open-label phase I study to assess the safety and clinical activity of multiple administrations of NKR-2 in patients with different metastatic tumour types

Introduction: NKR-2 are autologous T cells genetically modified to express a chimeric antigen receptor (CAR) comprising a fusion of the natural killer group 2D (NKG2D) receptor with the CD3 zeta signalling domain, which associates with the adaptor molecule DNAX-activating protein of 10 kDa (DAP10) to provide co-stimulatory signal upon ligand binding. NKG2D binds eight different ligands expressed on the cell surface of many tumour cells and which are normally absent on non-neoplastic cells. In preclinical studies, NKR-2 demonstrated long-term antitumour activity towards a breadth of tumour indications, with maximum efficacy observed after multiple NKR-2 administrations. Importantly, NKR-2 targeted tumour cells and tumour neovasculature and the local tumour immunosuppressive microenvironment and this mechanism of action of NKR-2 was established in the absence of preconditioning. Methods and analysis: This open-label phase I study will assess the safety and clinical activity of NKR-2 treatment administered three times, with a 2-week interval between each administration in different tumour types. The study will contain two consecutive segments: a dose escalation phase followed by an expansion phase. The dose escalation study involves two arms, one in solid tumours (five specific indications) and one in haematological tumours (two specific indications) and will include three dose levels in each arm: 3x10(8), 1x10(9) and 3x10(9) NKR-2 per injection. On the identification of the recommended dose in the first segment, based on dose-limiting toxicity occurrences, the study will expand to seven different cohorts examining the seven different tumour types separately. Clinical responses will be determined according to standard Response Evaluation Criteria In Solid Tumors (RECIST) criteria for solid tumours or international working group response criteria in haematological tumours. Ethics approval and dissemination: Ethical approval has been obtained at all sites. Written informed consent will be taken from all participants. The results of this study will be disseminated through presentation at international scientific conferences and reported in peer-reviewed scientific journals

2006 stock assessment of North Sea plaice using a Bayesian catch-at-age model

Projectverslag over de verbetering van de toestandsbeoordeling van schol en tong. Problemen ronde de onzekerheid en bias in de toestandsbeoordeling en de gegevens die daar voor worden gebruikt zijn onderzocht. Dit verslag betreft de onzekerheid in de toestandsbeoordeling van Noordzee schol aan de hand van een Bayesiaans 'catch at age'- model (vangst per leeftijd)