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Two Powerful Theorems in Clifford Analysis

Fred Brackx

AIP Conf. Proc. 1281, pp. 3-7; doi:http://dx.doi.org/10.1063/1.3498489 (5 pages)

Online Publication Date: 17 September 2010

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Two useful theorems in Euclidean and Hermitean Clifford analysis are discussed: the Fischer decomposition and the Cauchy‐Kovalevskaya extension.

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02.20.Tw	Infinite-dimensional Lie groups
02.30.Vv	Operational calculus
02.30.Fn	Several complex variables and analytic spaces
02.30.Sa	Functional analysis

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Numerical Energy Preservation of General Hamiltonian Systems

Ernst Hairer

AIP Conf. Proc. 1281, pp. 8-10; doi:http://dx.doi.org/10.1063/1.3498634 (3 pages)

Online Publication Date: 17 September 2010

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A class of partitioned methods, combining collocation with averaged vector fields, is presented. The methods exactly preserve energy for general Hamiltonian systems, they are invariant with respect to linear transformations, and they can be of arbitrarily high order.

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02.60.Lj	Ordinary and partial differential equations; boundary value problems
02.10.Yn	Matrix theory
02.30.Sa	Functional analysis
02.30.Ik	Integrable systems

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Exponential Time Integration of Evolution Equations

Alexander Ostermann

AIP Conf. Proc. 1281, pp. 11-14; doi:http://dx.doi.org/10.1063/1.3497888 (4 pages)

Online Publication Date: 17 September 2010

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The time discretization of semilinear parabolic problems requires integrators that treat the stiff part in an implicit way. Traditionally, linearly implicit methods had been used for this purpose. More recently, exponential integrators proved to be competitive for this kind of problems. In this short note, we will put emphasis on methods that linearize the problem along the numerical trajectory. We will show that the error analysis can be carried out in the framework of logarithmic matrix norms which gives rise to convergence results that are independent of the spatial grid size.

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02.30.Rz	Integral equations
02.10.Yn	Matrix theory
02.30.Sa	Functional analysis

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Efficient Solution of Fluid‐Structure Interaction Problems in Computational Hemodynamics

Alfio Quarteroni, Paolo Crosetto, and Simone Deparis

AIP Conf. Proc. 1281, pp. 15-18; doi:http://dx.doi.org/10.1063/1.3498124 (4 pages)

Online Publication Date: 17 September 2010

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87.19.U-	Hemodynamics
87.19.Wx	Pneumodyamics, respiration
83.60.Fg	Shear rate dependent viscosity
02.10.Yn	Matrix theory

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Ensemble Kalman and H_∞ Filters

Sebastian Reich

AIP Conf. Proc. 1281, pp. 19-22; doi:http://dx.doi.org/10.1063/1.3498332 (4 pages)

Online Publication Date: 17 September 2010

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The ensemble Kalman filter has become a popular method for nonlinear data assimilation. Standard ensemble Kalman filter implementations need to be modified to avoid filter divergence due to model and statistical errors. In this communication, we discuss ensemble inflation within the continuous ensemble Kalman filter approach and its link to H_∞ filtering.

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02.30.Hq	Ordinary differential equations
02.10.Yn	Matrix theory
42.79.Ci	Filters, zone plates, and polarizers
02.60.Cb	Numerical simulation; solution of equations

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The Acceptance Probability of the Hybrid Monte Carlo Method in High‐Dimensional Problems

A. Beskos, N. S. Pillai, G. O. Roberts, J. M. Sanz‐Serna, and A. M. Stuart

AIP Conf. Proc. 1281, pp. 23-26; doi:http://dx.doi.org/10.1063/1.3498436 (4 pages)

Online Publication Date: 17 September 2010

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We investigate the properties of the Hybrid Monte‐Carlo algorithm in high dimensions. In the simplified scenario of independent, identically distributed components, we prove that, to obtain an G(1) acceptance probability as the dimension d of the state space tends to ∞, the Verlet∕leap‐frog step‐size h should be scaled as h = ℓ×d^−1/4. We also identify analytically the asymptotically optimal acceptance probability, which turns out to be 0.651 (with three decimal places); this is the choice that optimally balances the cost of generating a proposal, which decreases as ℓ increases, against the cost related to the average number of proposals required to obtain acceptance, which increases as ℓ increases.

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02.50.Cw	Probability theory
02.70.Uu	Applications of Monte Carlo methods
02.30.Sa	Functional analysis
02.30.Jr	Partial differential equations

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Fast N‐Body Methods: Why, What, and Which

Robert D. Skeel

AIP Conf. Proc. 1281, pp. 27-30; doi:http://dx.doi.org/10.1063/1.3498450 (4 pages)

Online Publication Date: 17 September 2010

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Why do they matter? Applications abound, even to the extent that fast N‐body methods merit a place in the core of numerical analysis. Why are they fast? The basis for all fast N‐body solvers is (i) a separable approximation for a pairwise interaction kernel and (ii) exploitation of the associativity (and distributivity) of linear transformations. What are the various N‐body methods? Kernel splitting and hierarchical clustering are the two fundamental paradigms. Which is the best N‐body method? For molecular biophysics and structural biology, multilevel summation is suggested.

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02.60.Lj	Ordinary and partial differential equations; boundary value problems
33.15.Kr	Electric and magnetic moments (and derivatives), polarizability, and magnetic susceptibility
02.30.Tb	Operator theory
02.30.Jr	Partial differential equations

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Solving Differential Equations in R

Karline Soetaert, Filip Meysman, and Thomas Petzoldt

AIP Conf. Proc. 1281, pp. 31-34; doi:http://dx.doi.org/10.1063/1.3498463 (4 pages)

Online Publication Date: 17 September 2010

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The open‐source software R has become one of the most widely used systems for statistical data analysis and for making graphs, but it is also well suited for other disciplines in scientific computing. One of the fields where considerable progress has been made is the solution of differential equations. Here we first give an overview of the types of differential equations that R can solve, and then demonstrate how to use R for solving a 2‐Dimensional partial differential equation.

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02.30.Jr	Partial differential equations
02.30.Hq	Ordinary differential equations
02.10.Yn	Matrix theory
07.05.Bx	Computer systems: hardware, operating systems, computer languages, and utilities

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Remarks on the Complexity of the Schrödinger Equation

Harry Yserentant

AIP Conf. Proc. 1281, pp. 35-37; doi:http://dx.doi.org/10.1063/1.3498475 (3 pages)

Online Publication Date: 17 September 2010

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The solutions of the electronic Schrödinger equation are high‐dimensional objects depending on 3N variables, three for each of the N electrons under consideration. It is therefore rather surprising that simple expansions of the electronic wave functions can be constructed whose convergence rate, measured in terms of the number of determinants involved, is independent of the number of electrons and does not fall below that for a two‐ or even that for a one‐electron system approximated in the same way. In this sense, the complexity of the electronic Schrödinger equation does not exceed that of an equation in three space dimensions. A short report on these developments is given.

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03.65.Ge	Solutions of wave equations: bound states
02.30.Fn	Several complex variables and analytic spaces
02.30.Tb	Operator theory
31.15.E-	Density-functional theory

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SYMPOSIUM: 5th Symposium on Numerical Analysis of Fluid Flow and Heat Transfer

Pawel Kosinski

AIP Conf. Proc. 1281, pp. 38-38; doi:http://dx.doi.org/10.1063/1.3498484 (1 page)

Online Publication Date: 17 September 2010

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02.60.Cb	Numerical simulation; solution of equations
47.75.+f	Relativistic fluid dynamics
44.05.+e	Analytical and numerical techniques
47.55.pb	Thermal convection

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Turbulence Model Study for Unsteady Cavitating Flows

Jean Decaix and Eric Goncalvès

AIP Conf. Proc. 1281, pp. 39-42; doi:http://dx.doi.org/10.1063/1.3498488 (4 pages)

Online Publication Date: 17 September 2010

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A compressible, multiphase, one‐fluid RANS solver was developed to study cavitating flows. The interaction between turbulence and two‐phase structures is complex and not well known. This constitutes a critical point to accurately simulate unsteady behaviours of cavity sheets. In the present study, different transport‐equation turbulence models are investigated. Numerical results are given for a Venturi geometry and comparisons are made with experimental data.

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47.55.dp	Cavitation and boiling
47.27.E-	Turbulence simulation and modeling
47.55.nb	Capillary and thermocapillary flows
47.40.Dc	General subsonic flows

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The Effects of a Constant Bias Force on the Dynamics of a Periodically Forced Spherical Particle in a Newtonian Fluid at Low Reynolds Numbers

K. Madhukar, T. R. Ramamohan, and I. S. Shivakumara

AIP Conf. Proc. 1281, pp. 43-46; doi:http://dx.doi.org/10.1063/1.3498501 (4 pages)

Online Publication Date: 17 September 2010

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We make use of the formulation developed by Lovalenti and Brady [1] for the hydrodynamic force acting upon a spherical particle undergoing arbitrary time dependent motion in an arbitrary time dependent uniform flow field at low Reynolds numbers, to derive an expression for the effects of a constant bias force acting on a periodically forced rigid spherical particle in a Newtonian fluid. We use Newton’s second law to relate the total force acting on the particle to the motion of the particle. The total force is given by: Total force = F^ext+^FH, where, F^ext is the external force inclusive of both the periodic force and the constant bias force. F^H is the hydrodynamic force derived by Lovalenti and Brady [1] including both unsteady and convective inertia. The equation derived contains a nonlinear history term and is nonlinear. This equation is solved numerically using an adaptive step size Runge−Kutta scheme. We obtain several phase plots (plots between particle displacement and particle velocity), which show the effects of low Reynolds numbers, the periodic force and the effects of the constant bias force on the particle motion. It is observed that at low magnitudes of the periodic forcing the external constant force dominates and the particle moves along the direction of the external constant force. As we increase the magnitude of the periodic forcing, the periodic force is seen to dominate and the particle is seen to oscillate along a mean position with a slight drift along the direction of the periodic force and the external constant force, when they are imposed in the same direction. However the motion of the particle becomes more complicated when the directions of the periodic forcing and external constant force are opposite to each other. We also observe a reflection in phase space when the directions of both the forces are reversed. The phase plots typically are of a half sinusoidal, sinusoidal and a coiled (solenoidal) pattern. These plots include the effects of both periodic force and the constant bias force. As the Reynolds numbers increases the drift of the particle reduces, which indicates the effects of inertia. We present a preliminary analysis of the dynamics in this paper.

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47.15.G-	Low-Reynolds-number (creeping) flows
47.85.Dh	Hydrodynamics, hydraulics, hydrostatics
02.60.Cb	Numerical simulation; solution of equations

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Fully Implicit Coupling for Non‐Matching Grids

M. Darwish, W. Geahchan, and F. Moukalled

AIP Conf. Proc. 1281, pp. 47-50; doi:http://dx.doi.org/10.1063/1.3498513 (4 pages)

Online Publication Date: 17 September 2010

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The efficient solution of flow problems depends on quality meshing the computational domain. In problems with complex geometries or having a large spectrum of time or length scale, the meshing process greatly benefits from the subdivision of the original geometry (domain decomposition) into sub‐domains, that are meshed independently with suitable elements and mesh density. Procedures for solving multiblock meshes can be of two types explicit or implicit. In either case it is essential that the fluxes at the regions interfaces be conserved. In this paper an efficient fully implicit multi‐region coupling discretization procedure is presented. A test problem involving 1, 2, 4 and 8 blocks with a mesh size of about 100,000 elements, is solved to show that the coupling procedure yields the same number of iteration for multiple block as for a single block.

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47.11.Df	Finite volume methods
45.70.Vn	Granular models of complex systems; traffic flow
02.60.Ed	Interpolation; curve fitting

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Numerical Simulation of Free Convection in a Porous Annulus of Rhombic Cross Section

F. Moukalled and M. Darwish

AIP Conf. Proc. 1281, pp. 51-54; doi:http://dx.doi.org/10.1063/1.3498526 (4 pages)

Online Publication Date: 17 September 2010

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Numerical solutions are presented for laminar natural convection heat transfer in a fluid saturated porous enclosure between two isothermal concentric cylinders of rhombic cross sections. Simulations are conducted for four values of Raleigh number (Ra = 104, 105, 106, and 107), three values of Darcy number (Da = 10−1, 10‐3, and 10‐5), and four values of enclosure gap (Eg = 0.875, 0.75, 0.5, and 0.25). The porosity and Prandtl number are assigned the values of 0.6 and 0.7, respectively. The results are reported in terms of streamlines, isotherms, and average Nusselt number values. The flow strength and convection heat transfer increase with an increase in Ra, Da, and∕or Eg . At low Eg values, the flow in the enclosure is weak and convection heat transfer is low even though the total heat transfer is higher than at higher Eg values due to an increase in conduction heat transfer. Furthermore, predictions indicate the presence of a critical Ra number below which conduction is the dominant heat transfer mode. Convection starts affecting the total heat transfer at Ra values higher than the critical one. The critical Ra decreases with increasing Da, and increases with decreasing Eg.

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44.25.+f	Natural convection
44.40.+a	Thermal radiation
44.30.+v	Heat flow in porous media

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Numerical Simulation of Channel Flow with Fluid Injection Using MILES Approach

Magali Dupuy, Emmanuel Radenac, and Yves Fabignon

AIP Conf. Proc. 1281, pp. 55-58; doi:http://dx.doi.org/10.1063/1.3498537 (4 pages)

Online Publication Date: 17 September 2010

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A numerical simulation of the unsteady flowfield in a channel with fluid injection through a porous wall is performed using MILES approach. Different states in such flow evolution are identified. Near the head end, the flow is laminar. At the middle of the channel, turbulence appears and then develops until the channel exit. The perturbation necessary to launch the transition process for the MILES simulation is obtained thanks to the time integration scheme used with a CFL value large enough to introduce a numerical destabilization into the flowfield. Computed results are compared with existing experimental data and with a two‐dimensional RANS k‐l simulation, including mean velocity and turbulent profiles. Analysis of the results shows that mean flow properties and transition process are reproduced in good agreement with the experimental data. The three‐dimensional MILES simulation gives more reliable results at the beginning of the transition process compared with the two‐dimensional RANS computation.

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02.60.Cb	Numerical simulation; solution of equations
47.27.Cn	Transition to turbulence
47.56.+r	Flows through porous media
47.10.ad	Navier-Stokes equations

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Numerical Analysis of the Unsteady Rotor‐Stator Interaction in a Low Pressure Centrifugal Compressor by Using Adamczyk and Proper Orthogonal Decompositions

Mihai Leonida Niculescu and Sterian Dănăilă

AIP Conf. Proc. 1281, pp. 59-62; doi:http://dx.doi.org/10.1063/1.3498548 (4 pages)

Online Publication Date: 17 September 2010

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The aim of this paper is to study the unsteady rotor‐stator interaction in a low pressure centrifugal compressor using the finite volume method to solve the Unsteady Reynolds‐Averaged Navier‐Stokes (URANS) equations. In order to understand better, the rotor‐stator interaction, the unsteady results are processed using both Adamczyk decomposition and Proper Orthogonal Decomposition (POD). Both decompositions show the behavior of unsteady rotor‐stator interaction but the POD modes also show the numerical errors.

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47.27.E-	Turbulence simulation and modeling
47.32.C-	Vortex dynamics
47.11.St	Multi-scale methods
05.45.Pq	Numerical simulations of chaotic systems

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Numerical Simulation of Airfoil Vibrations Induced by Compressible Flow

Miloslav Feistauer, Václav Kučera, and Petr Šimánek

AIP Conf. Proc. 1281, pp. 63-66; doi:http://dx.doi.org/10.1063/1.3498558 (4 pages)

Online Publication Date: 17 September 2010

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The paper is concerned with the numerical solution of interaction of compressible flow and a vibrating airfoil with two degrees of freedom, which can rotate around an elastic axis and oscillate in the vertical direction. Compressible flow is described by the Euler or Navier‐Stokes equations written in the ALE form. This system is discretized by the semi‐implicit discontinuous Galerkin finite element method (DGFEM) and coupled with the solution of ordinary differential equations describing the airfoil motion. Computational results showing the flow induced airfoil vibrations are presented.

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47.40.Dc	General subsonic flows
47.10.ad	Navier-Stokes equations
47.11.Fg	Finite element methods
02.30.Hq	Ordinary differential equations
02.70.Dh	Finite-element and Galerkin methods

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Analysis of the Internal Ventilation for a Motorcycle Helmet

Flavio Cimolin

AIP Conf. Proc. 1281, pp. 67-70; doi:http://dx.doi.org/10.1063/1.3498569 (4 pages)

Online Publication Date: 17 September 2010

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This work deals with a methodology for the numerical simulation of the inner ventilation of a motorcycle helmet, based on a thermo‐fluid‐dynamic model capable of describing evaporation‐related heat transfer phenomena. The final purpose is the enhancment of the comfort of the rider and ultimately his safety. The fluid‐dynamic problem concerns the modelization of the filtration of a flow over a porous medium, while the (decoupled) thermodynamic model is associated with the heat and sweat removal by means of the airflow. The latter is based on a set of evolution equations for the three scalar unknowns temperature, absolute humidity and sweat. Simulations on a sample 2D problem show the applicability of the methodology, highlighting the implicitly‐defined free boundary separating the wet and dry regions as well as the zones where sweat accumulates.

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47.10.Fg	Dynamical systems methods
44.15.+a	Channel and internal heat flow
47.56.+r	Flows through porous media
47.11.Fg	Finite element methods

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Towards a Formally Path‐Consistent Roe Scheme for the Six‐Equation Two‐Fluid Model

Alexandre Morin, Tore Flåtten, and Svend T. Munkejord

AIP Conf. Proc. 1281, pp. 71-74; doi:http://dx.doi.org/10.1063/1.3498580 (4 pages)

Online Publication Date: 17 September 2010

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We start from the most common formulation of the six‐equation two‐fluid model, from which we remove the non‐conservative temporal term using an equivalent formulation derived in the literature. We derive a partially analytical, formally path‐consistent Roe scheme, using the flux‐splitting method.

We first expose the model in detail, and split the flux into a convective part, a pressure part, and a non‐conservative part. Then we derive an analytical Jacobian matrix of the fluxes, which allows the model to be written in quasilinear form. Finally, we explain the approach used to express formulas for the Roe‐averaging of the variables. Only a simplified Roe‐condition on the pressure remains. It can be fulfilled numerically, given any equation of state. In the present article, we do not show the full results, but rather explain the approach. The full results will be explained at the conference.

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47.55.dr	Interactions with surfaces
47.40.Dc	General subsonic flows
02.30.Jr	Partial differential equations

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Analytical‐Numerical Solution of a H₂/N₂ Flame Using the Reichardt’s Equation

A. L. De Bortoli

AIP Conf. Proc. 1281, pp. 75-78; doi:http://dx.doi.org/10.1063/1.3498593 (4 pages)

Online Publication Date: 17 September 2010

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The present work develops a method for the solution of a nonpremixed jet flame based on the Reichardt’s equation for the mixture fraction and on the Burke‐Schumann for the chemistry. The developed method allows decreasing the complexity to obtain the solution of low and moderate Reynolds jet diffusion flames. Numerical tests are carried out for a 50‐50% H₂/N₂ flame and the results are in agreement with the experimental data.

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47.27.tb	Turbulent diffusion
47.70.Pq	Flames; combustion
02.30.Jr	Partial differential equations
47.85.Dh	Hydrodynamics, hydraulics, hydrostatics

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On Analysis of Stationary Viscous Incompressible Flow Through a Radial Blade Machine

Tomáš Neustupa

AIP Conf. Proc. 1281, pp. 79-82; doi:http://dx.doi.org/10.1063/1.3498605 (4 pages)

Online Publication Date: 17 September 2010

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The paper is concerned with the analysis of the two dimensional model of incompressible, viscous, stationary flow through a radial blade machine. This type of turbine is sometimes called Kaplan’s turbine. In the technical area the use is either to force some regular characteristic to the flow of the medium going through the turbine (flow of melted iron, air conditioning) or to gain some energy from the flowing medium (water). The inflow and outflow part of boundary are in general a concentric circles. The larger one represents an inflow part of boundary the smaller one the outflow part of boundary. Between them are regularly spaced the blades of the machine. We study the existence of the weak solution in the case of nonlinear boundary condition of the “do‐nothing” type. The model is interesting for study the behavior of the flow when the boundary is formed by mutually disjoint and separated parts.

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47.10.ad	Navier-Stokes equations
47.20.Gv	Viscous and viscoelastic instabilities
47.15.Cb	Laminar boundary layers
02.60.Lj	Ordinary and partial differential equations; boundary value problems

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The ALE Discontinuous Galerkin Method for the Simulatio of Air Flow Through Pulsating Human Vocal Folds

Miloslav Feistauer, Václav Kučera, Jaroslav Prokopová, and Jaromír Horáček

AIP Conf. Proc. 1281, pp. 83-86; doi:http://dx.doi.org/10.1063/1.3498617 (4 pages)

Online Publication Date: 17 September 2010

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The aim of this work is the simulation of viscous compressible flows in human vocal folds during phonation. The computational domain is a bounded subset of IR², whose geometry mimics the shape of the human larynx. During phonation, parts of the solid impermeable walls are moving in a prescribed manner, thus simulating the opening and closing of the vocal chords. As the governing equations we take the compressible Navier‐Stokes equations in ALE form. Space semidiscretization is carried out by the discontinuous Galerkin method combined with a linearized semi‐implicit approach. Numerical experiments are performed with the resulting scheme.

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02.70.Dh	Finite-element and Galerkin methods
47.40.Dc	General subsonic flows
47.10.ad	Navier-Stokes equations
47.63.Jd	Microcirculation and flow through tissues

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Modeling Migration of Chemical Impurities in Drinking Water Supply Systems

P. Mercea, V. Tosa, Katalin Kovacs, and O. Piringer

AIP Conf. Proc. 1281, pp. 87-90; doi:http://dx.doi.org/10.1063/1.3498628 (4 pages)

Online Publication Date: 17 September 2010

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A numerical method based on finite differences was developed to solve the problem of impurities’ migration from a hollow core multilayer cylinder (pipe) filled with water. The numerical method is based on finite differences (FD) and the developed application is presented. The migration modeling is focused on the estimation of water contamination in a single household over a long period of time (up to 50 years). The input parameters for the FD algorithm are generated by Monte‐Carlo sampling of a short term water consumption pattern in the household.

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47.27.tb	Turbulent diffusion
92.40.Qk	Surface water, water resources
02.30.Jr	Partial differential equations

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The Extension of Convective Boundedness Criterion

Wu Jian, Philippe Traoré, and Romat Hubert

AIP Conf. Proc. 1281, pp. 91-94; doi:http://dx.doi.org/10.1063/1.3498642 (4 pages)

Online Publication Date: 17 September 2010

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The paper describes an extension of the well‐known Convective Boundedness Criterion (CBC). It is shown that the newly proposed criterion is a combination of the CBC and the extended convective boundedness criterion (ECBC), as shown in Fig.1. A new scheme (NECBC1) based on the new criterion is designed and tested by two problems: (1) convection of a stepwise profile in an oblique uniform velocity field and (2) convection of an elliptical profile in a stagnation point flow. The numerical tests show the effectiveness of the new criterion and reveal the limitation of the CBC and the ECBC. Moreover, some numerical experiments of some specially‐designed schemes and two TVD‐Type schemes: the van Albada scheme and Miroslav Čada & Manuel Torrilhon’s new third‐order scheme, are carried out. Through these numerical experiments, some extra constraints for the new criterion are observed and in the meantime some other possible regions in the normalized diagram (NV) for high‐resolution schemes reveal themselves.

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47.11.St	Multi-scale methods
47.55.P-	Buoyancy-driven flows; convection
47.27.tb	Turbulent diffusion
02.60.Ed	Interpolation; curve fitting

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Experimental and Numerical Simulation of the Mould Region of a Steel Continuous Caster

K. Pericleous, Z. Kountouriotis, G. Djambazov, J. F. Domgin, and P. Gardin

AIP Conf. Proc. 1281, pp. 95-98; doi:http://dx.doi.org/10.1063/1.3498655 (4 pages)

Online Publication Date: 17 September 2010

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A finite volume numerical model was developed to determine the fluid flow patterns and investigate the transient behaviour of the slag∕steel (oil∕water) interface using a water model configuration. This model includes a Lagrangian representation of argon bubble tracks and their influence on the flowfield (due to buoyancy) and on surface behaviour. In the process of validation between the multi‐phase model and the LDA experimental measurements several explanations are provided for the different observed phenomena and their influence on the Continuous Casting of steel. As a next aim in the project, the heat transfer between slag and steel in an industrial configuration is studied. These multi‐phase interactions involve the melting of the flux powder and the formation of the slag layer.

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47.40.Dc	General subsonic flows
47.11.Df	Finite volume methods
47.55.dr	Interactions with surfaces
47.20.Gv	Viscous and viscoelastic instabilities

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