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16
Algebraic flux correction III. Incompressible flow problems
 FluxCorrected Transport: Principles, Algorithms, and Applications
, 2005
"... Summary. Algebraic FEMFCT and FEMTVD schemes are integrated into incompressible flow solvers based on the ‘Multilevel Pressure Schur Complement’ (MPSC) approach. It is shown that algebraic flux correction is feasible for nonconforming (rotated bilinear) finite element approximations on unstructu ..."
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Cited by 10 (8 self)
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Summary. Algebraic FEMFCT and FEMTVD schemes are integrated into incompressible flow solvers based on the ‘Multilevel Pressure Schur Complement’ (MPSC) approach. It is shown that algebraic flux correction is feasible for nonconforming (rotated bilinear) finite element approximations on unstructured meshes. Both (approximate) operatorsplitting and fully coupled solution strategies are introduced for the discretized NavierStokes equations. The need for development of robust and efficient iterative solvers (outer Newtonlike schemes, linear multigrid techniques, optimal smoothers/preconditioners) for implicit highresolution schemes is emphasized. Numerical treatment of extensions (Boussinesq approximation, k − ε turbulence model) is addressed and pertinent implementation details are given. Simulation results are presented for threedimensional benchmark problems as well as for prototypical applications including multiphase and granular flows. 1
Numerical Aspects and Implementation of Population Balance Equations Coupled with Turbulent Fluid Dynamics
"... In this paper, we present numerical techniques for oneway coupling of CFD and Population Balance Equations (PBE) based on the incompressible flow solver FeatFlow which is extended with Chien’s LowReynolds number k − ε turbulence model, and breakage and coalescence closures. The presented implemen ..."
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Cited by 5 (4 self)
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In this paper, we present numerical techniques for oneway coupling of CFD and Population Balance Equations (PBE) based on the incompressible flow solver FeatFlow which is extended with Chien’s LowReynolds number k − ε turbulence model, and breakage and coalescence closures. The presented implementation ensures strictly conservative treatment of sink and source terms which is enforced even for geometric discretization of the internal coordinate. The validation of our implementation which covers wide range of computational and experimental problems enables us to proceed into threedimensional applications as, turbulent flows in a pipe and through a static mixer. The aim of this paper is to highlight the influence of different formulations of the novel theoretical breakage and coalescence models on the equilibrium distribution of population, and to propose an implementation strategy for threedimensional oneway coupled CFDPBE model. 1.
Pressure correction staggered schemes for barotropic monophasic and twophase flows. submitted
, 2011
"... We assess in this paper the capability of a pressure correction scheme to compute shock solutions of the homogeneous model for barotropic twophase flows. This scheme is designed to inherit the stability properties of the continuous problem: the unknowns (in particular the density and the dispersed ..."
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Cited by 4 (4 self)
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We assess in this paper the capability of a pressure correction scheme to compute shock solutions of the homogeneous model for barotropic twophase flows. This scheme is designed to inherit the stability properties of the continuous problem: the unknowns (in particular the density and the dispersed phase mass fraction y) are kept within their physical bounds, and the entropy of the system is conserved, thus providing an unconditional stability property. In addition, the scheme keeps the velocity and pressure constant through contact discontinuities. These properties are obtained by coupling the mass balance and the transport equation for y in an original pressure correction step. The space discretization is staggered; the numerical schemes which are considered are the MarkerAnd Cell (MAC) finite volume scheme and the nonconforming loworder RannacherTurek and CrouzeixRaviart finite element approximation. In either case, a finite volume technique is used for all convection terms. Numerical experiments performed here show that, provided that a sufficient dissipation is introduced in the scheme, it converges to the (weak) solution of the continuous hyperbolic system. Observed orders of convergence for
Population Balances Coupled with the CFDCode FeatFlow, Ergebnisberichte des Instituts für Angewandte
 Mathematik, Nr. 324, FB Mathematik, Universität Dortmund
, 2006
"... The simulation of drop size distributions in stirred liquidliquid systems is studied. The simulation is realized via the coupling of the CFD code FeatFlow with the population balance solver Parsival. It is shown how such a coupling may be constructed and the properties of the coupled solver are cr ..."
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Cited by 2 (2 self)
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The simulation of drop size distributions in stirred liquidliquid systems is studied. The simulation is realized via the coupling of the CFD code FeatFlow with the population balance solver Parsival. It is shown how such a coupling may be constructed and the properties of the coupled solver are critically analyzed. 1
Numerical Methods to Simulate Turbulent Dispersed Flows in Complex Geometries
"... Population Balance is a prominent ingredient of modeling transport phenomena. Population Balance Equations (PBEs) are coupled to Computational Fluid Dynamics (CFD) to simulate turbulent dispersed flows. One of the arising challenges is to obtain an appropriate discretization technique for the inter ..."
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Cited by 1 (1 self)
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Population Balance is a prominent ingredient of modeling transport phenomena. Population Balance Equations (PBEs) are coupled to Computational Fluid Dynamics (CFD) to simulate turbulent dispersed flows. One of the arising challenges is to obtain an appropriate discretization technique for the internal coordinate of PBEs, so the resulting equations can lead to acceptable solutions with affordable computational costs in reasonable time scales. On the other hand, geometries in the industrial problems can be very complex such that preprocessing steps require great effort and time, especially for pure hexahedral meshes. Nevertheless, instead of conventional meshing tools, a different approach based on the concept of “fictitious domains”, Fictitious Boundary Method (FBM), can be employed to mesh complex, moving and/or deforming geometries. In this study, we present efficient implementation strategies and numerical methods to couple PBEs to CFD and numerical simulation techniques using a finite element approach in combination with FBM. The presented methods are validated with a study of Sulzer static mixer, SMVTM [1], and simulations of rigid particulate flows [2], which were achieved in the FeatFlow environment.
Flow Control on the basis of a FeatflowMatlab Coupling
 In Active Flow Control 2006
"... For the modelbased active control of threedimensional flows at high Reynolds numbers in real time, lowdimensional models of the flow dynamics and efficient actuator and sensor concepts are required. Numerous successful approaches to derive such models have been proposed in the literature. We pro ..."
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For the modelbased active control of threedimensional flows at high Reynolds numbers in real time, lowdimensional models of the flow dynamics and efficient actuator and sensor concepts are required. Numerous successful approaches to derive such models have been proposed in the literature. We propose a software environment for a comfortable and performant testing of control, actuator and sensor concepts which may be based on such models. It is realized by providing an easily manageable MATLAB control interface for the k"model from the FEATFLOW CFD package. Potentials and limitations of this tool are discussed by considering exemplarily the control of the recirculation bubble behind a backward facing step. 1
AN ENTROPY PRESERVING FINITEELEMENT/FINITEVOLUME PRESSURE CORRECTION SCHEME FOR THE DRIFTFLUX MODEL
, 803
"... Abstract. We present in this paper a pressure correction scheme for the driftflux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical ..."
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Abstract. We present in this paper a pressure correction scheme for the driftflux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of a Darcylike relation, the drift term becomes dissipative. Finally, the present algorithm preserves a constant pressure and a constant velocity through moving interfaces between phases. To ensure the stability as well as to obtain this latter property, a key ingredient is to couple the mass balance and the transport equation for the dispersed phase in an original pressure correction step. The existence of a solution to each step of the algorithm is proven; in particular, the existence of a solution to the pressure correction step is derived as a consequence of a more general existence result for discrete problems associated to the driftflux model. Numerical tests show a nearfirstorder convergence rate for the scheme, both in time and space, and confirm its stability. 1991 Mathematics Subject Classification. 65N12,65N30,76N10,76T05,76M25. The dates will be set by the publisher. 1.
Mathematical modeling and numerical simulations of reactive flows
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Mathematical Modelling and Numerical Analysis Modélisation Mathématique et Analyse Numérique Will be set by the publisher AN ENTROPY PRESERVING FINITEELEMENT/FINITEVOLUME PRESSURE CORRECTION SCHEME FOR THE DRIFTFLUX MODEL
"... Abstract. We present in this paper a pressure correction scheme for the driftflux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical ..."
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Abstract. We present in this paper a pressure correction scheme for the driftflux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of a Darcylike relation, the drift term becomes dissipative. Finally, the present algorithm preserves a constant pressure and a constant velocity through moving interfaces between phases. To ensure the stability as well as to obtain this latter property, a key ingredient is to couple the mass balance and the transport equation for the dispersed phase in an original pressure correction step. The existence of a solution to each step of the algorithm is proven; in particular, the existence of a solution to the pressure correction step is derived as a consequence of a more general existence result for discrete problems associated to the driftflux model. Numerical tests show a nearfirstorder convergence rate for the scheme, both in time and space, and confirm its stability. 1991 Mathematics Subject Classification. 65N12,65N30,76N10,76T05,76M25. The dates will be set by the publisher. 1.
Tundish Flow Model Tuning and Validation: Steady State and Transient Casting Situations
"... ABSTRACT: Fluid flow modeling in continuous casting tundish is a normal procedure when designing or modifying a tundish. Both physical and mathematical modeling are used for this task, but mathematical modeling is becoming more popular because of advances in computer hardware and software developmen ..."
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ABSTRACT: Fluid flow modeling in continuous casting tundish is a normal procedure when designing or modifying a tundish. Both physical and mathematical modeling are used for this task, but mathematical modeling is becoming more popular because of advances in computer hardware and software development and because the effect of natural convection is difficult to take into account in physical modeling. This research focuses on tuning and validation of a commercial CFD package to be used in tundish simulations using physical modeling and plant trials. After physical modeling with a 1/3 scale water model was made, simulations of the water model were conducted first using a tundish with no flow modifiers and then to further test the tuned model two different flow modifier designs were simulated. To investigate how modeling works in the actual process, plant trials were made and simulation of a full scale tundish with steel was conducted. Experiments and simulations were done in steady state and in transient casting conditions. Different turbulence models and other important model variables were studied. 1.