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Two-Relaxation-Time Lattice Boltzmann Scheme:About Parametrization,Velocity,Pressure and Mixed Boundary Conditions

Communications in Computational Physics 2008年第2期3卷 427-478页

作者： Irina Ginzburg frederik verhaeghe Dominique d’Humieres Cemagref Antony Regional CentreParc de Tourvoie-BP 4492163 Antony CedexFrance Department of Metallurgy and Materials Engineering Katholieke Universiteit LeuvenKasteelpark Arenberg 443001LeuvenBelgium Laboratoire de Physique Statistique Ecole Normale Superieureassociated to CNRS and P.and M.Curie and D.Diderot Universities24 Rue Lhomond75231 Paris Cedex 05France.

We develop a two-relaxation-time (TRT) Lattice Boltzmann model for hydrodynamicequations with variable source terms based on equivalent equilibriumfunctions. A special parametrization of the free relaxation parameter is derived. Itcontrols, in addition to the non-dimensional hydrodynamic numbers, any TRT macroscopicsteady solution and governs the spatial discretization of transient flows. Inthis framework, the multi-reflection approach [16, 18] is generalized and extended forDirichlet velocity, pressure and mixed (pressure/tangential velocity) boundary *** propose second and third-order accurate boundary schemes and adapt themfor corners. The boundary schemes are analyzed for exactness of the parametrization,uniqueness of their steady solutions, support of staggered invariants and for the effectiveaccuracy in case of time dependent boundary conditions and transient *** the boundary scheme obeys the parametrization properly, the derived permeabilityvalues become independent of the selected viscosity for any porous structureand can be computed efficiently. The linear interpolations [5, 46] are improved withrespect to this property.

关键词： Lattice Boltzmann equation Dirichlet boundary conditions Chapman-Enskog expansion multiple-relaxation-timemodel BGKmodel TRTmodel Navier-Stokes equation Stokes equation recurrence equations staggered invariants.

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Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme

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Communications in Computational Physics 2008年第3期3卷 519-581页

作者： Irina Ginzburg frederik verhaeghe Dominique d’Humieres Cemagref Antony Regional CentreParc de Tourvoie–BP 4492163Antony CedexFrance Department of Metallurgy and Materials Engineering Katholieke Universiteit LeuvenKasteelpark Arenberg 443001LeuvenBelgium Laboratoire de Physique Statistique ´Ecole Normale Sup´erieureassociated to CNRS and P.and M.Curie and D.Diderot Universities24 Rue Lhomond75231 Paris C´edex 05France.

For simple hydrodynamic solutions, where the pressure and the velocity arepolynomial functions of the coordinates, exact microscopic solutions are constructedfor the two-relaxation-time (TRT) Lattice Boltzmann model with variable forcing andsupported by exact boundary schemes. We show how simple numerical and analyticalsolutions can be interrelated for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) multi-reflection (MR) type schemes. Special care is taken toadapt themfor corners, to examine the uniqueness of the obtained steady solutions andstaggered invariants, to validate their exact parametrization by the non-dimensionalhydrodynamic and a “kinetic” (collision) number. We also present an inlet/outlet“constant mass flux” condition. We show, both analytically and numerically, that thekinetic boundary schemes may result in the appearance of Knudsen layers which arebeyond the methodology of the Chapman-Enskog analysis. Time dependent Dirichletboundary conditions are investigated for pulsatile flow driven by an oscillating pressuredrop or forcing. Analytical approximations are constructed in order to extend thepulsatile solution for compressible regimes.

关键词： Lattice Boltzmann equation Dirichlet boundary conditions pressure boundary conditions two-relaxation-time model Knudsen layers exact hydrodynamic solutions staggered invariants pulsatile flow.

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Microstructural Evolution of Slags during EAF Stainless Steelmaking

Microstructural Evolution of Slags during EAF Stainless Stee...

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技术创新与循环经济——第二届宝钢学术年会

作者： Dirk DURINCK Peter Tom JONES frederik verhaeghe Heylen Gert Hendrickx Roel Baeten Rik Blanpain Bart Wollants Patrick Department of Metallurgy and Materials Engineering Katholieke Universiteit LeuvenKasteelpark Arenberg 44BE-3001 Heverlee(Leuven)Belgium

This paper investigates the microstructural evolution of stainless steelmaking slags during the electric arc furnace process.36 austenitic heats were sampled at 5 distinct *** probe microanalysis with energy dispersive spectroscopy(EPMA-EDS) was used to assess the *** microstructural data show that at high temperature the slag consists of a liquid slag matrix,*** different types of metallic particles and MgO(Cr,Al)O based spinel *** illustrate the effect of changing conditions on the slag microstructure, the interactions between these phases are *** calculations are used as a complementary *** is drawn to the implications of the slag microstructure on slag foaming and Cr recovery.

关键词： EAF steelmaking slag tnicrostructure spinel particles slag basicity Cr recovery

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