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A Semi-Implicit Fractional Step Method Immersed Boundary Method for the Numerical Simulation of Natural Convection Non-Boussinesq Flows

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Communications in Computational Physics 2022年第8期32卷 737-778页

作者： Dmitry Zviaga Ido Silverman alexander gelfgat Yuri Feldman Department of Mechanical Engineering Ben-Gurion University of the NegevP.O.Box 653Beer-Sheva 84105Israel Soreq Nuclear Research Center 81000 YavneIsrael School of Mechanical Engineering Tel Aviv UniversityTel Aviv 6997801Israel

The paper presents a novel pressure-corrected formulation of the immersed boundary method(IBM)for the simulation of fully compressible non-Boussinesq natural convection *** formulation incorporated into the pressure-based fractional step approach facilitates simulation of the flows in the presence of an immersed body characterized by a complex ***,we first present extensive grid independence and verification studies addressing incompressible pressure-driven flow in an extended channel and non-Boussinesq natural convection flow in a differentially heated ***,the steady-state non-Boussinesq natural convection flow developing in the presence of hot cylinders of various diameters placed within a cold square cavity is thoroughly *** obtained results are presented and analyzed in terms of the spatial distribution of path lines and temperature fields and of heat flux values typical of the hot cylinder and the cold cavity *** characteristics of multiple steady-state solutions discovered for several configurations are presented and discussed in detail.

关键词： Natural convection non-Boussinesq flows pressure-corrected immersed boundary method multiple steady state solutions

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Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation

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Communications in Computational Physics 2014年第1期15卷 1-45页

作者： Henk A.Dijkstra Fred W.Wubs Andrew K.Cliffe Eusebius Doedel Ioana F.Dragomirescu Bruno Eckhardt alexander Yu.gelfgat Andrew L.Hazel Valerio Lucarini Andy G.Salinger Erik T.Phipps Juan Sanchez-Umbria Henk Schuttelaars Laurette S.Tuckerman Uwe Thiele Institute for Marine and Atmospheric Research Utrecht Utrecht UniversityThe Netherlands. Department of Mathematics and Computer Science University of GroningenGroningenThe Netherlands. School of Mathematical Sciences University of NottinghamNottinghamUK Department of Computer Science Concordia UniversityMontrealCanada. National Centre for Engineering Systems of Complex Fluids University Politehnica of TimisoaraRomania. Fachbereich Physik Philipps-Universitat MarburgMarburgGermany. School of Mechanical Engineering Faculty of EngineeringTel-Aviv UniversityTel-AvivIsrael. School of Mathematics University of ManchesterManchesterUK. Meteorological Institute KlimacampusUniversity of HamburgHamburgGermany. Department of Mathematics and Statistics University of ReadingReadingUK. Sandia National Laboratories AlbuquerqueUSA. Departament de Fisica Aplicada Universitat Politecnica de CatalunyaBarcelonaSpain. Department of Applied Mathematical Analysis TU DelftDelftthe Netherlands. PMMH-ESPCI ParisFrance. Department of Mathematical Sciences Loughborough UniversityLoughboroughUK.

We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical *** of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are *** computation of the critical conditions associated with these transitions,popularly referred to as‘tipping points’,is important for understanding the transition *** describe the two basic classes of methods of numerical bifurcation analysis,which differ in the explicit or implicit use of the Jacobian matrix of the dynamical *** numerical challenges involved in both methods are mentioned and possible solutions to current bottlenecks are *** demonstrate that numerical bifurcation techniques are not restricted to relatively low-dimensional dynamical systems,we provide several examples of the application of the modern techniques to a diverse set of fluid mechanical problems.

关键词： Numerical bifurcation analysis transitions in fluid flows high-dimensional dynamical systems.

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