The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform
Miloslav Feistauer - One of the best experts on this subject based on the ideXlab platform.
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discontinuous galerkin method analysis and applications to Compressible Flow
2015Co-Authors: Vít Dolejší, Miloslav FeistauerAbstract:The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of Compressible Flow. Itdeals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the books uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey ofthe latest efficient, accurate and robust discontinuous Galerkin schemes for thesolution of Compressible Flow.
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Viscous Compressible Flow
Discontinuous Galerkin Method, 2015Co-Authors: Vít Dolejší, Miloslav FeistauerAbstract:This chapter is devoted to the numerical simulation of viscous Compressible Flow. The methods treated here represent the generalization of techniques for solving inviscid Flow problems contained in Chap. 8. Viscous Compressible Flow is described by the continuity equation , the Navier–Stokes equations of motion and the energy equation, to which we add closing thermodynamical relations.
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Inviscid Compressible Flow
Discontinuous Galerkin Method, 2015Co-Authors: Vít Dolejší, Miloslav FeistauerAbstract:In previous chapters we introduced and analyzed the discontinuous Galerkin method (DGM) for the numerical solution of several scalar equations. However, many practical problems are described by systems of partial differential equations. In the second part of this book, we present the application of the DGM to solving Compressible Flow problems. The numerical schemes, analyzed for a scalar equation, are extended to a system of equations and numerically verified. We also deal with an efficient solution of resulting systems of algebraic equations.
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On numerical solution of Compressible Flow in time-dependent domains
Mathematica Bohemica, 2012Co-Authors: Miloslav Feistauer, Jaromír Horáček, Václav Kučera, J ProkopovaAbstract:This work is concerned with the simulation of inviscid Compressible Flow in time-dependent domains. We present an arbitrary Lagrangian-Eulerian (ALE) formulation of the Euler equations describing Compressible Flow, discretize them in space by the discontinous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution of the complete problem. Special attention is paid to the treatment of boundary conditions and the limiting procedure avoiding the Gibbs phenomenon in the vicinity of discontinuities. The presented computational results show the applicability of the developed method. © 2009 IMACS.
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Numerical Simulation of Airfoil Vibrations Induced by Compressible Flow
2010Co-Authors: Miloslav Feistauer, Václav Kučera, Petr ŠimánekAbstract: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.
Vít Dolejší - One of the best experts on this subject based on the ideXlab platform.
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discontinuous galerkin method analysis and applications to Compressible Flow
2015Co-Authors: Vít Dolejší, Miloslav FeistauerAbstract:The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of Compressible Flow. Itdeals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the books uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey ofthe latest efficient, accurate and robust discontinuous Galerkin schemes for thesolution of Compressible Flow.
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Viscous Compressible Flow
Discontinuous Galerkin Method, 2015Co-Authors: Vít Dolejší, Miloslav FeistauerAbstract:This chapter is devoted to the numerical simulation of viscous Compressible Flow. The methods treated here represent the generalization of techniques for solving inviscid Flow problems contained in Chap. 8. Viscous Compressible Flow is described by the continuity equation , the Navier–Stokes equations of motion and the energy equation, to which we add closing thermodynamical relations.
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Inviscid Compressible Flow
Discontinuous Galerkin Method, 2015Co-Authors: Vít Dolejší, Miloslav FeistauerAbstract:In previous chapters we introduced and analyzed the discontinuous Galerkin method (DGM) for the numerical solution of several scalar equations. However, many practical problems are described by systems of partial differential equations. In the second part of this book, we present the application of the DGM to solving Compressible Flow problems. The numerical schemes, analyzed for a scalar equation, are extended to a system of equations and numerically verified. We also deal with an efficient solution of resulting systems of algebraic equations.
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a semi implicit discontinuous galerkin finite element method for the numerical solution of inviscid Compressible Flow
Journal of Computational Physics, 2004Co-Authors: Vít Dolejší, Miloslav FeistauerAbstract:The paper is concerned with the numerical solution of an inviscid Compressible Flow with the aid of the discontinuous Galerkin finite element method. Since the explicit time discretization requires a high restriction of the time step, we propose semi-implicit numerical schemes based on the homogeneity of inviscid fluxes, allowing a simple linearization of the Euler equations which leads to a linear algebraic system on each time level. Numerical experiments performed for the Ringleb Flow problem verify a higher order of accuracy of the presented method and demonstrate lower CPU-time costs in comparison with an explicit method. Then the method is tested on more complex unsteady Euler Flows.
Cheng Yu - One of the best experts on this subject based on the ideXlab platform.
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global weak solution and large time behavior for the Compressible Flow of liquid crystals
Archive for Rational Mechanics and Analysis, 2012Co-Authors: Dehua Wang, Cheng YuAbstract:The three-dimensional equations for the Compressible Flow of liquid crystals are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of a global weak solution are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent $${\gamma > \frac{3}{2}}$$ .
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InCompressible limit for the Compressible Flow of liquid crystals
arXiv: Analysis of PDEs, 2011Co-Authors: Dehua Wang, Cheng YuAbstract:The connection between the Compressible Flow of liquid crystals with low Mach number and the inCompressible Flow of liquid crystals is studied in a bounded domain. In particular, the convergence of weak solutions of the Compressible Flow of liquid crystals to the weak solutions of the inCompressible Flow of liquid crystals is proved when the Mach number approaches zero; that is, the inCompressible limit is justified for weak solutions in a bounded domain.
Dehua Wang - One of the best experts on this subject based on the ideXlab platform.
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global weak solutions to the equations of Compressible Flow of nematic liquid crystals in two dimensions
arXiv: Analysis of PDEs, 2012Co-Authors: Fei Jiang, Song Jiang, Dehua WangAbstract:We consider weak solutions to a two-dimensional simplified Ericksen-Leslie system of Compressible Flow of nematic liquid crystals. An initial-boundary value problem is first studied in a bounded domain. By developing new techniques and estimates to overcome the difficulties induced by the supercritical nonlinearity in the equations of angular momentum on the direction field, and adapting the standard three-level approximation scheme and the weak convergence arguments for the Compressible Navier-Stokes equations, we establish the global existence of weak solutions under a restriction imposed on the initial energy including the case of small initial energy. Then the Cauchy problem with large initial data is investigated, and we prove the global existence of large weak solutions by using the domain expansion technique and the rigidity theorem, provided that the second component of initial data of the direction field satisfies some geometric angle condition.
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global weak solution and large time behavior for the Compressible Flow of liquid crystals
Archive for Rational Mechanics and Analysis, 2012Co-Authors: Dehua Wang, Cheng YuAbstract:The three-dimensional equations for the Compressible Flow of liquid crystals are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of a global weak solution are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent $${\gamma > \frac{3}{2}}$$ .
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InCompressible limit for the Compressible Flow of liquid crystals
arXiv: Analysis of PDEs, 2011Co-Authors: Dehua Wang, Cheng YuAbstract:The connection between the Compressible Flow of liquid crystals with low Mach number and the inCompressible Flow of liquid crystals is studied in a bounded domain. In particular, the convergence of weak solutions of the Compressible Flow of liquid crystals to the weak solutions of the inCompressible Flow of liquid crystals is proved when the Mach number approaches zero; that is, the inCompressible limit is justified for weak solutions in a bounded domain.
Xiyun Lu - One of the best experts on this subject based on the ideXlab platform.
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large eddy simulation of the Compressible Flow past a wavy cylinder
Journal of Fluid Mechanics, 2010Co-Authors: Changyue Xu, Liwei Chen, Xiyun LuAbstract:Numerical investigation of the Compressible Flow past a wavy cylinder was carried out using large-eddy simulation for a free-stream Mach number M ∞ = 0.75 and a Reynolds number based on the mean diameter Re = 2 × 10 5 . The Flow past a corresponding circular cylinder was also calculated for comparison and validation against experimental data. Various fundamental mechanisms dictating the intricate Flow phenomena, including drag reduction and fluctuating force suppression, shock and shocklet elimination, and three-dimensional separation and separated shear-layer instability, have been studied systematically. Because of the passive control of the Flow over a wavy cylinder, the mean drag coefficient of the wavy cylinder is less than that of the circular cylinder with a drag reduction up to 26%, and the fluctuating force coefficients are significantly suppressed to be nearly zero. The vortical structures near the base region of the wavy cylinder are much less vigorous than those of the circular cylinder. The three-dimensional shear-layer shed from the wavy cylinder is more stable than that from the circular cylinder. The vortex roll up of the shear layer from the wavy cylinder is delayed to a further downstream location, leading to a higher-base-pressure distribution. The spanwise pressure gradient and the baroclinic effect play an important role in generating an oblique vortical perturbation at the separated shear layer, which may moderate the increase of the fluctuations at the shear layer and reduce the growth rate of the shear layer. The analysis of the convective Mach number indicates that the instability processes in the shear-layer evolution are derived from oblique modes and bi-dimensional instability modes and their competition. The two-layer structures of the shear layer are captured using the instantaneous Lamb vector divergence, and the underlying dynamical processes associated with the drag reduction are clarified. Moreover, some phenomena relevant to the Compressible effect, such as shock waves, shocklets and shock/turbulence interaction, are analysed. It is found that the shocks and shocklets which exist in the circular cylinder Flow are eliminated for the wavy cylinder Flow and the wavy surface provides an effective way of shock control. As the shock/turbulence interaction is avoided, a significant drop of the turbulent fluctuations around the wavy cylinder occurs. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the passive control of the Compressible Flow past a wavy surface.
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numerical investigation of the Compressible Flow past an aerofoil
Journal of Fluid Mechanics, 2010Co-Authors: Liwei Chen, Changyue Xu, Xiyun LuAbstract:Numerical investigation of the Compressible Flow past an 18% thick circular-arc aerofoil was carried out using detached-eddy simulation for a free-stream Mach number M? = 0.76 and a Reynolds number Re = 1.1 × 107. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the intricate Flow phenomena, including moving shock wave behaviours, turbulent boundary layer characteristics, kinematics of coherent structures and dynamical processes in Flow evolution, have been studied systematically. A feedback model is developed to predict the self-sustained shock wave motions repeated alternately along the upper and lower surfaces of the aerofoil, which is a key issue associated with the complex Flow phenomena. Based on the moving shock wave characteristics, three typical Flow regimes are classified as attached boundary layer, moving shock wave/turbulent boundary layer interaction and intermittent boundary layer separation. The turbulent statistical quantities have been analysed in detail, and different behaviours are found in the three Flow regimes. Some quantities, e.g. pressure-dilatation correlation and dilatational dissipation, have exhibited that the compressibility effect is enhanced because of the shock wave/boundary layer interaction. Further, the kinematics of coherent vortical structures and the dynamical processes in Flow evolution are analysed. The speed of downstream-propagating pressure waves in the separated boundary layer is consistent with the convection speed of the coherent vortical structures. The multi-layer structures of the separated shear layer and the moving shock wave are reasonably captured using the instantaneous Lamb vector divergence and curl, and the underlying dynamical processes are clarified. In addition, the proper orthogonal decomposition analysis of the fluctuating pressure field illustrates that the dominated modes are associated with the moving shock waves and the separated shear layers in the trailing-edge region. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex Flow.
