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Wall Boundary Conditions (wall + boundary_condition)
Selected AbstractsExact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions: Antiferroelectric PhaseCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2010Pavel Bleher We obtain the large- n asymptotics of the partition function Zn of the six-vertex model with domain wall boundary conditions in the antiferroelectric phase region, with the weights a = sinh(, , t), b = sinh(, + t), c = sinh(2,), |t| < ,. We prove the conjecture of Zinn-Justin, that as n , ,, Zn = C,4(n,)F [1 + O(n,1)], where , and F are given by explicit expressions in , and t, and ,4(z) is the Jacobi theta function. The proof is based on the Riemann-Hilbert approach to the large- n asymptotic expansion of the underlying discrete orthogonal polynomials and on the Deift-Zhou nonlinear steepest-descent method. © 2009 Wiley Periodicals, Inc. [source] A critical look at the kinematic-wave theory for sedimentation,consolidation processes in closed vesselsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2001R. Bürger Abstract The two-phase flow of a flocculated suspension in a closed settling vessel with inclined walls is investigated within a consistent extension of the kinematic wave theory to sedimentation processes with compression. Wall boundary conditions are used to spatially derive one-dimensional field equations for planar flows and flows which are symmetric with respect to the vertical axis. We analyse the special cases of a conical vessel and a roof-shaped vessel. The case of a small initial time and a large time for the final consolidation state leads to explicit expressions for the flow fields, which constitute an important test of the theory. The resulting initial-boundary value problems are well posed and can be solved numerically by a simple adaptation of one of the newly developed numerical schemes for strongly degenerate convection-diffusion problems. However, from a physical point of view, both the analytical and numerical results reveal a deficiency of the general field equations. In particular, the strongly reduced form of the linear momentum balance turns out to be an oversimplification. Included in our discussion as a special case are the Kynch theory and the well-known analyses of sedimentation in vessels with inclined walls within the framework of kinematic waves, which exhibit the same shortcomings. In order to formulate consistent boundary conditions for both phases in a closed vessel and in order to predict boundary layers in the presence of inclined walls, viscosity terms should be taken into account. Copyright © 2001 John Wiley & Sons, Ltd. [source] URANS computations for an oscillatory non-isothermal triple-jet using the k,, and second moment closure turbulence modelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2003M. Nishimura Abstract Low Reynolds number turbulence stress and heat flux equation models (LRSFM) have been developed to enhance predictive capabilities. A new method is proposed for providing the wall boundary condition for dissipation rate of turbulent kinetic energy, ,, to improve the model capability upon application of coarse meshes for practical use. The proposed method shows good agreement with accepted correlations and experimental data for flows with various Reynolds and Prandtl numbers including transitional regimes. Also, a mesh width about 5 times or larger than that used in existing models is applicable by using the present boundary condition. The present method thus enhanced computational efficiency in applying the complex turbulence model, LRSFM, to predictions of complicated flows. Unsteady Reynolds averaged Navier,Stokes (URANS) computations are conducted for an oscillatory non-isothermal quasi-planar triple-jet. Comparisons are made between an experiment and predictions with the LRSFM and the standard k,, model. A water test facility with three vertical jets, the cold in between two hot jets, simulates temperature fluctuations anticipated at the outlet of a liquid metal fast reactor core. The LRSFM shows good agreement with the experiment, with respect to mean profiles and the oscillatory motion of the flow, while the k,, model under-predicts the mixing due to the oscillation, such that a transverse mean temperature difference remains far downstream. Copyright © 2003 John Wiley & Sons, Ltd. [source] The harmonic adjoint approach to unsteady turbomachinery designINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3-4 2002M. C. Duta Abstract In recent years, there has been rapid progress in aerodynamic optimization methods which use adjoint flow analysis to efficiently calculate the sensitivity of steady-state objective functions to changes in the underlying design variables. This paper shows that the same adjoint approach can be used in turbomachinery applications in which the primary concern is blade vibration due to harmonic flow unsteadiness. The paper introduces the key engineering concepts and discusses the derivation of the adjoint analysis at the algebraic level. The emphasis is on the algorithmic aspects of the analysis, on the iterative solution method and on the role played by the strong solid wall boundary condition, in particular. The novel ideas are exploited to reveal the potential of the approach in the minimization of the unsteady vibration of turbomachinery blades due to incident wakes. Copyright © 2002 John Wiley & Sons, Ltd. [source] A 3D incompressible Navier,Stokes velocity,vorticity weak form finite element algorithmINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2002K. L. Wong Abstract The velocity,vorticity formulation is selected to develop a time-accurate CFD finite element algorithm for the incompressible Navier,Stokes equations in three dimensions. The finite element implementation uses equal order trilinear finite elements on a non-staggered hexahedral mesh. A second order vorticity kinematic boundary condition is derived for the no slip wall boundary condition which also enforces the incompressibility constraint. A biconjugate gradient stabilized (BiCGSTAB) sparse iterative solver is utilized to solve the fully coupled system of equations as a Newton algorithm. The solver yields an efficient parallel solution algorithm on distributed-memory machines, such as the IBM SP2. Three dimensional laminar flow solutions for a square channel, a lid-driven cavity, and a thermal cavity are established and compared with available benchmark solutions. Copyright © 2002 John Wiley & Sons, Ltd. [source] Numerical investigation of gas mixing in gas-solid fluidized bedsAICHE JOURNAL, Issue 9 2010Tingwen Li Abstract Gas mixing in a tall narrow fluidized bed operated in the slugging fluidization regime is simulated with the aid of computational fluid dynamics. In the first part, a parametric study is conducted to investigate the influence of various parameters on the gas mixing. Among the parameters studied, the specularity coefficient for the partial-slip solid-phase wall boundary condition had the most significant effect on gas mixing. It was found that the solid-phase wall boundary condition needs to be specified with great care when gas mixing is modeled, with free slip, partial slip and no-slip wall boundary conditions giving substantial differences in the extent of gas back mixing. Axial and radial tracer concentration profiles for different operating conditions are generally in good agreement with experimental data from the literature. Detailed analyses of tracer back mixing are carried out in the second part. Two parameters, the tracer backflow fraction and overall gas backflow fraction, in addition to axial profiles of cross-sectional averaged tracer concentrations, are evaluated for different flow conditions. Qualitative trends are consistent with reported experimental findings. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010I. Kalashnikova Abstract A reduced order model (ROM) based on the proper orthogonal decomposition (POD)/Galerkin projection method is proposed as an alternative discretization of the linearized compressible Euler equations. It is shown that the numerical stability of the ROM is intimately tied to the choice of inner product used to define the Galerkin projection. For the linearized compressible Euler equations, a symmetry transformation motivates the construction of a weighted L2 inner product that guarantees certain stability bounds satisfied by the ROM. Sufficient conditions for well-posedness and stability of the present Galerkin projection method applied to a general linear hyperbolic initial boundary value problem (IBVP) are stated and proven. Well-posed and stable far-field and solid wall boundary conditions are formulated for the linearized compressible Euler ROM using these more general results. A convergence analysis employing a stable penalty-like formulation of the boundary conditions reveals that the ROM solution converges to the exact solution with refinement of both the numerical solution used to generate the ROM and of the POD basis. An a priori error estimate for the computed ROM solution is derived, and examined using a numerical test case. Published in 2010 by John Wiley & Sons, Ltd. [source] On the computation of steady-state compressible flows using a discontinuous Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008Hong Luo Abstract Computation of compressible steady-state flows using a high-order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics-based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low-storage p -multigrid method is used for solving the governing compressible Euler equations to obtain steady-state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady-state flows. Copyright © 2007 John Wiley & Sons, Ltd. [source] Numerical investigation of gas mixing in gas-solid fluidized bedsAICHE JOURNAL, Issue 9 2010Tingwen Li Abstract Gas mixing in a tall narrow fluidized bed operated in the slugging fluidization regime is simulated with the aid of computational fluid dynamics. In the first part, a parametric study is conducted to investigate the influence of various parameters on the gas mixing. Among the parameters studied, the specularity coefficient for the partial-slip solid-phase wall boundary condition had the most significant effect on gas mixing. It was found that the solid-phase wall boundary condition needs to be specified with great care when gas mixing is modeled, with free slip, partial slip and no-slip wall boundary conditions giving substantial differences in the extent of gas back mixing. Axial and radial tracer concentration profiles for different operating conditions are generally in good agreement with experimental data from the literature. Detailed analyses of tracer back mixing are carried out in the second part. Two parameters, the tracer backflow fraction and overall gas backflow fraction, in addition to axial profiles of cross-sectional averaged tracer concentrations, are evaluated for different flow conditions. Qualitative trends are consistent with reported experimental findings. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] On Boundary Conditions Modelling of the Fluid-Structure Interaction at Wind Tunnel TestingPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005ko Ra, uoArticle first published online: 20 DEC 200 The present paper discusses some newer developments, but concentrates mainly on the specification of the wall boundary conditions that are of importance for the calculation of the wind tunnel wall interference. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions: Antiferroelectric PhaseCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2010Pavel Bleher We obtain the large- n asymptotics of the partition function Zn of the six-vertex model with domain wall boundary conditions in the antiferroelectric phase region, with the weights a = sinh(, , t), b = sinh(, + t), c = sinh(2,), |t| < ,. We prove the conjecture of Zinn-Justin, that as n , ,, Zn = C,4(n,)F [1 + O(n,1)], where , and F are given by explicit expressions in , and t, and ,4(z) is the Jacobi theta function. The proof is based on the Riemann-Hilbert approach to the large- n asymptotic expansion of the underlying discrete orthogonal polynomials and on the Deift-Zhou nonlinear steepest-descent method. © 2009 Wiley Periodicals, Inc. [source] | |||||||||||||