摘要:

AbstractThe modelling of liquid flow in gas‐stirred vessels is described. A simple two‐phase model accounts for the buoyancy effect of bubbles. Friction between liquid and gas is modelled with the hypothesis of independent bubbles. The resulting PDE system is discretized with an original version of the SUPG‐FEM technique which stabilizes both the convection term and equal‐order interpolations for velocity and pressure, which are known to be unstable for incompressible flows. The resulting steady state discrete system is solved via pseudotemporal explicit iteration with a local time step and a preconditioning to homogenize the temporal scales for liquid

ISSN:0271-2091    

DOI:10.1002/fld.1650190103

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractWe investigate the instability of 2D incompressible flows in a rough planar channel by tracking the growth of the unstable mode in its early stage. We develop both second‐ and fourth‐order finite difference methods on a staggered grid, together with a fully implicit time‐marching scheme, using grid generation to accommodate fairly general geometries. A multigrid full approximation scheme based on the line‐distributive relaxation method is used for fast convergence. For a 2D smooth channel, numerical results show good agreement with the analytic solution obtained from linear theory for small disturbances. Numerical results for a 2D channel with one and two roughness elements are analysed by Fourier analysis. They show how the roughness elements affect the growth of the pertu

ISSN:0271-2091    

DOI:10.1002/fld.1650190104

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractNewton's method is applied to the finite volume approximation for the steady state heat transfer, fluid flow and unknown interfaces in a floating molten zone. The streamfunction/vorticity and temperature formulation of the Navier–Stokes and energy equations and their associated boundary conditions are written in generalized curvilinear co‐ordinates and conservative law form with the Boussinesq approximation. During Newton iteration the ILU(0) preconditioned GMRES matrix solver is applied for solving the linear system, where the sparse Jacobian matrix is estimated by finite differences. Nearly quadratic convergence of the method is observed. Sample calculations are reported for sodium nitrate, a high‐Prandtl‐number material (Pr= 9.12). Both natural convection and thermocapillary flow as well as an overall mass balance constraint in the molten zone are considered. The effects of convection and heat input on the flow patterns, zone position and interface shapes are illustrated. After the lens effect due to the molten zone is considered, the calculated flow patterns and interface shapes are compared with the observed ones and are found to be in good ag

ISSN:0271-2091    

DOI:10.1002/fld.1650190105

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe linear system arising from a Lagrange‐Galerkin mixed finite element approximation of the Navier–Stokes and continuity equations is symmetric indefinite and has the same block structure as a system arising from a mixed finite element discretization of a Stokes problem. This paper considers the iterative solution of such a system, comparing the performance of the one‐level preconditioned conjugate residual method for indefinite matrices with that of a more traditional two‐level pressure correction approach. Asymptotic estimates for the amount of work involved in each method are given together with the results of related numerical expe

ISSN:0271-2091    

DOI:10.1002/fld.1650190106

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650190107

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650190108

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650190102

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY