摘要:

AbstractA Chebyshev collocation method is proposed for the computation of laminar flame propagation in a two‐dimensional gaseous medium. The method is based on a domain decomposition technique associated with co‐ordinate transforms to map the infinite physical subdomains into finite computational ones. The influence matrix method is used to handle the patching conditions at the interfaces. This technique is particularly efficient since at each time step only matrix products have to be performed. The method is tested first on an elliptic model problem; it is then applied to laminar flame computations, including calculations of cellular instabilities of flame fro

ISSN:0271-2091    

DOI:10.1002/fld.1650090502

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractAn efficient Euler and full Navier–Stokes solver based on a flux splitting scheme is presented. The original Van Leer flux vector splitting form is extended to arbitrary body‐fitted co‐ordinates in the physical domain so that it can be used with a finite volume scheme. The block matrix is inverted by Gauss–Seidel iteration. It is verified that the often used reflection boundary condition will produce incorrect flux crossing the wall and cause too large numerical dissipation if flux vector splitting is used. To remove such errors, an appropriate treatment of wall boundary conditions is suggested. Inviscid and viscous steady transonic internal flows are analysed, including the case of shock‐induced boundary layer s

ISSN:0271-2091    

DOI:10.1002/fld.1650090503

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThis paper treats the mathematical derivation of a novel formulation of the Navier–Stokes equation for general non‐orthogonal curvilinear co‐ordinates. The covariant velocity components are solved in this FVM formulation, which leads to the pressure‐velocity coupling becoming relatively easy to handle at the expense of a more complicated expression of the convective and diffusive fluxes. When a velocity component is solved at a point P, the neighbouring velocities are projected in the direction of the velocity component at the point P. Thus the base vectors are changed at the neighbouring points. This renders a simpler expression for the covariant derivatives. Neither the Cristoffel symbol nor its derivatives need be computed. This contributes to the accuracy of the formulation. The procedure of changing the base vectors affects only the convected velocity. The convecting term (dot product of velocity and area) is calculated without any change of the base vectors. The same is true for the operator on the covariant velocity in the diffusion term.It is shown that when using upwind differencing the use of projected velocities gives better results than when curvature effects are included in the source term. The discretized equations are written in a form which enables the use of the tridiagonal matrix algorithm (TDMA). The equations can be solved using either the SIMPLEC or the PISO procedure.Two examples of laminar flows ar

ISSN:0271-2091    

DOI:10.1002/fld.1650090504

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe flow and solidification of planar jets are analysed by means of an efficient inverse isotherm finite element method. The method is based on a tessellation that is constructed by isotherms as characteristic co‐ordinate lines transverse to the flow direction. Thus opposite sides of finite elements lie on isotherms. The method allows the simultaneous determination of the location of the isotherms with the primary unknowns, namely, the velocity, the pressure, the temperature and the location of the free surface. Thus the determination of the location of the solidification front (which is known to pose significant computational difficulties) is automatic. This facilitates the control of the location of the solidification front by controlling macroscopic variables such as the flow rate, the cooling rate and the capillary design. The location of the solidification may then be suitably chosen to influence the frozen‐in orientation and structure in extrusion of high‐performance materials such as composites and polymers, in continuous casting of metals and in growth of cry

ISSN:0271-2091    

DOI:10.1002/fld.1650090505

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA pressure‐smoothing scheme for Stokes and Navier–Stokes flows of Newtonian fluids and for Stokes flow of Maxwell fluids is described. The stress deviator obtained from the calculated velocity field is substituted into the governing equilibrium equation. The resulting equation is then solved to obtain a new, smoothed pressure by a least square finite element met

ISSN:0271-2091    

DOI:10.1002/fld.1650090506

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA sharp interface problem arising in the flow of two immiscible fluids, slag and molten metal in a blast furnace, is formulated using a two‐dimensional model and solved numerically. This problem is a transient two‐phase free or moving boundary problem, the slag surface and the slag–metal interface being the free boundaries. At each time step the hydraulic potential of each fluid satisfies the Laplace equation which is solved by the finite element method. The ordinary differential equations determining the motion of the free boundaries are treated using an implicit time‐stepping scheme. The systems of linear equations obtained by discretization of the Laplace equations and the equations of motion of the free boundaries are incorporated into a large system of linear equations. At each time step the hydraulic potential in the interior domain and its derivatives on the free boundaries are obtained simultaneously by solving this linear system of equations. In addition, this solution directly gives the shape of the free boundaries at the next time step. The implicit scheme mentioned above enables us to get the solution without handling normal derivatives, which results in a good numerical solution of the present problem. A numerical example that simulates the flow in a blast furnace i

ISSN:0271-2091    

DOI:10.1002/fld.1650090507

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe paper describes a numerical scheme for solving a convection–diffusion elliptic system with very small diffusion coefficients. This iterative numerical procedure is unconditionally stable and converges very rapidly. Although only linear equations are considered here, this technique can be easily extended to non‐linear equations, while keeping its main features as for the linear case. The numerical experiments presented are quite general and confirm most of these features. These examples also show a good way of implementing this sch

ISSN:0271-2091    

DOI:10.1002/fld.1650090508

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIn problems such as the computation of incompressible flows with moving boundaries, it may be necessary to solve Poisson's equation on a large sequence of related grids. In this paper the LU decomposition of the matrixA0representing Poisson's equation discretized on one grid is used to efficiently obtain an approximate solution on a perturbation of that grid. Instead of doing an LU decomposition of the new matrixA, the RHS is perturbed by a Taylor expansion ofA−1aboutA0. Each term in the resulting series requires one ‘backsolve’ using the originalLU.Tests using Laplace's equation on a square/rectangle deformation look promising; three and seven correction terms for deformations of 20% and 40% respectively yielded better than 1% accuracy.As another test, Poisson's equation was solved in an ellipse (fully developed flow in a duct) of aspect ratio 2/3 by perturbing about a circle; one correction term yielded better than 1% accuracy.Envisioned applications other than the computation of unsteady incompressible flow include: three‐dimensional parabolic problems in tubes of varying cross‐section, use of ‘elimination’ techniques other than LU decomposition, and the solution of PDEs other than Poiss

ISSN:0271-2091    

DOI:10.1002/fld.1650090509

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA calculation procedure is presented for predicting steady two‐dimensional elliptic flows. The method introduces a density correction concept and an algebraic equation for the velocity correction instead of the troublesome pressure correction equation in the SIMPLER procedure. Computations show that the method has the same rate of convergence as SIMPLER while saving about 20% computational effort per iteration. Although the method is described for steady two‐dimensional situations, its extension to three‐dimensional problems is very straightfo

ISSN:0271-2091    

DOI:10.1002/fld.1650090510

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650090511

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY