摘要:

AbstractA first‐order non‐conforming numerical methodology,Separation method, for fluid flow problems with a 3‐point exponential interpolation scheme has been developed. The flow problem is decoupled into multiple one‐dimensional subproblems and assembled to form the solutions. A fully staggered grid and a conservational domain centred at the node of interest make the decoupling scheme first‐order‐accurate. The discretization of each one‐dimensional subproblem is based on a 3‐point interpolation function and a conservational domain centred at the node of interest. The proposed scheme gives a guaranteed first‐order accuracy. It is shown that the traditional upwind (or exponentially weighted upstream) scheme is less than first‐order‐accurate. The pressure is decoupled from the velocity field using the pressure correction method of SIMPLE. Thomas algorithm (tri‐diagonal solver) is used to solve the algebraic equations iteratively. The numerical advantage of the proposed scheme is tested for laminar fluid flows in a torus and in a square‐driven cavity. The convergence rates are compared with the traditional schemes for the square‐driven cavity problem. Good behaviour of the pro

ISSN:0271-2091    

DOI:10.1002/fld.1650160802

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA numerical solution for the Navier‐Stokes equations in the unbounded region is considered for the interaction of an isolated vortex and shear flow. A Chebyshey collocation method in space and finite‐difference method for temporal discretization are used. The results of the numerical experiments for the interaction are discussed. It is shown that shear flow can both increase and decrease the vortex dissipation r

ISSN:0271-2091    

DOI:10.1002/fld.1650160803

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractAdaptive and non‐adaptive finite difference methods are used to study one‐dimensional reaction‐diffusion equations whose solutions are characterized by the presence of steep, fast‐moving flame fronts. Three non‐adaptive techniques based on the methods of lines are described. The first technique uses a finite volume method and yields a system of non‐linear, first‐order, ordinary differential equations in time. The second technique uses time linearization, discretizes the time derivatives and yields a linear, second‐order, ordinary differential equation in space, which is solved by means of three‐point, fourth‐order accurate, compact differences. The third technique takes advantage of the disparity in the time scales of the reaction and diffusion processes, splits the reaction‐‐diffusion operator into a sequence of reaction and diffusion operators and solves the diffusion operator by means of either a finite volume method or a three‐point, fourth‐order accurate compact difference expression. The non‐adaptive methods of lines presented in this paper may use equaliy or non‐equally spaced fixed grids and require a large number of grid points to solve accurately one‐dimensional problems characterized by the presence of steep, fast‐moving fronts. Three adaptive methods for the solution of reaction‐diffusion equations are considered. The first adaptive technique is static and uses a subequidistribution principle to determine the grid points, avoid mesh tangling and node overtaking and obtain smooth grids. The second adaptive technique is dynamic, uses an equidistribution principle with spatial and temporal smoothing and yields a system of first‐order, non‐linear, ordinary differential equations for the grid point motion. The third adaptive technique is hybrid, combines some features of static and dynamic methods, and uses a predictor‐corrector strategy to predict the grid and solve for the dependent variables, respectively. The three adaptive techniques presented in this paper use physical co‐ordinates and may employ finite volume or three‐point, compact methods. The adaptive and non‐adaptive finite difference methods presented in the paper are used to study a decomposition chemical reaction characterized by a scalar, one‐dimensional reaction‐diffusion equation, the propagation of a one‐dimensional, confined, laminar flame in Cartesian co‐ordinates and the Dwyer‐Sanders model of one‐dimensional flame propagation. It is shown that the adaptive moving method presented in this paper requires a smaller number of grid points than adaptive static, adaptive hybrid and non‐adaptive methods. The adaptive hybrid method requires a smaller time step than adaptive static techniques, due to the lag between the grid prediction and the solution of the dependent variables. Non‐adaptive methods of lines may yield temperature oscillations in front of and behind the flame front if Crank‐Nicolson techniques are used to evaluate the time derivatives. Fourth‐order accurate methods of lines in space yield larger temperature oscillations than second‐order accurate methods of lines, and the magnitude of these oscillations decreases as the time step is decreased. It is also shown that three‐point, fourth‐order accurate discretizations of the spatial derivatives require the same number of grid points as second‐order accurate, finite volume methods, in

ISSN:0271-2091    

DOI:10.1002/fld.1650160804

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper describes a two‐dimensional numerical model to solve the generalized Serre equations. In order to solve the system equations, written in the conservative form, we use an explicit finite‐difference method based on the MacCormack time‐splitting scheme. The numerical method and the computational model are validated by comparing one‐ and two‐dimensional numerical solutions with theoretical and experimental results. Finally, the two‐dimensional model (in a horizontal plane) is tested in a domain with complicated boundary

ISSN:0271-2091    

DOI:10.1002/fld.1650160805

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe unsteady, compressible, Reynolds‐averaged Navier‐Stokes equations are solved numerically for an oblique shock‐wave‐induced turbulent boundary layer sepration. For the freestream Mach number 6 and the freestream Reynolds number 66·1 × 106m−1, a time‐dependent computation is performed, using MacCormack's explicit‐implicit finite difference method with 82 × 42 grid points. A two‐layer eddy viscosity turbulence model is employed in conjunction with a relaxation modification. Comparisons of the mean wall pressure and the mean heat transfer coefficient with the available experimental results are made and the evaluation of unsteady data for surface pressure and heat flux fluctuations is presented. It is found that the fluctuations in heat flux have qualitatively the same features as those of wall pressure but are differ

ISSN:0271-2091    

DOI:10.1002/fld.1650160806

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650160807

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650160801

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY