T. Chinyoka  O. D. Makinde 《国际流体数值方法杂志》2012,69(2):353-365

This paper examines the combined effects of a transverse magnetic field and variable viscosity on unsteady flow of a reactive third‐grade electrically conducting fluid and heat transfer in a channel with convective cooling at the surface. It is assumed that the fluid has small electrical conductivity and the electromagnetic force produced is very small. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi‐implicit finite‐difference scheme. Both numerical and graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system. It is in general noted that those parameters that increase/decrase one flow quantity (velocity or temperature) also lead to the increase/decrease respectively of the other quantity. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

Qiuhua Liang 《国际流体数值方法杂志》2012,69(2):442-458

This paper presents a new simplified grid system that provides local refinement and dynamic adaptation for solving the 2D shallow water equations (SWEs). Local refinement is realized by simply specifying different subdivision levels to the cells on a background uniform coarse grid that covers the computational domain. On such a non‐uniform grid, the structured property of a regular Cartesian mesh is maintained and neighbor information is determined by simple algebraic relationships, i.e. data structure becomes unnecessary. Dynamic grid adaptation is achieved by changing the subdivision level of a background cell. Therefore, grid generation and adaptation is greatly simplified and straightforward to implement. The new adaptive grid‐based SWE solver is tested by applying it to simulate three idealized test cases and promising results are obtained. The new grid system offers a simplified alternative to the existing approaches for providing adaptive mesh refinement in computational fluid dynamics. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

Wu‐Shung Fu  Chung‐Gang Li  Wei‐Fong Lin  Yu‐Hsu Chen 《国际流体数值方法杂志》2009,61(8):888-910

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K. Steenhauer  D. Pokrajac  T. O'Donoghue 《国际流体数值方法杂志》2012,70(6):682-702

The paper details the implementation of the Godunov‐type finite volume Arbitrary high order schemes using Derivatives (ADER) scheme for the case of a large source term in the continuity equation of the nonlinear shallow water equations. The particular application is the movement of a bore on a highly permeable slope. The large source term is caused by the infiltration into the initially unsaturated slope material. Infiltration is modelled as vertical downwards piston‐like flow with Forchheimer quadratic parameterisation of the resistance law. The corresponding ODE is solved using the fourth‐order Runge–Kutta method. The surface and subsurface flow models have been tested by comparison with analytical solutions. Example predictions of surface bore propagation and wetting front propagation are presented for a range of slope permeabilities. The effects of permeability on bore run‐up, water depths and velocities are illustrated. The ADER scheme is capable of handling the source term, including the extreme case when this term dominates the volume balance. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

Wanai Li  Yu-Xin Ren 《国际流体数值方法杂志》2012,70(6):742-763

This paper presents a family of High‐order finite volume schemes applicable on unstructured grids. The k‐exact reconstruction is performed on every control volume as the primary reconstruction. On a cell of interest, besides the primary reconstruction, additional candidate reconstruction polynomials are provided by means of very simple and efficient ‘secondary’ reconstructions. The weighted average procedure of the WENO scheme is then applied to the primary and secondary reconstructions to ensure the shock‐capturing capability of the scheme. This procedure combines the simplicity of the k‐exact reconstruction with the robustness of the WENO schemes and represents a systematic and unified way to construct High‐order accurate shock capturing schemes. To further improve the efficiency, an efficient problem‐independent shock detector is introduced. Several test cases are presented to demonstrate the accuracy and non‐oscillation property of the proposed schemes. The results show that the proposed schemes can predict the smooth solutions with uniformly High‐order accuracy and can capture the shock waves and contact discontinuities in high resolution. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

X.L. Luo  Z.L. Gu  K.B. Lei  S. Wang  K. Kase 《国际流体数值方法杂志》2012,69(12):1939-1959

A three‐dimensional Cartesion cut cell method is presented for the simulations of incompressible viscous flows with irregular domains. A new model (referred to as ‘6+N’ model) is proposed to describe arbitrarily shaped cut cells and treat all the cells as polyhedrons with 6+N faces. The finite volume discretization of the Navier–Stokes equation is then implemented by using the ‘6+N’ model to separate the surface flux integrals into two parts, that is, the fluxes through the basic face of the hexahedron and those through the cutting surfaces. The previously proposed Kitta Cube algorithm and volume computer‐aided design platform (J. Comput. Aided. Des. 2005; 37(4): 1509–1520. Doi:10.1016/j.cad.2005.03.006) are adopted to generate cut cells and provide shape data and physical attributes for the numerical analysis. A modified SIMPLE‐based smoothing pressure correction scheme is applied to suppress checkerboard pressure oscillations caused by the collocated arrangement of velocities and pressure. The calculation accuracy of the numerical method expressed by L₁ and L _∞ norm errors is first demonstrated by the simulation of a pipe flow. Then its feasibility, efficiency, and potential in engineering applications are verified by applying it to solve natural convections between concentric spheres and between eccentric spheres. The heat transfer patterns in eccentric spheres are also obtained by using the numerical method. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

W.‐P. Düll  G. Schneider  H. Uecker 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2011,91(3):247-256

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Jihn‐Sung Lai  Wen‐Dar Guo  Gwo‐Fong Lin  Yih‐Chi Tan 《国际流体数值方法杂志》2010,62(8):927-944

This study extends the upstream flux‐splitting finite‐volume (UFF) scheme to shallow water equations with source terms. Coupling the hydrostatic reconstruction method (HRM) with the UFF scheme achieves a resultant numerical scheme that adequately balances flux gradients and source terms. The proposed scheme is validated in three benchmark problems and applied to flood flows in the natural/irregular river with bridge pier obstructions. The results of the simulations are in satisfactory agreement with the available analytical solutions, experimental data and field measurements. Comparisons of the present results with those obtained by the surface gradient method (SGM) demonstrate the superior stability and higher accuracy of the HRM. The stability test results also show that the HRM requires less CPU time (up to 60%) than the SGM. The proposed well‐balanced UFF scheme is accurate, stable and efficient to solve flow problems involving irregular bed topography. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

    

G. Palani  Kwang‐Yong Kim 《国际流体数值方法杂志》2010,63(4):517-532

An analysis is performed to study the free convection of a dusty‐gas flow along a semi‐infinite isothermal vertical cylinder. The governing equations of the flow problem are transformed into non‐dimensional form and the resulting nonlinear, coupled parabolic partial differential equations have been solved numerically using an implicit finite difference scheme of Crank–Nicholson type. The flow variables such as gas–velocity, dust‐particle velocity and temperature, shearing stress and heat transfer coefficients are calculated numerically for various parameters occurring in the problem. It is observed that due to the presence of dust particles, the gas velocity is found to decrease. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

    

M.A. Kamal  A.Z.A. Siddiqui 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2004,84(2):96-113

The ‘time‐marching study’ of non‐steady flow around a rotating and oscillating circular cylinder of a viscous incompressible micropolar fluid, for low values of Keulegan‐Carpenter number K_c and different values of Stokes parameter β is being undertaken. In the present studies we have investigated the Magnus effects on stirring or orbital flow for different values of rotation parameter α in the range 0 to 4.5 at various time levels. In this numerical attempt we have adopted the scheme, which consists of two steps. In the first step a 4th order special finite‐difference method is used to approximate the constitutive equations. This method transforms the governing partial differential equations to a system of finite‐difference equations, which are solved numerically by S.O.R. iterative method. In the second step, the results obtained are further refined and upgraded by Richardson's extrapolation method. That is why this scheme yields the sixth order accurate solution. To check the accuracy of the results these results are compared on five different grid sizes. The results compare very well.  相似文献