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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >On an equal fourth-order-accurate temporal/spatial scheme for the convection-diffusion equation
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On an equal fourth-order-accurate temporal/spatial scheme for the convection-diffusion equation

机译：对流扩散方程的等价四阶精确时空方案

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摘要

In this article, the convection-diffusion equation is discretized using the Pade method for the temporal derivative term and the wavenumber-extended method for the spatial derivative term. These temporal and spatial approximations result in two explicit equations and two implicitly coupled equations. To construct an equal-order scheme for the solution obtained at n Delta t, both temporal/spatial derivatives are approximated to render fourth-order accuracy without using solutions obtained previously at (n-2)Delta t, (n-3)Delta t, etc. When approximating the first-order derivative term, it is essential to take the upwind nodal points into consideration. For revealing the dispersion and dissipation natures of the proposed scheme, both von Neumann (Fourier) and dispersion analyses were conducted. We validate the proposed method by solving several problems that are amenable to exact solutions. Results with theoretical rates of convergence are obtained for each of the one- and two-dimensional problems investigated.
机译：在本文中，对流扩散方程使用时间导数项的Pade方法和空间导数项的波数扩展方法离散化。这些时间和空间近似导致两个显式方程和两个隐式耦合方程。为了为在n Delta t处获得的解构建等阶方案，在不使用先前在（n-2）Delta t，（n-3）Delta t处获得的解的情况下，对时间/空间导数都进行近似以提供四阶精度。等等，当近似一阶导数项时，必须考虑到迎风节点。为了揭示所提出方案的色散和耗散特性，对冯·诺伊曼（Fourier）和色散进行了分析。我们通过解决适合精确解决方案的几个问题来验证所提出的方法。对于所研究的一维和二维问题，均获得了具有理论收敛速度的结果。

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