基于无结构网格单元中心有限体积法的二维对流扩散方程离散

Discretization of Two-dimensional Advection-Diffusion Equation with Unstructured Cell Center Finite Volume Method

在无结构网格单元中心有限体积法二维水流模型基础上,建立物质输运对流扩散方程离散模式.通过通量重构法和SOM(Support Operators Method),分别对输运方程的对流项和扩散项进行离散.该离散模式具有空间二阶精度,并适用于任意多边形无结构网格.通过纯对流和纯扩散算例对模型进行检验和验证,结果表明,模型能够较好地模拟物质输运的对流扩散问题.应用模型模拟瓯江河口的盐度输运,通过计算值与实测值对比,进一步检验模型.

In a two-dimensional shallow water flow model advective-diffusion derivative equation is discretized with cell center finite volume method. Flux reconstruction and support operators method are used for advective and diffusive terms, respectively. The model is second order and can be used for arbitrarily unstructured grids. A pure advective problem and a pure diffusion problem verify the algorithm. The model is used to simulate salt transport in Oujiang estuary. Water level, velocity and salt calculated are in good agreement with measurement.