指数型弥散过程的解析解

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基金项目: 石油大学基础研究基金项目资助

An Analytical Solution for an Exponential- Type Dispersion Process

Department of Applied Mathematics, University of Petroleum, Dongying, Shandong 257062, P R China

摘要: 对具有指数型弥散系数的弥散过程建立了数学模型,应用积分变换把变系数的偏微分方程变为变系数的常微分方程,应用超几何函数方法和反演技术得到了两类边界条件下的解析解.利用解析解的表达式和计算结果,分析了指数型弥散过程和经典线性弥散过程的差异.
- 非均质多孔介质 /
- 弥散 /
- 超几何函数 /
- 解析解
Abstract: The dispersion process in heterogeneous porous media is distance-dependent,which results from multi-scaling property of heterogeneous structure.An analytical model describing the dispersion with an exponential dispersion function is build,which is transformed into ODE problem with variable coefficients,and obtained analytical solution for two type boundary conditions using hypergeometric function and inversion technique.Acoording to the analytical solution and computing results the difference between the exponential dispersion and constant dispersion process is analyzed.
- heterogeneous porous media /
- dispersion /
- hypergeometric function /
- analytical solution

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