海水入侵数值模拟的分数步长特征差分法

滨海含水层中的海水入侵数值模拟和理论分析，是环境科学中十分重要的理论和实际问题．其中数学模型是一类三维非线性抛物型偏微分方程组的初、边值问题．一个是关于压力的流动方程，另一个是关于含盐浓度的对流方程．在考虑三维有界区域的一般情况下，提出了一类分数步长特征差分格式．应用粗细网格配套、乘积型叁二次插值、变分形式、高阶差分算子的分解和乘积交换性理论和技巧，得到最佳阶l^2误差估计．

Fractional Step Difference Scheme for Sea Water Intrusion Model

The numerical simulation and theoretical analysis for sea water intrusion in coastal region are very important in the theory and practice of the environmental science.The mathematical model can be described by a system of three dimensional nonlinear hyperbolic partial differential equations.One is fluid equation for the pressure,the other convection-dispersion equation for the saltwater concentration.For a general case of three dimensional bounded region,we put forward a kind of fractional step characteristic difference schemes.By using thick and thin grids,piecewise product threefold-quadratic interpolation,calculus of variations,decomposition of high order difference operators and multiplication commutation rule and technique,we obtain optimal of order l~2 error estimates.