不同时空格式在求解污染物对流扩散方程中的应用

为了研究污染物对流扩散方程中不同时空格式的适用性,针对对流扩散方程的一维﹑二维和三维3种情况,分别建立了预报-校正的有限差分数值模型。在时间步进格式上分别采用了Crank-Nicolson格式或混合4阶Adams-Bashforth-Moulton格式,对对流项分别采用2阶精度或4阶精度,对扩散项采用了2阶精度。利用建立的数值模型求解了经典的污染物浓度场对流扩散,通过数值解与解析解的比较讨论了不同时空格式对数值模型计算结果的影响。结果表明:对空间一次导数采用4阶精度可以避免采用2阶精度带来的误差。采用混合4阶Adams-Bashforth-Moulton格式或Crank-Nicolson格式数值计算结果均与解析解吻合程度较好,但对于数组为40,40,40]的三维对流扩散问题,前者比后者省时20.7%。

The Application of Different Time & Space Schemes in Pollutant Convective-diffusive Equation

In order to understand the application of the different time and space derivative schemes in pollutant convective-diffusive equation,one-dimension,two-dimension and three-dimension models were established based on predict-correct finite difference method.In these models,time marching schemes included Crank-Nicolson scheme and a composite fourth order Adams-Bashforth-Moulton scheme.Second order accuracy or fourth order accuracy in space derivatives for convective terms and second order accuracy for diffusive terms were considered.Numerical simulations were carried out upon a classical pollutant concentration problem with these models,through the comparisons among the numerical results and the analytical solution,the effects of different schemes of time and space derivative were investigated.The results show that: Fourth order accuracy in space derivatives for convective terms can better simulate pollutant convective-diffusive problem,while second order accuracy for convective terms can not well simulate this problem.The computed results by a composite fourth order Adams-Bashforth-Moulton scheme or Crank-Nicloson scheme can better agree with the analytical solution,but for a three-dimension 40,40,40] space array,the first scheme can save 20.7% time.