Three High-Order Splitting Schemes for the 3D Transport Equation
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摘要: 在算子分裂法思想的基础上，将两种高精度的离散格式推广应用于三维对流扩散方程，同时对经典ADI格式的对流项做了改进，改进后的格式的对流项对空间具有4阶精度，而经典ADI格式对空间只有2阶精度，由此可见，提高了该格式的实用性．最后对两种典型的浓度场进行了数值模拟，将3种格式的计算结果与解析解以及其它传统差分格式的计算结果进行了对比，得出当Peclet数不大于5时，3种格式均获得了令人满意的数值结果，说明推广的这三种方法具有很高的准确性和可靠性．Abstract: Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by these two schemes, only three computational grid points were needed in each direction but the accuracy reaches the spatial fourth-order. The third scheme proposed is based on the classical ADI scheme and the accuracy of the advection term of it can reach the spatial fourth-order. Finally, two typical numerical experiments show that the solutions of these three schemes compare well with that given by the analytical solution when the Peclet number is not bigger than 5.
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