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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[1] Komatsu T,Ohgushi K,Asai K.Refined numerical scheme for advective transport in diffusion simulation[J].Journal of Hydraulic Engineering,1997,123(1):41—50. doi: 10.1061/(ASCE)0733-9429(1997)123:1(41) [2] ZHENG Yong-hong,SHEN Yong-ming,QIU Da-hong.A high-order splitting scheme for the advection diffusion equation[J].Journal of Environmental Sciences,2001,13(4):444—448. [3] 郑永红,沈永明,王利生,等.污染物移流扩散方程的高精度分裂格式[J].水利学报,2002,(2):41—46. [4] 郑永红.波浪、潮流、污染物迁移扩散数学模型及其数值模拟[R]. 博士后工作报告.大连：大连理工大学,2000，79—103. [5] Lardner R W,Song Y.An algorithm for three-dimensional convection and diffusion with very different horizontal and vertical scales[J].Internat J Numer Methods Engrg,1991,32:1303—1319. doi: 10.1002/nme.1620320609 [6] Sommeijer B P,Kok J.Implementation and performance of the time integration of a 3D numerical transport model[J].Internat J Numer Methods Fluids,1995,21:349—367. doi: 10.1002/fld.1650210407 [7] Sankaranayanan S,Shankar N J,Cheong H F.Three-dimensional finite difference model for transport of conservative pollutants[J].Ocean Engineering,1998,25(6):425—442. doi: 10.1016/S0029-8018(97)00008-5 [8] Szymkiewicz R.Oscillation-free solution of shallow water equations for nonstaggeted grid[J].Journal of Hydraulic Engineering,1993,119(10):1118—1137. doi: 10.1061/(ASCE)0733-9429(1993)119:10(1118) -
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