Three High-Order Splitting Schemes for the 3D Transport Equation

WANG Shou-dong; SHEN Yong-ming

Volume 26 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(8): 921-928

WANG Shou-dong, SHEN Yong-ming. Three High-Order Splitting Schemes for the 3D Transport Equation[J]. Applied Mathematics and Mechanics, 2005, 26(8): 921-928.

Citation:

WANG Shou-dong, SHEN Yong-ming. Three High-Order Splitting Schemes for the 3D Transport Equation[J]. Applied Mathematics and Mechanics, 2005, 26(8): 921-928.

Citation:

WANG Shou-dong, SHEN Yong-ming. Three High-Order Splitting Schemes for the 3D Transport Equation[J]. Applied Mathematics and Mechanics, 2005, 26(8): 921-928.

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Three High-Order Splitting Schemes for the 3D Transport Equation

State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, P. R. China

Received Date: 2004-04-13
Rev Recd Date: 2005-03-29
Publish Date: 2005-08-15

Abstract

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.
- 3-D advection and diffusion equation,
- operator splitting method,
- high-order scheme,
- numerical modeling

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References(8)

References

[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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