Velocity-correction Schemes for Solving Incompressible Navier-Stokes Equations Based on Picard Iteration

doi:10.19596/j.cnki.1001-246x.8810

Abstract

Abstract:

The implementation flow of processing incompressible Navier-Stokes equations based on velocity-correction schemes is introduced, and velocity-correction schemes based on Picard iteration is developed by introducing Picard linearization to process the convection term in the velocity governing equation. Compared with the traditional method, the projection method after Picard linearization can be solved with a larger time step, which improves the stability of the solution method, and the convergence accuracy meets the requirements, which confirms the reliability of the solution method.

Key words: Navier-Stokes equations, Picard linearization, velocity-correction schemes

Linmao YIN, Yulong ZHANG, Yang YANG, Fujian XIAO, Bingyan JIANG. Velocity-correction Schemes for Solving Incompressible Navier-Stokes Equations Based on Picard Iteration[J]. Chinese Journal of Computational Physics, 2025, 42(1): 10-17.

Figures/Tables 11

References 26

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	60	90	120	150	收敛阶
E₂_u-TPM	4.64×10^-4	2.01×10^-4	1.14×10^-4	7.39×10^-5	1.952 3
E₂_u-PPM	4.16×10^-4	1.87×10^-4	1.06×10^-4	6.88×10^-5	1.954 6
E₂_v-TPM	1.28×10^-4	5.65×10^-5	3.19×10^-5	2.05×10^-5	1.979 2
E₂_v-PPM	1.43×10^-4	6.33×10^-5	3.56×10^-5	2.28×10^-5	1.997 9
E₂_p-TPM	9.19×10^-4	4.22×10^-4	2.48×10^-4	1.66×10^-4	1.820 5
E₂_p-PPM	1.64×10^-3	7.34×10^-4	4.18×10^-4	2.72×10^-4	1.940 8

	60	90	120	150	收敛阶
E₂_u-TPM	4.64×10^-4	2.01×10^-4	1.14×10^-4	7.39×10^-5	1.952 3
E₂_u-PPM	4.16×10^-4	1.87×10^-4	1.06×10^-4	6.88×10^-5	1.954 6
E₂_v-TPM	1.28×10^-4	5.65×10^-5	3.19×10^-5	2.05×10^-5	1.979 2
E₂_v-PPM	1.43×10^-4	6.33×10^-5	3.56×10^-5	2.28×10^-5	1.997 9
E₂_p-TPM	9.19×10^-4	4.22×10^-4	2.48×10^-4	1.66×10^-4	1.820 5
E₂_p-PPM	1.64×10^-3	7.34×10^-4	4.18×10^-4	2.72×10^-4	1.940 8

	Re	1	100	400	1 000	5 000
σ_min	传统投影法	0.0	1.5	30.4	71.2	243.5
	Picard投影法	0.0	0.0	5.4	23.9	147.6

	Re	1	100	400	1 000	5 000
σ_min	传统投影法	0.0	1.5	30.4	71.2	243.5
	Picard投影法	0.0	0.0	5.4	23.9	147.6

Re	传统投影法		Picard投影法
Re	最优σ	迭代步数	最优σ	迭代步数
400	30.4	1 706	5.4	525
1 000	71.2	8 131	23.9	3 037