一阶线性变系数对流方程的稳定性分析

doi:10.3976/j.issn.1002-4026.2021.06.015

Abstract

Abstract:

The stability of upwind schemes for first-order linear convection equations with variable coefficients is studied herein. The conditions to ensure the stability of upwind scheme are obtained using the energy inequality and freezing coefficient methods, and the accuracy of the stability analysis theory is verified via numerical experiments.

Key words: convection equation with variable coefficients, upwind scheme, stability, energy inequality method, freezing coefficient method

CLC Number:

O241.84

ZHANG Tian-tian, XU Wen-wen, GUO Hong, DU Ming-yang, YU Chang-biao. Stability analysis of first-order linear convection equations with variable coefficients[J].Shandong Science, 2021, 34(6): 112-118.

Figures/Tables 3

References 12

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节点	迎风格式数值解	解析解	误差
x=0.1,t=0.01	0.012 2	0.010 1	0.002 1
x=0.2,t=0.02	0.045 0	0.040 8	0.004 2
x=0.3,t=0.03	0.099 1	0.092 7	0.006 4
x=0.4,t=0.04	0.175 0	0.166 5	0.008 5
x=0.5,t=0.05	0.273 5	0.262 8	0.010 7
x=0.6,t=0.06	0.395 2	0.382 3	0.012 9
x=0.7,t=0.07	0.540 7	0.525 5	0.015 2
x=0.8,t=0.08	0.710 8	0.693 3	0.017 5
x=0.9,t=0.09	0.906 1	0.886 3	0.019 8
x=1.0,t=0.10	1.127 4	1.105 2	0.022 2

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Stability analysis of first-order linear convection equations with variable coefficients

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