基于广义梯形公式的二维Burgers方程三阶数值解法OA
A 3rd-Order Numerical Method for 2D Burgers Equations Based on the Generalized Trapezoid Formula
Burgers 方程因其对非线性传输与耗散机制的精准描述,在流体力学等多个领域有着广泛的应用.本文研究了一类二维非线性 Burgers 方程的数值解法.首先,通过 Hopf-Cole 变换将 Burgers 方程转换成一类热传导方程,在空间方向利用高阶重心有理谱逼近,得到半离散格式.然后,在时间方向采用含参数 δ 的广义梯形公式离散,从而得到变换后方程的全离散格式.当参数 δ=1/3 时,时间方向截断误差达到三阶精度.最后,借助数值算例验证了截断误差分析的正确性.
The Burgers equation has been widely applied in many fields such as fluid mechanics due to its accu-rate description of nonlinear transport and dissipation mechanisms.A numerical method for a class of 2D non-linear Burgers equations was studied.Firstly,the Burgers equation was transformed into a class of heat conduc-tion equations via the Hopf-Cole transformation.Then,the high-order barycentric rational spectral approxima-tion was used in the spatial direction to obtain the semi-discrete scheme,and the generalized trapezoidal formu-la with parameterδwas adopted in the temporal direction,thus to obtain the fully discrete scheme for the trans-formed equation.For parameter δ=1/3,the truncation error in the temporal direction has 3rd-order accuracy.Finally,numerical examples verify the correctness of the truncation error analysis.
刘陶;刘利斌
南宁师范大学 广西应用数学中心,南宁 530100南宁师范大学 广西应用数学中心,南宁 530100
数理科学
Burgers方程Hopf-Cole高阶重心有理插值配置法广义梯形公式
Burgers equationHopf-Colehigh-order barycentric rational interpolation collocation methodgeneralized trapezoidal formula
《应用数学和力学》 2026 (9)
1197-1210,14
国家自然科学基金(12361087)广西自然科学基金(2025GXNSFAA069738)
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