摘要
对于常系数或弱非线性导热方程采用经典的有限容积离散格式就可以获得较高精度的数值解,而对于变系数或强线性导热方程则会产生较大的误差,为获得满意的结果需要加密网格,因此会大量消耗存储空间和运算时间从而增加计算成本.针对上述问题,本文基于微元体平衡法并结合控制容积积分法,由能量守恒定律重新推导了关于节点温度的差分方程,给出了导热方程的高精度离散格式,并推导了各坐标系下差分方程系数的计算公式.通过几个代表性的算例对本文格式进行了考核并与文献中经典离散格式的计算结果进行了对比.数值试验结果表明,无论是非线性还是变截面导热问题,采用本文格式在较少的网格数下均能获得高精度的解.
For constant coefficient or wear nonlinearity heat conduction equation, the highly accuracy numerical solution can be obtained by the classical discretization scheme based on the finite volume method. And as for variable coefficient or strong nonlinear heat conduction equation, big error may occur by using above classical discretization scheme. The mesh system should be refined to obtain highly accuracy numerical solution, which will consume large storage space and operation time, and the cost will increase significantly. In order to solve this problem, a highly accuracy discretization scheme based on the element balance method and control volume integral method is proposed and coefficients of the equation discrete equation are derived by using energy conservation law. The new scheme is evaluated by solving several typical problems. And the solutions obtained through different discretization schemes are compared with each other. Numerical tests show that whatever the heat conduction problem is, the highly accuracy numerical solution can be always obtained by using the new scheme proposed in this paper, even if the cell number is very small.
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2010年第3期412-417,共6页
Journal of Central China Normal University：Natural Sciences
基金
国家自然科学基金资助项目(50376043)
关键词
导热方程
非线性
变系数
离散格式
元体平衡法
控制容积积分法
heat conduction equations
nonlinearity
variable coefficient
discretization scheme
element balance method
control volume integral method
