三维非笛卡儿张量的空间度量张量的计算

Calculation of Space Metric Tensor for 3-Dimensional Non-Cartesian Tensor

文章提出了三维非笛卡儿张量的空间度量张量的一系列计算公式,可借以建立油气输送等复杂系统的动量或能量传递的物理问题在任意坐标系中的数学模型。通过示例说明,在正交或非正交的任意曲线坐标系中选择和确定物理基及空间度量张量的方法,得到了与以往文献吻合的满意结果。

A series of formulae of calculating physical base and space metric tensor for 3-dimensional non-Cartesian tensor are presented which can be used to obtain the mathematical model for describing geometry and mechanics of continua such as oil and gas in energy-deliverying. A method for choicing and determining physical base and space metric tensor in an arbitrary curvilinear (orthogonal and non-orthogonal) coordinate system is illustrated by examples. The calculation shows clearly that this method is correct and effective. And the results are in excellent agreement with those in references publicated already.