Abstract A novel formulation for numerical solution of heat conduction problems using superposition of exact solutions (SES) to represent temperature on sub-elements of a region is described and demonstrated. A simple 1-D linear problem is used to describe the method and highlight potential benefits; however, extensions to higher geometric dimensions and linearization for temperature-dependent properties are possible. Significant new features of this method which are not part of conventional approaches are: local functions for temperature are both time- and space-dependent; both heat flux and temperature at the boundaries of each element have continuous representation; temperature and heat flux can be evaluated at every location in the domain; and heat fluxes on both internal and external boundaries are represented as linear functions of time. The SES method is validated against several exact solutions for the linear case (constant thermophysical properties) and is shown to have accuracy orders of magnitude greater than conventional Crank-Nicolson method. Extension to higher geometries and temperature-dependent properties are discussed.

中文翻译：

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使用精确解叠加的热传导新数值方法

摘要 描述并演示了一种使用精确解叠加 (SES) 来表示区域子元素温度的热传导问题数值解的新公式。一个简单的一维线性问题被用来描述该方法并突出潜在的好处；然而，可以扩展到更高的几何尺寸和线性化温度相关特性。这种方法不属于传统方法的重要新特征是： 温度的局部函数既依赖于时间又依赖于空间；每个单元边界处的热通量和温度均具有连续表示；可以在域中的每个位置评估温度和热通量；内部和外部边界上的热通量表示为时间的线性函数。SES 方法针对线性情况（恒定热物理特性）的几种精确解进行了验证，并且显示出比传统的 Crank-Nicolson 方法高几个数量级的精度。讨论了对更高几何形状和温度相关特性的扩展。