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为研究平面导热问题中常用的3种有限体积方案(FVM2、FVM3、FVM4)和新提出的方案(FVM1)的精度差异问题.采用理论推导和实例验证的方法,对解算区域进行三角形网格划分,建立了平面导热问题有限体积法数学模型,推导出了有限体积法解决平面温度场问题的线性方程组,分析了各种有限体积法方案以及有限单元法计算公式的类似性和公式中参数的差异.编制了数值计算软件,结合特例,解算出不同有限体积方案的温度分布,并与理论解进行了对比.研究结果表明:方案FVM1与FEM精度相同,且与理论值基本一致,为最优方案.在不考虑第三类边界情况下,FVM4的精度也与FEM精度相同.该结果对工程计算数值模拟有一定的参考价值.
In order to study the difference of accuracy between the three finite volume schemes (FVM2, FVM3 and FVM4) and the newly proposed scheme (FVM1) which are commonly used in the plane thermal conduction problem, a triangular meshes The finite volume method is used to solve the problem of plane temperature field and the linear equations are solved. The finite volume method and the similarity between the finite element method and the formula The numerical simulation software is compiled and the special cases are used to calculate the temperature distribution of different finite volume schemes and compared with the theoretical solution.The results show that the accuracy of the scheme FVM1 and FEM are the same and the theoretical values are basically the same The optimal solution is that FVM4 has the same precision as FEM without considering the third type of boundary.The result is of certain value to numerical simulation of engineering calculation.