导热问题中4种有限体积方案对比  

Four finite volume schemes for heat transfer problems

作　　者：秦跃平[1] 贾敬艳[1] 刘伟[1] 杨小彬[1] 

机构地区：[1]中国矿业大学(北京)资源与安全工程学院,北京100083

出　　处：《辽宁工程技术大学学报（自然科学版）》2013年第6期763-767,共5页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学资金资助项目(50674091)

摘　　要：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 compare the new finite volume scheme we proposed with three common schemes, this study derived the heat equilibrium equations based on the principle of FVM. Taking triangular elements to establish a mathematical model of the FVM on planar steady heat transfer, linear equations are put forward which are similar to the equations of FEM but with different parameters. To exam a specific case, a software is developed to calculate the temperature distribution under different conditions, and modeled results are compared with the theoretical solutions. Through analyzing, the optimal scheme FVM1 is obtained which has the same precision with FEM and without considering the third boundary, FVM4 is also feasible.

关 键 词：数值模拟 有限体积法 有限单元法 导热 三角形网格 控制体积 圈划方法 精度差异 

分 类 号：TK123[动力工程及工程热物理—工程热物理]