非稳态导热问题有限体积法  

Unsteady heat transfer problems with finite volume method

作　　者：秦跃平[1] 孟君[1,2] 贾敬艳[1] 杨小彬[1] 刘伟[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 [2]西山煤电(集团)有限责任公司,山西太原030053

出　　处：《辽宁工程技术大学学报（自然科学版）》2013年第5期577-581,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：为了研究非稳态导热问题中的常用有限体积方案(FVM1)和新提出的有限体积方案(FVM2)的精度差异问题,采用理论推导和实例验证的方法,建立基于有限体积法原理的热平衡积分方程,利用矩形网格进行离散化,建立了平面非稳态热传导问题有限体积法数学模型,推导出与有限单元法(FEM)方案相类似的线性方程组,对比分析所建立的各个方程组中参数的差异.研究结果表明:方案FVM2与FEM精度相同,为较优方案.最后结合一个典型实例,用VB编制了数值计算软件,对比分析这两种方案,验证了上述结果.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 proposed new fmite volume scheme with the common scheme, this study derived heat equilibrium equations based on the principle of FVM, established a mathematical model of the FVM on planar unsteady heat transfer by utilizing rectangular mesh discretization, and put forward linear equations which are similar to the equations of FEM but with different parameters. The result of comparing and analyzing of these two schemes shows that FVM2 is a better scheme which has the same precision as of FEM. The conclusion is verified by a typical ease study using a VB program, and brings reference value to engineering calculations and numerical simulations.

关 键 词：有限体积法 有限单元法 控制体积 圈划方法 非稳态导热 矩形网格 精度差异 数值计算 

分 类 号：TK123[动力工程及工程热物理—工程热物理]