CAJ | 학술논문

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。
위료연구비은태도열문제중적상용유한체적방안（FVM1）화신제출적유한체적방안（FVM2）적정도차이문제，채용이론추도화실례험증적방법，건립기우유한체적법원리적열평형적분방정，이용구형망격진행리산화，건립료평면비은태열전도문제유한체적법수학모형，추도출여유한단원법（FEM）방안상유사적선성방정조，대비분석소건립적각개방정조중삼수적차이。연구결과표명：방안FVM2여FEM정도상동，위교우방안。최후결합일개전형실례，용 VB 편제료수치계산연건，대비분석저량충방안，험증료상술결과。해결과대공정계산수치모의유일정적삼고개치。
In order to compare the proposed new finite 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 case study using a VB program, and brings reference value to engineering calculations and numerical simulations.