时域推进与边界元混合瞬态热传导问题

 对时间变量在小区间内应用多项式插值,对空间变量采用边界元求解,提出一种新的分析瞬态热传导问题的计算格式。与现行的利用含时间变量的基本解所得到的边界元计算格式相比较,具有基本解简单易得、系数矩阵容易计算以及无重复积分等优点;与向前差分消去时间因子的边界元计算格式相比较,则在算法稳定性、计算精度以及时间步长的选取等方面具有明显的优势,并且很容易推广到求解非线性问题。算例表明,采用时域推进与边界元混合方法分析瞬态热传导问题有效可行。

UNCONDITIONALLY STABLE TIME-STEP-TIME METHOD COMBINED WITH BOUNDARY ELEMENT TECHNIQUE FOR TRANSIENT HEAT CONDUCTION ANALYSIS

By utilizing a polynomial interpolation for the time variable in a partitioned small interval and boundary element approximation for the spatial variables,a new analyzing technique for transient heat conduction problems is presented in this paper. Compared with those boundary element formulation procedures based on time-dependent fundamental solutions, the proposed method has the advantages that a fundamental solution is simple and much easier to be obtained, the boundary element coefficient matrices require less labourious computations and repeated integration on the time variable disappears. The present method also has advantages over a forward-difference based solution procedure. Several numerical examples show that the solutions with the present method converge to the exact ones far quickly and a larger time step selection is permitted.