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对流-扩散方程逆过程反问题是一个不适定问题。利用伴随同化方法及处理数学物理反问题的技巧对该问题进行了数值研究。为了克服反问题中不适定性带来的困难,利用反问题中正则化思想,这里在目标函数中引入了正则项,其目的是克服不适定和计算不稳定。数值模拟结果表明,与通常的伴随同化方法相比,该方法无论是目标函数的下降速度、解的精确度都有较明显改进。因而,利用此方法求解对流-扩散方程逆过程反问题具有稳定性好、精度高的特点。利用该方法反演对流-扩散方程逆过程反问题的初值是可行的。
Adverse-inverse problem of convection-diffusion equation is an ill-posed problem. The problem is studied numerically by using the assimilation method and the skill of dealing with the inverse problem of mathematical physics. In order to overcome the ill-posed problems in the inverse problem, we use the regularization idea in the inverse problem. Here we introduce the regular term in the objective function to overcome the ill-posedness and the calculation uncertainty. The numerical simulation results show that compared with the usual concomitant assimilation method, this method shows a significant improvement in both accuracy and resolution of the objective function. Therefore, using this method to solve the inverse problem of inverse convection-diffusion equation has the advantages of good stability and high precision. It is feasible to use this method to retrieve the inverse of inverse process of convection - diffusion equation.