用伴随方程研究烟幕施放的优化问题

从描述烟幕扩散的基本方程出发，提出了一类烟幕施放的优化问题．文中指出，这类问题由于约束条件为复杂的偏微分方程，计算量很大，难以直接求解．为了解决这一问题，引入了一种伴随方法以降低计算量．推导了三维非平坦地形下大气平流一扩散方程的伴随方程，利用伴随方程和原方程的关系，对优化问题进行了等价变形，大大降低了计算量．最后通过一个算例，对这一方法的有效性进行了演示。

Adjoint equation for optimal planning of smog screen

Start from the basic equation that describes the behaviors of smog screen in the atmosphere, a kind of optimal problems for planning smog screen are proposed. It turns out that such kind of optimal problems are very time consuming and difficult to solve in a direct way because the constraints of the problems are complex partial differential equations. An adjoint method is introduced to reduce computational demands. The adjoint equation of the three-dimensional atmospheric advection-diffusion equation for uneven terrain is derived, and the optimal problem is transformed equivalently by applying the relationships between the basic and adjoint equations. In this way, the computational demands are considerably reduced. An example is presented to illustrate the validity of the method.