This work aims to develop and test a projection technique for the construction of closing equations of moment systems. One possibility to define such a closure consists in reconstructing an underlying kinetic distribution from a vector of moments, then expressing the closure based on this reconstructed function.Exploiting the geometry of the realizability domain, i.e. the set of moments of positive distribution function, we decompose any realizable vectors into two parts, one corresponding to the moments of a chosen equilibrium function, and one obtain by a projection onto the boundary of the realizability domain in the direction of equilibrium function. A realizable closure of both of these parts are computed with standard techniques providing a realizable closure for the full system. This technique is tested for the reduction of a radiative transfer equation in slab geometry.

中文翻译：

---

基于可实现性域边界上的投影的矩闭合：一维情况

这项工作旨在开发和测试一种投影技术，用于构造力矩系统的闭合方程。定义这种闭合的一种可能性在于，根据矩矢量来重构基本的动力学分布，然后基于该重构函数来表达闭合。利用可实现域的几何结构，即对于正分布函数的矩集，我们将任何可实现的向量分解为两部分，一个对应于所选均衡函数的矩，一个通过在均衡函数方向上投影到可实现性域的边界上而获得。这两个部分的可实现的闭合都是使用标准技术计算的，从而为整个系统提供了可实现的闭合。测试该技术可简化平板几何中的辐射传递方程。