In the present work, an approach to the moment closure problem on the basis of orthogonal polynomials derived from Gram matrices is proposed. Its properties are studied in the context of the moment closure problem arising in gas kinetic theory, for which the proposed approach is proven to have multiple attractive mathematical properties. Numerical studies are carried out for model gas particle distributions and the approach is compared to other moment closure methods, such as Grad's closure and the maximum-entropy method. The proposed ``Gramian'' closure is shown to provide very accurate results for a wide range of distribution functions.

翻译：本文提出了一种基于格拉姆矩阵导出的正交多项式解决矩闭合问题的方法。在气体动理学理论中出现的矩闭合问题背景下，研究了该方法的性质，证明了所提方法具有多个吸引人的数学特性。针对模型气体粒子分布进行了数值研究，并将该方法与格拉姆闭合、最大熵方法等其他矩闭合方法进行了比较。研究表明，所提出的"格拉姆矩阵"闭合方法能在广泛的分布函数范围内提供非常精确的结果。