On Nonlinear Closures for Moment Equations Based on Orthogonal Polynomials
It addresses the moment closure problem in gas kinetic theory, offering a new method that outperforms existing approaches like Grad's closure and maximum-entropy for certain distributions.
The paper proposes a moment closure method based on orthogonal polynomials from Gram matrices, proving attractive mathematical properties and demonstrating very accurate results for a wide range of distribution functions in gas kinetic theory.
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.