Advanced techniques for entropy-based moment methods for linear kinetic equations
Final Report Abstract
In the project ‘Advanced techniques for entropy-based moment methods for linear kinetic equations’ the applicant and co-authors developed a novel modification for the entropy-based moment equations which greatly simplifies their otherwise complicated numerical solution with high-order methods. The regularization technique was thoroughly analyzed and proven to stand on much more theoretically secure ground than the realizability limiter which was expected to be the solution. The main advantages of the regularization technique are that it is simple to implement, retains or accurately approximates almost all of the attractive theoretical properties of the original entropybased moment equations, and is provably convergent to the solution of the original equations under some mild assumptions. Other areas of the project did not yield particularly promising results. The implementation of filters in more general equations, namely in uncertainty quantification for scalar conservation laws with the Intrusive Polynomial Moment method, did smooth the solutions, but the choice of the filtering parameter remains a challenge. We were also unable to find a suitable semi-implicit or implicit time integration method for moment equations with stiff collision terms. Perhaps the combination of semi-implicit methods with the new regularization technique will offer a promising avenue for future research.
Publications
- A regularized entropy-based moment method for kinetic equations. SIAM Journal on Applied Mathematics Volume 79–5 (2019), pp. 1627–1653
G.W. Alldredge, M. Frank, C.D. Hauck
(See online at https://doi.org/10.1137/18M1181201) - Maximum-principle-satisfying second-order Intrusive Polynomial Moment scheme. SMAI Journal of Computational Mathematics, 5 (2019), pp. 23-51
J. Kusch, G.W. Alldredge, M. Frank
(See online at https://doi.org/10.5445/IR/1000092820)
