An adaptive quadrature-based moment closure

Autor: Martin Frank, Jonas Kusch
Rok vydání: 2019
Předmět:
Zdroj: International Journal of Advances in Engineering Sciences and Applied Mathematics. 11:174-186
ISSN: 0975-5616
0975-0770
DOI: 10.1007/s12572-019-00252-7
Popis: Methods to numerically quantify uncertainties in hyperbolic equations can be divided into intrusive and non-intrusive techniques. Standard intrusive methods such as Stochastic Galerkin yield oscillatory solutions in the vicinity of shocks and require a new implementation. The more advanced Intrusive Polynomial Moment (IPM) method necessitates a costly solution reconstruction, but promises bounds on oscillatory over- and undershoots. Non-intrusive methods such as Stochastic Collocation (SC) can suffer from aliasing errors, and their black-box nature comes at the cost of loosing control over the time evolution of the solution. In this paper, we derive an intrusive method, which adaptively switches between SC and IPM updates by locally refining the quadrature set on which the solution is calculated. The IPM reconstruction of the solution is performed on the quadrature set and uses suitable basis vectors, which reduces numerical costs and allows non-oscillatory reconstructions. We test the method on Burger’s equation, where we obtain non-oscillating solution approximations fulfilling the maximum principle.
Databáze: OpenAIRE
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