An adaptive quadrature-based moment closure
| Autor: | Martin Frank, Jonas Kusch |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Polynomial
Computer science Collocation (remote sensing) 01 natural sciences 010305 fluids & plasmas Quadrature (mathematics) Moment (mathematics) Maximum principle Moment closure 0103 physical sciences Applied mathematics 010306 general physics Adaptive quadrature Hyperbolic partial differential equation |
| Zdroj: | International Journal of Advances in Engineering Sciences and Applied Mathematics. 11:174-186 |
| ISSN: | 0975-5616 0975-0770 |
| 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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