A Flux Reconstruction Stochastic Galerkin Scheme for Hyperbolic Conservation Laws
文献类型：期刊论文
| 作者 | Xiao TB(肖天白); Kusch, Jonas3; Koellermeier, Julian4; Frank, Martin2 |
| 刊名 | JOURNAL OF SCIENTIFIC COMPUTING
 |
| 出版日期 | 2023-04 |
| 卷号 | 95期号:1页码:18 |
| 关键词 | Computational fluid dynamics High order methods Flux reconstruction Uncertainty quantification Stochastic Galerkin |
| ISSN号 | 0885-7474 |
| DOI | 10.1007/s10915-023-02143-3 |
| 英文摘要 | The study of uncertainty propagation poses a great challenge to design high fidelity numerical methods. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction scheme for hyperbolic conservation laws with random inputs. High order numerical approximation is adopted simultaneously in physical and random space, i.e., the modal representation of solutions is based on an orthogonal polynomial basis and the nodal representation is based on solution collocation points. Therefore, the numerical behaviors of the scheme in the (physical random) phase space can be designed and understood uniformly. A family of filters is developed in multi dimensional cases to mitigate the Gibbs phenomenon arising from discontinuities in both physical and random space. The filter function is switched on and off by the dynamic detection of discontinuous solutions, and a slope limiter is employed to preserve the positivity of physically realizable solutions. As a result, the proposed method is able to capture the stochastic flow evolution where resolved and unresolved regions coexist. Numerical experiments including a wave propagation, a Burgers' shock, a one dimensional Riemann problem, and a two dimensional shock vortex interaction problem are presented to validate the current scheme. The order of convergence of the high order scheme is identified. The capability of the scheme for simulating smooth and discontinuous stochastic flow dynamics is demonstrated. The open source codes to reproduce the numerical results are available under the MIT license (Xiao et al. in FRSG: stochastic Galerkin method with flux reconstruction. |
| 分类号 | 一类 |
| WOS研究方向 | Mathematics, Applied |
| 语种 | 英语 |
| WOS记录号 | WOS:000936836100001 |
| 资助机构 | Alexander von Humboldt Foundation [3.5 CHN 1210132 HFST P] ; Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [258734477 SFB 1173] ; CogniGron research center ; Ubbo Emmius Funds (University of Groningen) |
| 其他责任者 | Xiao, TB (corresponding author), Chinese Acad Sci, Inst Mech, State Key Lab High Temp Gas Dynam, Beijing, Peoples R China. |
| 源URL | [http://dspace.imech.ac.cn/handle/311007/91839]  |
| 专题 | 力学研究所_高温气体动力学国家重点实验室 |
| 作者单位 | 1.Univ Groningen, Bernoulli Inst Math, Comp Sci & Artificial Intelligence, Groningen, Netherlands 2.Chinese Acad Sci, Inst Mech, State Key Lab High Temp Gas Dynam, Beijing, Peoples R China 3.Karlsruhe Inst Technol, Steinbuch Ctr Comp, Karlsruhe, Germany 4.Univ Innsbruck, Inst Math, Innsbruck, Austria |
| 推荐引用方式 GB/T 7714 | Xiao TB,Kusch, Jonas,Koellermeier, Julian,et al. A Flux Reconstruction Stochastic Galerkin Scheme for Hyperbolic Conservation Laws[J]. JOURNAL OF SCIENTIFIC COMPUTING,2023,95(1):18. |
| APA | 肖天白,Kusch, Jonas,Koellermeier, Julian,&Frank, Martin.(2023).A Flux Reconstruction Stochastic Galerkin Scheme for Hyperbolic Conservation Laws.JOURNAL OF SCIENTIFIC COMPUTING,95(1),18. |
| MLA | 肖天白,et al."A Flux Reconstruction Stochastic Galerkin Scheme for Hyperbolic Conservation Laws".JOURNAL OF SCIENTIFIC COMPUTING 95.1(2023):18. |
入库方式： OAI收割
来源：力学研究所
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