A high-order discontinuous Galerkin method for unsteady advection-diffusion problems

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• 作者：Raunak Borker^a ; ^{rborker@stanford.edu} ; Charbel Farhat^a ; ^b ; ^c ; ^{cfarhat@stanford.edu} ; Radek Tezaur^a ; ^{rtezaur@stanford.edu}
• 关键词：Unsteady advection&ndash ; diffusion ; Discontinuous Galerkin ; Lagrange multipliers ; High-order ; Enriched finite element methods
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：332
• 期：Complete
• 页码：520-537
• 全文大小：3863 K
• 卷排序：332

文摘

A high-order discontinuous Galerkin method with Lagrange multipliers is presented for the solution of unsteady advection–diffusion problems in the high Péclet number regime. It operates directly on the second-order form of the governing equation and does not require any stabilization. Its spatial basis functions are chosen among the free-space solutions of the homogeneous form of the partial differential equation obtained after time-discretization. It also features Lagrange multipliers for enforcing a weak continuity of the approximated solution across the element interface boundaries. This leads to a system of differential–algebraic equations which are time-integrated by an implicit family of schemes. The numerical stability of these schemes and the well-posedness of the overall discretization method are supported by a theoretical analysis. The performance of this method is demonstrated for various high Péclet number constant-coefficient model flow problems.