Publication
Very high-order accurate discontinuous Galerkin method for curved boundaries with polygonal meshes
| Summary: | Preserving the optimal convergence order of discontinuous Galerkin (DG) discretisations in curved domains is a critical and well-known issue. The proposed approach relies on the reconstruction for off-site data (ROD) method developed originally within the finite volume framework. The main advantages are simplicity, since the PDE solver only considers polyg- onal domains, and versatility, since any type of boundary condition can be imposed. The developed DG–ROD method consists in splitting the boundary conditions treatment and the leading discrete equations from a classical DG formulation into two independent solvers coupled in a simple and efficient iterative procedure. A numerical benchmark is provided to assess the capability of the method with Dirichlet and Neumann boundary conditions pre- scribed on curved boundaries, demonstrating that the optimal convergence order is effectively achieved. |
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| Main Authors: | Santos, Milene |
| Other Authors: | Araújo, Adérito; Barbeiro, Sílvia; Clain, Stéphane; Costa, Ricardo Daniel Pereira da; Machado, Gaspar J. |
| Subject: | Arbitrary curved boundaries Discontinuous Galerkin method Reconstruction for off-site data method Very high-order of convergence 65K10 65N30 Ciências Naturais::Matemáticas |
| Year: | 2024 |
| Country: | Portugal |
| Document type: | article |
| Access type: | open access |
| Associated institution: | Universidade do Minho |
| Language: | English |
| Origin: | RepositóriUM - Universidade do Minho |
| Summary: | Preserving the optimal convergence order of discontinuous Galerkin (DG) discretisations in curved domains is a critical and well-known issue. The proposed approach relies on the reconstruction for off-site data (ROD) method developed originally within the finite volume framework. The main advantages are simplicity, since the PDE solver only considers polyg- onal domains, and versatility, since any type of boundary condition can be imposed. The developed DG–ROD method consists in splitting the boundary conditions treatment and the leading discrete equations from a classical DG formulation into two independent solvers coupled in a simple and efficient iterative procedure. A numerical benchmark is provided to assess the capability of the method with Dirichlet and Neumann boundary conditions pre- scribed on curved boundaries, demonstrating that the optimal convergence order is effectively achieved. |
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