Quadrature-free discontinuous Galerkin method with code generation features for shallow water equations on automatically generated block-structured meshes

• Published in: Advances in water resources Vol. 138; p. 103552
• Main Authors: Faghih-Naini, Sara, Kuckuk, Sebastian, Aizinger, Vadym, Zint, Daniel, Grosso, Roberto, Köstler, Harald
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2020
• Subjects: algorithms; Block-structured mesh; Code generation domain specific languages (DSL); equations; Local discontinuous Galerkin method (LDG); porous media; Python SymPy; Quadrature-free formulation; Shallow water equations; water resources; Shallow water equations; Quadrature-free formulation; Python SymPy; Local discontinuous Galerkin method (LDG); Code generation domain specific languages (DSL); Block-structured mesh
• ISSN: 0309-1708; 1872-9657; 1872-9657
• DOI: 10.1016/j.advwatres.2020.103552

•Quadrature-free discontinuous Galerkin discretizations have the potential to increase model code performance.•Block-structured grids are a compromise between the structured (not geometrically flexible) and unstructured (difficult to make computationally efficient) ones.•Code generation and domain-specific languages allow for a separation of concerns between applications scientists and code developers. Although discretizations of the shallow water equations (SWE) based on the discontinuous Galerkin (DG) method are well established, their computational performance still generally lags behind that of the finite volume discretizations. In explicit and semi-implicit time stepping schemes commonly used in connection with the SWE models, the most computationally expensive parts of a DG algorithm are the element and edge integrals computed via loops over quadrature points. We propose a quadrature-free DG formulation for the SWE that replaces quadrature integrations by analytical evaluations. The method is implemented within the code generation framework of the ExaStencils project using the SymPy Python library. The new formulation uses block-structured triangular meshes automatically generated for a given number of blocks.