Direct reconstruction method for discontinuous Galerkin methods on higher-order mixed-curved meshes. II: Surface integration

DOI10.1016/j.jcp.2020.109514zbMath1437.76025OpenAlexW2949085903MaRDI QIDQ781979

Hojun You, Chongam Kim

Publication date: 21 July 2020

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2020.109514

zbMATH Keywords

surface integrationadaptive modified Gram-Schmidt orthonormalization processdirect reconstruction methodmixed-curved meshquadrature-free method

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Compressible Navier-Stokes equations (76N06)

Related Items

A low dissipation finite difference nested multi-resolution WENO scheme for Euler/Navier-Stokes equations, A new finite volume multi-resolution central WENO scheme for Navier-Stokes equations on staggered meshes, Implicit Quadrature-Free Direct Reconstruction Method for Efficient Scale-Resolving Simulations, Architecture-based and target-oriented algorithm optimization of high-order methods via complete-search tensor contraction, Deneb: an open-source high-performance multi-physical flow solver based on high-order DRM-DG method, Direct reconstruction method for discontinuous Galerkin methods on higher-order mixed-curved meshes III. Code optimization via tensor contraction, New finite difference unequal-sized Hermite WENO scheme for Navier-Stokes equations

Uses Software

• polyquad

Cites Work

• A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers
• A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
• Polymorphic nodal elements and their application in discontinuous Galerkin methods
• Influence of reference-to-physical frame mappings on approximation properties of discontinuous piecewise polynomial spaces
• High-order multi-dimensional limiting strategy with subcell resolution. I: Two-dimensional mixed meshes
• On the identification of symmetric quadrature rules for finite element methods
• Direct reconstruction method for discontinuous Galerkin methods on higher-order mixed-curved meshes. I: Volume integration
• Agglomeration based discontinuous Galerkin discretization of the Euler and Navier-Stokes equations
• Discontinuous Galerkin solution of the Reynolds-averaged Navier-Stokes and \(k-\omega\) turbulence model equations
• Interpolation error bounds for curvilinear finite elements and their implications on adaptive mesh refinement
• Efficient quadrature-free high-order spectral volume method on unstructured grids: theory and 2D implementation
• Numerical Integration in Multiple Dimensions with Designed Quadrature
• Explicit Runge–Kutta Methods with Estimates of the Local Truncation Error
• On a Cell Entropy Inequality for Discontinuous Galerkin Methods
• A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
• Generalized Gaussian quadrature rules on arbitrary polygons
• Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equations