Impact and importance of hyperdiffusion on the spectral element method: a linear dispersion analysis

DOI10.1016/j.jcp.2018.06.035zbMath1416.65360OpenAlexW2810842845WikidataQ58057452 ScholiaQ58057452MaRDI QIDQ2002260

Daniel R. Reynolds, Paul A. Ullrich, Mark A. Taylor, Jorge E. Guerra

Publication date: 11 July 2019

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2018.06.035

zbMATH Keywords

spectral element methodfinite element methodshigh-orderdynamical coredispersion analysislinear gravity waves

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items

Entropy stable discontinuous Galerkin methods for balance laws in non-conservative form: applications to the Euler equations with gravity, Conservation and stability in a discontinuous Galerkin method for the vector invariant spherical shallow water equations, Dispersion analysis of compatible Galerkin schemes on quadrilaterals for shallow water models, Fourier Analyses of High-Order Continuous and Discontinuous Galerkin Methods, Petrov-Galerkin flux upwinding for mixed mimetic spectral elements, and its application to geophysical flow problems, On the stability of exponential integrators for non-diffusive equations

Uses Software

• NICAM
• DYNAMICO
• ICON

Cites Work

• Unnamed Item
• Dispersive behaviour of high order finite element schemes for the one-way wave equation
• A review of element-based Galerkin methods for numerical weather prediction: finite elements, spectral elements, and discontinuous Galerkin
• The spectral element method for the shallow water equations on the sphere
• A spectral element method for fluid dynamics: Laminar flow in a channel expansion
• One step integration methods of third-fourth order accuracy with large hyperbolic stability limits
• Idempotent filtering in spectral and spectral element methods
• A compatible and conservative spectral element method on unstructured grids
• Family of spectral filters for discontinuous problems
• The Lagrange-Galerkin spectral element method on unstructured quadrilateral grids
• The variational multiscale method -- a paradigm for computational mechanics
• A spectral element basin model for the shallow water equations
• Variational multiscale stabilization of high-order spectral elements for the advection-diffusion equation
• Continuous and discontinuous Galerkin methods for a scalable three-dimensional nonhydrostatic atmospheric model: limited-area mode
• Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations
• A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows
• Filter-based stabilization of spectral element methods
• Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA)
• Dispersive and Dissipative Behavior of the Spectral Element Method
• Convergence of Spectral Methods for Nonlinear Conservation Laws
• High-Order Methods for Incompressible Fluid Flow
• Residual‐based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods
• Global optimization of explicit strong-stability-preserving Runge-Kutta methods
• Spectral methods for hyperbolic problems