A review of element-based Galerkin methods for numerical weather prediction: finite elements, spectral elements, and discontinuous Galerkin
From MaRDI portal
Publication:525344
DOI10.1007/s11831-015-9152-1zbMath1360.86004OpenAlexW1578649609WikidataQ59200218 ScholiaQ59200218MaRDI QIDQ525344
Publication date: 3 May 2017
Published in: Archives of Computational Methods in Engineering (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/2117/85001
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) Meteorology and atmospheric physics (86A10) Computational methods for problems pertaining to geophysics (86-08)
Related Items
A spectral deferred correction method for incompressible flow with variable viscosity, Multigrid preconditioners for the hybridised discontinuous Galerkin discretisation of the shallow water equations, A statically condensed discontinuous Galerkin spectral element method on Gauss-Lobatto nodes for the compressible Navier-Stokes equations, A horizontally explicit, vertically implicit (HEVI) discontinuous Galerkin scheme for the 2-dimensional Euler and Navier-Stokes equations using terrain-following coordinates, High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid, Convection experiments with the exponential time integration scheme, Entropy stable discontinuous Galerkin methods for balance laws in non-conservative form: applications to the Euler equations with gravity, Review of the strain-based formulation for analysis of plane structures Part I: Formulation of basics and the existing elements, A priori error analysis of new semidiscrete, Hamiltonian HDG methods for the time-dependent Maxwell’s equations, A family of well-balanced WENO and TENO schemes for atmospheric flows, Domain-specific implementation of high-order discontinuous Galerkin methods in spherical geometry, A novel multivariate spectral local quasilinearization method (MV-SLQLM) for modelling flow, moisture, heat, and solute transport in soil, A discontinuous Galerkin approach for Atmospheric flows with implicit condensation, Impact and importance of hyperdiffusion on the spectral element method: a linear dispersion analysis
Uses Software
Cites Work
- Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations
- An unstructured-mesh atmospheric model for nonhydrostatic dynamics
- Adaptive discontinuous evolution Galerkin method for dry atmospheric flow
- Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations
- A primal-dual mimetic finite element scheme for the rotating shallow water equations on polygonal spherical meshes
- Mass conservation of the unified continuous and discontinuous element-based Galerkin methods on dynamically adaptive grids with application to atmospheric simulations
- Extension of fractional step techniques for incompressible flows: the preconditioned Orthomin(1) for the pressure Schur complement
- EULAG, a computational model for multiscale flows
- Computational aspects of a scalable high-order discontinuous Galerkin atmospheric dynamical core
- Modelling atmospheric flows with adaptive moving meshes
- Classical and variational multiscale LES of the flow around a circular cylinder on unstructured grids
- MCore: a non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods
- Implementation of the entropy viscosity method with the discontinuous Galerkin method
- Entropy viscosity method for nonlinear conservation laws
- Finite element methods for linear hyperbolic problems
- Well balanced finite volume methods for nearly hydrostatic flows
- A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media
- The NCAR spectral element climate dynamical core: semi-implicit Eulerian formulation
- Stabilized methods for compressible flows
- The spectral element method for the shallow water equations on the sphere
- A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
- A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes --application to vortex shedding
- A parameter-free dynamic alternative to hyper-viscosity for coupled transport equations: application to the simulation of 3D squall lines using spectral elements
- Variational multiscale turbulence modelling in a high-order spectral element method
- A spectral element method for fluid dynamics: Laminar flow in a channel expansion
- Adaptive mesh refinement for hyperbolic partial differential equations
- Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations
- Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows
- A massively parallel fractional step solver for incompressible flows
- Idempotent filtering in spectral and spectral element methods
- SUPG finite element computation of inviscid supersonic flows with \(YZ \beta\) shock-capturing
- A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations
- Entropy-based nonlinear viscosity for Fourier approximations of conservation laws
- Numerical techniques for global atmospheric models.
- Three-dimensional elliptic grid generation with fully automatic boundary constraints
- On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations. I: A review
- The variational multiscale method for laminar and turbulent flow
- A new finite element formulation for computational fluid dynamics. II. Beyond SUPG
- A new finite element formulation for computational fluid dynamics. III: The generalized streamline operator for multidimensional advective- diffusive systems
- Adaptive grid refinement for numerical wather prediction
- Local adaptive mesh refinement for shock hydrodynamics
- A new approach for the FEM simulation of viscoelastic flows
- Transformation of three-dimensional regions onto rectangular regions by elliptic systems
- A finite-element method for a 1-D water flooding problem with gravity
- Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
- Family of spectral filters for discontinuous problems
- A relationship between stabilized finite element methods and the Galerkin method with bubble functions
- Stabilized finite element methods. I.: Application to the advective- diffusive model
- The intrinsic time for the streamline upwind/Petrov-Galerkin formulation using quadratic elements
- Characteristic-Galerkin and Galerkin/least-squares space-time formulations for the advection-diffusion equation with time-dependent domains
- On the use of a coordinate transformation for the solution of the Navier- Stokes equations
- Uniform convergence of the upwind finite element approximation for semilinear parabolic problems
- Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: Preserving boundary conditions and interpretation of the filter as a diffusion
- The variational multiscale method -- a paradigm for computational mechanics
- Stabilized spectral methods for the Navier-Stokes equations: residual-free bubbles and preconditioning
- A discontinuous Galerkin method for the viscous MHD equations
- A spectral element basin model for the shallow water equations
- Explicit streamline diffusion finite element methods for the compressible Euler equations in conservation variables
- Analysis of a stabilized finite element approximation of the transient convection-diffusion-reaction equation using orthogonal subscales
- Lagrange-Galerkin methods on spherical geodesic grids
- \(b=\int g\)
- Bubble-stabilized spectral methods for the incompressible Navier-Stokes equations
- High-order accurate discontinuous finite element solution of the 2D Euler equations
- A two-dimensional moving finite element method with local refinement based on a posteriori error estimates
- Spectral element methods for transitional flows in complex geometries
- Large eddy simulation of low Mach number flows using dynamic and orthogonal subgrid scales
- A conservative staggered-grid Chebyshev multidomain method for compressible flows. II: A semi-structured method
- Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods
- Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies
- Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
- Stabilized finite element approximation of transient incompressible flows using orthogonal subscales
- A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow
- Stabilization of spectral methods by finite element bubble functions
- A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation
- Bubble stabilization of spectral Legendre methods for the advection-diffusion equation
- A semi-implicit semi-Lagrangian scheme using the height coordinate for a nonhydrostatic and fully elastic model of atmospheric flows
- A semi-implicit, semi-Lagrangian, \(p\)-adaptive discontinuous Galerkin method for the shallow water equations
- Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.)
- SUPG finite element computation of compressible flows with the entropy and conservation variables formulations
- An entropy-variable-based VMS/GLS method for the simulation of compressible flows on unstructured grids
- A dynamic variational multiscale method for large eddy simulations on unstructured meshes
- Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES
- A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
- Subgrid stabilized projection method for 2D unsteady flows at high Reynolds numbers
- A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method
- A multi-scale formulation for compressible turbulent flows suitable for general variational discretization techniques
- A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: equation sets and test cases
- 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
- A variational multiscale stabilized finite element method for the solution of the Euler equations of nonhydrostatic stratified flows
- Limiters for high-order discontinuous Galerkin methods
- A stabilized finite element method based on SGS models for compressible flows
- Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations
- Geophysical-astrophysical spectral-element adaptive refinement (GASpAR): object-oriented \(h\)-adaptive fluid dynamics simulation
- A variational multiscale higher-order finite element formulation for turbomachinery flow computations
- Adaptive atmospheric modeling. Key techniques in grid generation, data structures, and numerical operations with applications
- A space-time formulation for multiscale phenomena
- Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Spectral element formulations on non-conforming grids: a comparative study of pointwise matching and integral projection methods
- Filter-based stabilization of spectral element methods
- Physics-Based Stabilization of Spectral Elements for the 3D Euler Equations of Moist Atmospheric Convection
- Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA)
- Deflated preconditioned conjugate gradient solvers for the pressure-Poisson equation: Extensions and improvements
- Entropy Viscosity Method for High-Order Approximations of Conservation Laws
- A Taylor-Galerkin method for convective transport problems
- Turbulence: Space-time statistical properties and behavior in supersonic flows
- p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
- A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations
- Moving Mesh Generation Using the Parabolic Monge–Ampère Equation
- Construction of curvilinear co-ordinate systems and applications to mesh generation
- The application of the finite-element method to meteorological simulations—a review
- The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
- A variational multiscale model for the advection-diffusion-reaction equation
- Euler solutions using flux-based wave decomposition
- A physically motivated approach for filtering acoustic waves from the equations governing compressible stratified flow
- A Conservative Discontinuous Galerkin Semi-Implicit Formulation for the Navier–Stokes Equations in Nonhydrostatic Mesoscale Modeling
- Convergence of Spectral Methods for Nonlinear Conservation Laws
- An Absolutely Stabilized Finite Element Method for the Stokes Problem
- Galerkin-Type Approximations which are Discontinuous in Time for Parabolic Equations in a Variable Domain
- Thep-Version of the Finite Element Method
- Generation of boundary-conforming grids around wing-body configurations using transfinite interpolation
- Finite element methods for second order differential equations with significant first derivatives
- On the Convergence of Shock-Capturing Streamline Diffusion Finite Element Methods for Hyperbolic Conservation Laws
- A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- A VARIABLE-ORDER SPECTRAL ELEMENT METHOD FOR INCOMPRESSIBLE VISCOUS FLOW SIMULATION
- A linelet preconditioner for incompressible flow solvers
- Waves and Compressible Flow
- Spectral Vanishing Viscosity Method For Nonlinear Conservation Laws
- A staggered spectral element model with application to the oceanic shallow water equations
- A general algorithm for compressible and incompressible flow—Part I. the split, characteristic‐based scheme
- The characteristic-based-split procedure: an efficient and accurate algorithm for fluid problems
- Residual‐based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods
- Computation of inviscid compressible flows with the V‐SGS stabilization and YZβ shock‐capturing
- Variational Multiscale Analysis: the Fine‐scale Green’s Function, Projection, Optimization, Localization, and Stabilized Methods
- A Simple Finite Element Method for Meteorological Problems
- CONVECTION TREATMENT USING SPECTRAL ELEMENTS OF DIFFERENT ORDER
- Spectral/hp Element Methods for Computational Fluid Dynamics
- Variational methods for the solution of problems of equilibrium and vibrations
- Large eddy simulation and the variational multiscale method
- Time integration of the shallow water equations in spherical geometry