A divergence-free hybrid finite volume / finite element scheme for the incompressible MHD equations based on compatible finite element spaces with a posteriori limiting
DOI10.1016/j.apnum.2024.01.014MaRDI QIDQ6546897
Michael Dumbser, Enrico Zampa, Saray Busto
Publication date: 30 May 2024
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
staggered unstructured meshescompatible finite elements with a posteriori limitingdivergence-free schemesfinite element exterior calculus (FEEC)incompressible magnetohydrodynamics (MHD)semi-implicit hybrid finite volume/finite element methods
Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)
Cites Work
- Gauss-compatible Galerkin schemes for time-dependent Maxwell equations
- A New Thermodynamically Compatible Finite Volume Scheme for Magnetohydrodynamics
- Asymptotic adaptive methods for multi-scale problems in fluid mechanics
- Discrete Hodge operators
- Divergence-free adaptive mesh refinement for magnetohydrodynamics.
- An Implicit Staggered Hybrid Finite Volume/Finite Element Solver for the Incompressible Navier-Stokes Equations
- Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations
- Unisolvent and minimal physical degrees of freedom for the second family of polynomial differential forms
- A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations
- Structure preserving transport stabilized compatible finite element methods for magnetohydrodynamics
- A new family of semi-implicit finite volume/virtual element methods for incompressible flows on unstructured meshes
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A staggered semi-implicit discontinuous Galerkin method for the two dimensional incompressible Navier-Stokes equations
- Multidimensional HLLC Riemann solver for unstructured meshes -- with application to Euler and MHD flows
- A projection hybrid finite volume/element method for low-Mach number flows
- Multidimensional Riemann problem with self-similar internal structure. I: Application to hyperbolic conservation laws on structured meshes
- \textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
- Three dimensional HLL Riemann solver for conservation laws on structured meshes; application to Euler and magnetohydrodynamic flows
- Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations
- A correction technique for the dispersive effects of mass lumping for transport problems
- Implementation of the entropy viscosity method with the discontinuous Galerkin method
- A high-order finite volume method for systems of conservation laws-multi-dimensional optimal order detection (MOOD)
- Entropy viscosity method for nonlinear conservation laws
- Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field
- A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
- FORCE schemes on unstructured meshes. II: Non-conservative hyperbolic systems
- Geometric decompositions and local bases for spaces of finite element differential forms
- A simple robust and accurate \textit{a posteriori} sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes
- A staggered space-time discontinuous Galerkin method for the three-dimensional incompressible Navier-Stokes equations on unstructured tetrahedral meshes
- Multidimensional Riemann problem with self-similar internal structure. Part II: Application to hyperbolic conservation laws on unstructured meshes
- Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers
- Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics
- A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension
- Entropy-based nonlinear viscosity for Fourier approximations of conservation laws
- Triangulations. Structures for algorithms and applications
- Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics
- A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes
- Time-accurate solution of advection-diffusion problems by finite elements
- Mixed finite elements in \(\mathbb{R}^3\)
- The effect of nonzero \(\bigtriangledown\cdot B\) on the numerical solution of the magnetohydrodynamic equations
- Maintaining pressure positivity in magnetohydrodynamic simulations
- Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry
- A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations
- Divergence correction techniques for Maxwell solvers based on a hyperbolic model
- Hyperbolic divergence cleaning for the MHD equations
- Space-time adaptive ADER discontinuous Galerkin finite element schemes with \textit{a posteriori} sub-cell finite volume limiting
- Ideal GLM-MHD: about the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations
- A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers
- High order schemes for hyperbolic problems using globally continuous approximation and avoiding mass matrices
- Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
- A sixth-order finite volume scheme for the steady-state incompressible Stokes equations on staggered unstructured meshes
- Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes
- A projection hybrid high order finite volume/finite element method for incompressible turbulent flows
- Arbitrary high order accurate space-time discontinuous Galerkin finite element schemes on staggered unstructured meshes for linear elasticity
- An entropy stable finite volume scheme for the two dimensional Navier-Stokes equations on triangular grids
- An unsplit Godunov method for ideal MHD via constrained transport
- A solution-adaptive upwind scheme for ideal magnetohydrodynamics
- The extension of incompressible flow solvers to the weakly compressible regime
- Theory and practice of finite elements.
- Second-order implicit-explicit total variation diminishing schemes for the Euler system in the low Mach regime
- Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus
- An arbitrary-Lagrangian-Eulerian hybrid finite volume/finite element method on moving unstructured meshes for the Navier-Stokes equations
- A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics
- A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers
- A staggered semi-implicit hybrid FV/FE projection method for weakly compressible flows
- An all speed second order well-balanced IMEX relaxation scheme for the Euler equations with gravity
- Helicity-conservative finite element discretization for incompressible MHD systems
- A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and \(\operatorname{div} B = 0\)
- A 3D cell-centered ADER MOOD finite volume method for solving updated Lagrangian hyperelasticity on unstructured grids
- TVD-MOOD schemes based on implicit-explicit time integration
- A second order all Mach number IMEX finite volume solver for the three dimensional Euler equations
- A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes
- Multidimensional HLLE Riemann solver: application to Euler and magnetohydrodynamic flows
- Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problems
- An explicit divergence-free DG method for incompressible magnetohydrodynamics
- The effect of the consistent mass matrix on the maximum-principle for scalar conservation equations
- Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials
- New central and central discontinuous Galerkin schemes on overlapping cells of unstructured grids for solving ideal magnetohydrodynamic equations with globally divergence-free magnetic field
- Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms
- A two-dimensional HLLC Riemann solver for conservation laws: application to Euler and magnetohydrodynamic flows
- The discontinuous Galerkin method with Lax--Wendroff type time discretizations
- Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms
- Higher order triangular finite elements with mass lumping for the wave equation
- Towards very high order Godunov schemes
- On high order finite element spaces of differential forms
- Entropy Stable Finite Volume Scheme for Ideal Compressible MHD on 2-D Cartesian Meshes
- A staggered discontinuous Galerkin method for the convection–diffusion equation
- A staggered discontinuous Galerkin method for the curl-curl operator
- A Taylor-Galerkin method for convective transport problems
- Finite element exterior calculus, homological techniques, and applications
- A Discrete Duality Finite Volume Approach to Hodge Decomposition and div‐curl Problems on Almost Arbitrary Two‐Dimensional Meshes
- Robust Numerical Methods for Singularly Perturbed Differential Equations
- A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems
- Finite element exterior calculus: from Hodge theory to numerical stability
- Whitney Forms of Higher Degree
- An Unstaggered, High‐Resolution Constrained Transport Method for Magnetohydrodynamic Flows
- Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
- Riemann Solvers and Numerical Methods for Fluid Dynamics
- Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
- Compressible and incompressible fluids
- A fully divergence-free finite element method for magnetohydrodynamic equations
- The Multidimensional Optimal Order Detection method in the three‐dimensional case: very high‐order finite volume method for hyperbolic systems
- Splitting-Based Structure Preserving Discretizations for Magnetohydrodynamics
- Generalized finite difference schemes with higher order Whitney forms
- Minimal Sets of Unisolvent Weights for High Order Whitney Forms on Simplices
- An All Speed Second Order IMEX Relaxation Scheme for the Euler Equations
- A discrete duality finite volume discretization of the vorticity‐velocity‐pressure stokes problem on almost arbitrary two‐dimensional grids
- A Staggered Discontinuous Galerkin Method for the Stokes System
- Systems of conservation laws
Related Items (2)
This page was built for publication: A divergence-free hybrid finite volume / finite element scheme for the incompressible MHD equations based on compatible finite element spaces with a posteriori limiting