Conservative polytopal mimetic discretization of the incompressible Navier-Stokes equations

DOI10.1016/j.cam.2018.02.007zbMath1432.76153OpenAlexW2791860884MaRDI QIDQ1636789

M. J. H. Anthonissen, Barry Koren, René Beltman

Publication date: 12 June 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2018.02.007

zbMATH Keywords

incompressible Navier-Stokes equationsexterior calculusprimal and dual meshescell-complexmimetic discretizationexact discrete conservation

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) 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) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items

Application of discrete mechanics model to jump conditions in two-phase flows, Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs, PolyMAC: Staggered Finite Volume Methods on General Meshes for Incompressible Navier–Stokes Problems

Uses Software

• ISNaS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
• A symmetry-preserving Cartesian grid method for computing a viscous flow past a circular cylinder
• Mimetic finite difference method
• Mimetic scalar products of discrete differential forms
• Boundary treatment for fourth-order staggered mesh discretizations of the incompressible Navier-Stokes equations
• Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes
• The dual variable method for solving fluid flow difference equations on Delaunay triangulations
• The LS-STAG method: a new immersed boundary/level-set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties
• Discrete calculus methods for diffusion
• Manifolds, tensor analysis, and applications.
• Error estimates for MAC-like approximations to the linear Navier-Stokes equations
• Fully conservative higher order finite difference schemes for incompressible flow
• Accuracy and conservation properties of a three-dimensional unstructured staggered mesh scheme for fluid dynamics
• A hybrid high-order locking-free method for linear elasticity on general meshes
• High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
• Symmetry-preserving discretization of turbulent flow.
• Conservation properties of unstructured staggered mesh schemes
• An extension of the MAC scheme to locally refined meshes: convergence analysis for the full tensor time-dependent Navier-Stokes equations
• Energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations
• The mimetic finite difference method for elliptic problems
• Vorticity and Incompressible Flow
• Towards Time-Stable and Accurate LES on Unstructured Grids
• Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
• Analysis of compatible discrete operator schemes for the Stokes equations on polyhedral meshes
• Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
• Suitability of Upwind-Biased Finite Difference Schemes for Large-Eddy Simulation of Turbulent Flows
• Analysis and Convergence of the MAC Scheme. I. The Linear Problem
• Exact fully 3D Navier–Stokes solutions for benchmarking
• A New Mixed Finite Element Formulation and the MAC Method for the Stokes Equations
• Analysis and convergence of the MAC scheme. II. Navier-Stokes equations
• Finite-element error estimates for the MAC scheme
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• The Hitchhiker's Guide to the Virtual Element Method
• New perspectives on polygonal and polyhedral finite element methods
• A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS
• Benchmark Proposal for the FVCA8 Conference: Finite Volume Methods for the Stokes and Navier–Stokes Equations
• Application of the LS-STAG Immersed Boundary/Cut-Cell Method to Viscoelastic Flow Computations
• Divergence‐free discontinuous Galerkin schemes for the Stokes equations and the MAC scheme
• Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
• Conforming polygonal finite elements
• A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES
• The ISNaS incompressible Navier-Stokes solver: invariant discretization