Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 07/2019, Volume 42, Issue 11, pp. 4008 - 4016

This short note reports a lowest order divergence‐free Stokes element on quadrilateral meshes. The velocity space is based on a P1 spline element over the...

divergence‐free | stokes element | fluid mechanics | quadrilateral | finite elements | MATHEMATICS, APPLIED | FINITE-ELEMENTS | divergence-free | Quadrilaterals | Subspace methods | Divergence

divergence‐free | stokes element | fluid mechanics | quadrilateral | finite elements | MATHEMATICS, APPLIED | FINITE-ELEMENTS | divergence-free | Quadrilaterals | Subspace methods | Divergence

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2004, Volume 194, Issue 2, pp. 588 - 610

In this paper, we develop the locally divergence-free discontinuous Galerkin method for numerically solving the Maxwell equations. The distinctive feature of...

Divergence-free solutions | Discontinuous Galerkin method | Maxwell equations | Divergence-free | FIELDS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | discontinuous Galerkin method | SYSTEMS | divergence-free solutions | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | FINITE-ELEMENT-METHOD

Divergence-free solutions | Discontinuous Galerkin method | Maxwell equations | Divergence-free | FIELDS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | discontinuous Galerkin method | SYSTEMS | divergence-free solutions | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | FINITE-ELEMENT-METHOD

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 12/2019

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 01/2019, Volume 89, Issue 1-2, pp. 16 - 42

Summary In this paper, we present a novel pressure‐based semi‐implicit finite volume solver for the equations of compressible ideal, viscous, and resistive...

ideal magnetohydrodynamics | viscous and resistive MHD | all Mach number flow solver | divergence‐free | finite volume schemes | semi‐implicit | compressible low Mach number flows | general equation of state | pressure‐based method | pressure-based method | semi-implicit | divergence-free | HLLC RIEMANN SOLVER | TANG VORTEX SYSTEM | THERMODYNAMIC PROPERTIES | PHYSICS, FLUIDS & PLASMAS | 1ST-ORDER HYPERBOLIC FORMULATION | GODUNOV-TYPE SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | ORDER ADER SCHEMES | DISCONTINUOUS GALERKIN METHODS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | Fluid dynamics | Viscosity | Magnetohydrodynamics | Divergence | Compressibility | Methodology | Fluid flow | Finite volume method | Energy | Mathematical analysis | Solvers | Evolution | Mach number | Computational fluid dynamics | Momentum equation | Curl (vectors) | Dimensions | Momentum | Pressure | Velocity | Equations | Internal energy | Incompressible flow | Simulation | Energy equation | Volume | Newton methods | Computer applications | Scaling | Magnetic fields | Computing time | Riemann solver | Linear functions

ideal magnetohydrodynamics | viscous and resistive MHD | all Mach number flow solver | divergence‐free | finite volume schemes | semi‐implicit | compressible low Mach number flows | general equation of state | pressure‐based method | pressure-based method | semi-implicit | divergence-free | HLLC RIEMANN SOLVER | TANG VORTEX SYSTEM | THERMODYNAMIC PROPERTIES | PHYSICS, FLUIDS & PLASMAS | 1ST-ORDER HYPERBOLIC FORMULATION | GODUNOV-TYPE SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | ORDER ADER SCHEMES | DISCONTINUOUS GALERKIN METHODS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | Fluid dynamics | Viscosity | Magnetohydrodynamics | Divergence | Compressibility | Methodology | Fluid flow | Finite volume method | Energy | Mathematical analysis | Solvers | Evolution | Mach number | Computational fluid dynamics | Momentum equation | Curl (vectors) | Dimensions | Momentum | Pressure | Velocity | Equations | Internal energy | Incompressible flow | Simulation | Energy equation | Volume | Newton methods | Computer applications | Scaling | Magnetic fields | Computing time | Riemann solver | Linear functions

Journal Article

Communications in Computational Physics, ISSN 1815-2406, 02/2017, Volume 21, Issue 2, pp. 423 - 442

In this paper we consider a discontinuous Galerkin discretization of the ideal magnetohydrodynamics (MHD) equations on unstructured meshes, and the divergence...

Ideal magnetohydrodynamics equations | divergence free constraint | divergence free cleaning technique | discontinuous Galerkin method | locally divergence free projection | IDEAL MHD EQUATIONS | FRAMEWORK | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | FINITE-ELEMENT-METHOD | SCHEMES

Ideal magnetohydrodynamics equations | divergence free constraint | divergence free cleaning technique | discontinuous Galerkin method | locally divergence free projection | IDEAL MHD EQUATIONS | FRAMEWORK | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | FINITE-ELEMENT-METHOD | SCHEMES

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 01/2018, Volume 75, Issue 1, pp. 199 - 217

We propose a new method for analyzing the limit (safe) load of elastoplastic media governed by the Hencky plasticity law and deduce fully computable bounds of...

Divergence free fields | Hencky’s plasticity | Computable bounds | Penalization | Limit load

Divergence free fields | Hencky’s plasticity | Computable bounds | Penalization | Limit load

Journal Article

Magnetic Resonance in Medicine, ISSN 0740-3194, 02/2015, Volume 73, Issue 2, pp. 828 - 842

Purpose To investigate four‐dimensional flow denoising using the divergence‐free wavelet (DFW) transform and compare its performance with existing techniques....

four‐dimensional flow | wavelet denoising | divergence‐free | Divergence-free | Wavelet denoising | Four-dimensional flow | VISUALIZATION | GRAPPA | four-dimensional flow | RECONSTRUCTION | K-T BLAST | NOISE-REDUCTION | SHRINKAGE | PHASE-CONTRAST MR | DYNAMIC MRI | SENSE | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | TURBULENT FLOWS | divergence-free | Reproducibility of Results | Coronary Circulation - physiology | Humans | Image Interpretation, Computer-Assisted - methods | Signal-To-Noise Ratio | Male | Artifacts | Algorithms | Wavelet Analysis | Sensitivity and Specificity | Female | Magnetic Resonance Angiography - methods | Image Enhancement - methods | Blood Flow Velocity - physiology | Child | Noise control | Usage | Visualization (Computers)

four‐dimensional flow | wavelet denoising | divergence‐free | Divergence-free | Wavelet denoising | Four-dimensional flow | VISUALIZATION | GRAPPA | four-dimensional flow | RECONSTRUCTION | K-T BLAST | NOISE-REDUCTION | SHRINKAGE | PHASE-CONTRAST MR | DYNAMIC MRI | SENSE | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | TURBULENT FLOWS | divergence-free | Reproducibility of Results | Coronary Circulation - physiology | Humans | Image Interpretation, Computer-Assisted - methods | Signal-To-Noise Ratio | Male | Artifacts | Algorithms | Wavelet Analysis | Sensitivity and Specificity | Female | Magnetic Resonance Angiography - methods | Image Enhancement - methods | Blood Flow Velocity - physiology | Child | Noise control | Usage | Visualization (Computers)

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 04/2014, Volume 263, pp. 206 - 221

Methodologies to acquire three-dimensional velocity fields are becoming increasingly available, generating large datasets of steady state and transient flows...

Velocity field de-noising | Divergence-free filtering | Particle image velocimetry | Magnetic resonance velocimetry | Matching pursuit | INTERPOLATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Divergence free filtering | Velocity field de noising | MAGNETIC-RESONANCE VELOCIMETRY | PIV | PHYSICS, MATHEMATICAL | Filtration | Filtering | Computation | Noise reduction | Magnetic resonance | Velocity measurement | Linear operators | Three dimensional

Velocity field de-noising | Divergence-free filtering | Particle image velocimetry | Magnetic resonance velocimetry | Matching pursuit | INTERPOLATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Divergence free filtering | Velocity field de noising | MAGNETIC-RESONANCE VELOCIMETRY | PIV | PHYSICS, MATHEMATICAL | Filtration | Filtering | Computation | Noise reduction | Magnetic resonance | Velocity measurement | Linear operators | Three dimensional

Journal Article

SIAM Review, ISSN 0036-1445, 2017, Volume 59, Issue 3, pp. 492 - 544

The divergence constraint of the incompressible Navier-Stokes equations is revisited in the mixed finite element framework. While many stable and convergent...

Pressure-robust discretization | Incompressible Navier-Stokes and Stokes equations | Divergence-free properties | Mixed finite elements | MATHEMATICS, APPLIED | GRAD-DIV STABILIZATION | VELOCITY ERRORS | RIGHT-INVERSE | incompressible Navier-Stokes and Stokes equations | PIECEWISE POLYNOMIALS | OSEEN PROBLEM | EXTERIOR CALCULUS | 3 DIMENSIONS | MASS CONSERVATION | NAVIER-STOKES EQUATIONS | mixed finite elements | COMPUTATIONAL FLUID-DYNAMICS | pressure-robust discretization | divergence-free properties

Pressure-robust discretization | Incompressible Navier-Stokes and Stokes equations | Divergence-free properties | Mixed finite elements | MATHEMATICS, APPLIED | GRAD-DIV STABILIZATION | VELOCITY ERRORS | RIGHT-INVERSE | incompressible Navier-Stokes and Stokes equations | PIECEWISE POLYNOMIALS | OSEEN PROBLEM | EXTERIOR CALCULUS | 3 DIMENSIONS | MASS CONSERVATION | NAVIER-STOKES EQUATIONS | mixed finite elements | COMPUTATIONAL FLUID-DYNAMICS | pressure-robust discretization | divergence-free properties

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 10/2019, Volume 113, Issue 4, pp. 443 - 448

In this short note we obtain a canonical form for commuting divergence-free vector fields.

Secondary 57R30 | 34A26 | 34C20 | Mathematics, general | Primary 37C10 | Mathematics | Divergence-free $${\mathbb {R}}^n$$ R n actions | Flowbox coordinates | Foliations | MATHEMATICS | LYAPUNOV EXPONENTS | Divergence-free R-n actions

Secondary 57R30 | 34A26 | 34C20 | Mathematics, general | Primary 37C10 | Mathematics | Divergence-free $${\mathbb {R}}^n$$ R n actions | Flowbox coordinates | Foliations | MATHEMATICS | LYAPUNOV EXPONENTS | Divergence-free R-n actions

Journal Article

Mathematics and Computers in Simulation, ISSN 0378-4754, 04/2020, Volume 170, pp. 51 - 78

The performance of different classic or more recent finite element formulations for Stokes, coupled Stokes–Darcy and Brinkman problems is discussed....

Coupled Stokes–Darcy flow | Discontinuous Galerkin | Mixed finite elements methods | Divergence-free simulation | Stokes flow

Coupled Stokes–Darcy flow | Discontinuous Galerkin | Mixed finite elements methods | Divergence-free simulation | Stokes flow

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2019, Volume 88, Issue 316, pp. 553 - 581

We develop a class of mixed finite element schemes for stationary magnetohydrodynamics (MHD) models, using the magnetic field \bm B and the current density \bm...

Divergence-free | MHD equations | Stationary | Finite element | MATHEMATICS, APPLIED | CONSERVATIVE SCHEME | stationary | finite element | EXTERIOR CALCULUS | FLOWS

Divergence-free | MHD equations | Stationary | Finite element | MATHEMATICS, APPLIED | CONSERVATIVE SCHEME | stationary | finite element | EXTERIOR CALCULUS | FLOWS

Journal Article

13.
Full Text
A lowest-order weak Galerkin finite element method for Stokes flow on polygonal meshes

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2020, Volume 368, p. 112479

This paper presents a lowest-order weak Galerkin (WG) finite element method for solving the Stokes equations on convex polygonal meshes. Constant vectors are...

Discretely divergence-free | Polygonal meshes | Weak Galerkin | Lowest-order finite elements | Stokes flow | MATHEMATICS, APPLIED | DISCONTINUOUS GALERKIN

Discretely divergence-free | Polygonal meshes | Weak Galerkin | Lowest-order finite elements | Stokes flow | MATHEMATICS, APPLIED | DISCONTINUOUS GALERKIN

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2009, Volume 228, Issue 18, pp. 6703 - 6725

The stability and accuracy of three methods which enforce either a divergence-free velocity field, density invariance, or their combination are tested here...

Accuracy | Stability | Divergence-free velocity field | Density invariance | Incompressible smoothed particle hydrodynamics (ISPH) | SMOOTHED PARTICLE HYDRODYNAMICS | SIMULATION | PHYSICS, MATHEMATICAL | FREE-SURFACE | WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | FLOWS | Fluid dynamics | Anisotropy | Mechanical engineering | Analysis | Methods | RANDOMNESS | VELOCITY | DISTURBANCES | INSTABILITY | SPIN | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STABILITY | HYDRODYNAMICS | NOISE | ANISOTROPY | ACCURACY | DENSITY | INTERPOLATION | REYNOLDS NUMBER | OSCILLATIONS

Accuracy | Stability | Divergence-free velocity field | Density invariance | Incompressible smoothed particle hydrodynamics (ISPH) | SMOOTHED PARTICLE HYDRODYNAMICS | SIMULATION | PHYSICS, MATHEMATICAL | FREE-SURFACE | WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | FLOWS | Fluid dynamics | Anisotropy | Mechanical engineering | Analysis | Methods | RANDOMNESS | VELOCITY | DISTURBANCES | INSTABILITY | SPIN | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STABILITY | HYDRODYNAMICS | NOISE | ANISOTROPY | ACCURACY | DENSITY | INTERPOLATION | REYNOLDS NUMBER | OSCILLATIONS

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 06/2019, Volume 90, Issue 6, pp. 296 - 321

Summary In this paper, we present an efficient semi‐implicit scheme for the solution of the Reynolds‐averaged Navier‐Stokes equations for the simulation of...

nonhydrostatic | Voronoi mesh | high order | divergence‐free | semi‐implicit | free surface flows | hydrostatic | semi-implicit | divergence-free | NUMBER | COMPRESSIBLE FLOWS | ELEMENT-METHOD | PHYSICS, FLUIDS & PLASMAS | DISCONTINUOUS GALERKIN METHOD | MODEL | SEMIIMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | FINITE-DIFFERENCE METHODS | VOLUME SCHEMES | ADVECTION | Viscosity | Reconstruction | Divergence | Fluid dynamics | Computer simulation | Trajectories | Velocity distribution | Velocity | Equations | Finite element method | Interpolation | Continuity equation | Free surfaces | Surface flow

nonhydrostatic | Voronoi mesh | high order | divergence‐free | semi‐implicit | free surface flows | hydrostatic | semi-implicit | divergence-free | NUMBER | COMPRESSIBLE FLOWS | ELEMENT-METHOD | PHYSICS, FLUIDS & PLASMAS | DISCONTINUOUS GALERKIN METHOD | MODEL | SEMIIMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | FINITE-DIFFERENCE METHODS | VOLUME SCHEMES | ADVECTION | Viscosity | Reconstruction | Divergence | Fluid dynamics | Computer simulation | Trajectories | Velocity distribution | Velocity | Equations | Finite element method | Interpolation | Continuity equation | Free surfaces | Surface flow

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 08/2018, Volume 87, Issue 10, pp. 529 - 542

Summary A divergence‐free moving particle semi‐implicit framework has been formulated for modeling of multiple miscible fluids having small density ratios (≤...

free surface | divergence‐free | density‐dependent flow | low density ratio | density-dependent flow | divergence-free | ISPH | SEMIIMPLICIT METHOD | PHYSICS, FLUIDS & PLASMAS | GRAVITY CURRENTS | ALGORITHM | SPH PROJECTION METHOD | SMOOTHED PARTICLE HYDRODYNAMICS | FREE-SURFACE FLOWS | WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INCOMPRESSIBLE FLOWS | NUMERICAL-SIMULATION | Divergence | Computational fluid dynamics | Fluid flow | Variations | Density | Velocity | Surface treatment | Pressure gradients | Fluids | Ratios | Modelling | Mathematical models | Framework | Free surfaces

free surface | divergence‐free | density‐dependent flow | low density ratio | density-dependent flow | divergence-free | ISPH | SEMIIMPLICIT METHOD | PHYSICS, FLUIDS & PLASMAS | GRAVITY CURRENTS | ALGORITHM | SPH PROJECTION METHOD | SMOOTHED PARTICLE HYDRODYNAMICS | FREE-SURFACE FLOWS | WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INCOMPRESSIBLE FLOWS | NUMERICAL-SIMULATION | Divergence | Computational fluid dynamics | Fluid flow | Variations | Density | Velocity | Surface treatment | Pressure gradients | Fluids | Ratios | Modelling | Mathematical models | Framework | Free surfaces

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 07/2019, Volume 127, pp. 67 - 88

We extend our analysis of divergence-free positive symmetric tensors (DPT) begun in a previous paper. On the one hand, we refine the statements and give more...

Divergence-free tensors | Maxwell's equations | Integrability | Determinant | Vlasov–Poisson equation | Vlasov-Poisson equation | MATHEMATICS | MATHEMATICS, APPLIED

Divergence-free tensors | Maxwell's equations | Integrability | Determinant | Vlasov–Poisson equation | Vlasov-Poisson equation | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 03/2017, Volume 51, Issue 2, pp. 509 - 535

In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of...

Polygonal meshes | Stokes problem | Virtual element method | Divergence free approximation | MATHEMATICS, APPLIED | polygonal meshes | POLYHEDRAL MESHES | EQUATIONS | FINITE-DIFFERENCE METHOD | FORMULATION | ELLIPTIC PROBLEMS | DISCONTINUOUS GALERKIN METHODS | LINEAR ELASTICITY PROBLEMS | ERROR | divergence free approximation | Degrees of freedom | Divergence | Error analysis | Test procedures

Polygonal meshes | Stokes problem | Virtual element method | Divergence free approximation | MATHEMATICS, APPLIED | polygonal meshes | POLYHEDRAL MESHES | EQUATIONS | FINITE-DIFFERENCE METHOD | FORMULATION | ELLIPTIC PROBLEMS | DISCONTINUOUS GALERKIN METHODS | LINEAR ELASTICITY PROBLEMS | ERROR | divergence free approximation | Degrees of freedom | Divergence | Error analysis | Test procedures

Journal Article