Journal of Computational Physics, ISSN 0021-9991, 05/2018, Volume 361, pp. 442 - 476

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two...

Mixed Galerkin methods | Systems of conservation laws with boundary energy flows | Structure-preserving discretization | Geometric spatial discretization | Port-Hamiltonian systems | WHITNEY FORMS | MODEL | FORMULATION | PHYSICS, MATHEMATICAL | ELEMENT EXTERIOR CALCULUS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | REDUCTION | SCHEMES | Analysis | Environmental law | College teachers

Mixed Galerkin methods | Systems of conservation laws with boundary energy flows | Structure-preserving discretization | Geometric spatial discretization | Port-Hamiltonian systems | WHITNEY FORMS | MODEL | FORMULATION | PHYSICS, MATHEMATICAL | ELEMENT EXTERIOR CALCULUS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | REDUCTION | SCHEMES | Analysis | Environmental law | College teachers

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2017, Volume 328, pp. 200 - 220

In this work we present a mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations that in the limit of vanishing dissipation...

Energy conserving discretization | Enstrophy conserving discretization | Spectral element method | Incompressible Navier–Stokes equations | Mimetic discretization | Physics and Astronomy (miscellaneous) | Computer Science Applications | Computational Mathematics | Numerical Analysis | Physics and Astronomy(all) | Modelling and Simulation | Applied Mathematics | FINITE-DIFFERENCE SCHEMES | BOX-SCHEME | PRESERVING DISCRETIZATION | DISCONTINUOUS GALERKIN METHOD | DISCRETE OPERATOR SCHEMES | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | DIRECT NUMERICAL-SIMULATION | ELLIPTIC PROBLEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Incompressible Navier-Stokes equations | LARGE-EDDY SIMULATION | CONSERVATION PROPERTIES | Mechanical engineering | Force and energy | Aerospace engineering

Energy conserving discretization | Enstrophy conserving discretization | Spectral element method | Incompressible Navier–Stokes equations | Mimetic discretization | Physics and Astronomy (miscellaneous) | Computer Science Applications | Computational Mathematics | Numerical Analysis | Physics and Astronomy(all) | Modelling and Simulation | Applied Mathematics | FINITE-DIFFERENCE SCHEMES | BOX-SCHEME | PRESERVING DISCRETIZATION | DISCONTINUOUS GALERKIN METHOD | DISCRETE OPERATOR SCHEMES | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | DIRECT NUMERICAL-SIMULATION | ELLIPTIC PROBLEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Incompressible Navier-Stokes equations | LARGE-EDDY SIMULATION | CONSERVATION PROPERTIES | Mechanical engineering | Force and energy | Aerospace engineering

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2014, Volume 258, pp. 246 - 267

A fully-conservative discretization is presented in this paper. The same principles followed by Verstappen and Veldman (2003) [3] are generalized for...

Checkerboard | Differentially heated cavity | Unstructured grid | Symmetry-preserving discretization | Regularization | Collocated formulation | INCOMPRESSIBLE-FLOW | COMPLEX | FINITE-DIFFERENCE SCHEMES | NONUNIFORM MESHES | CONVECTION | MODEL | LARGE-EDDY SIMULATION | FLUID | CONSERVATION PROPERTIES | Symmetry preserving discretization | TURBULENT-FLOW | PHYSICS, MATHEMATICAL | MESH SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Fluid dynamics | Turbulence | Operators | Turbulent flow | Discretization | Mathematical analysis | Dissipation | Buoyancy | Mathematical models | Navier-Stokes equations

Checkerboard | Differentially heated cavity | Unstructured grid | Symmetry-preserving discretization | Regularization | Collocated formulation | INCOMPRESSIBLE-FLOW | COMPLEX | FINITE-DIFFERENCE SCHEMES | NONUNIFORM MESHES | CONVECTION | MODEL | LARGE-EDDY SIMULATION | FLUID | CONSERVATION PROPERTIES | Symmetry preserving discretization | TURBULENT-FLOW | PHYSICS, MATHEMATICAL | MESH SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Fluid dynamics | Turbulence | Operators | Turbulent flow | Discretization | Mathematical analysis | Dissipation | Buoyancy | Mathematical models | Navier-Stokes equations

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2011, Volume 240, Issue 21, pp. 1724 - 1760

This study derives geometric, variational discretization of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of...

Magnetohydrodynamics | Fluid dynamics | Complex fluids | Structure-preserving schemes | Geometric discretization | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | MESH | PHYSICS, MATHEMATICAL | GODUNOV METHOD | NUMERICAL-SOLUTION | LIE-GROUPS | MECHANICS | REDUCTION | CONSERVATION PROPERTIES | INTEGRATORS | SEMIDIRECT PRODUCTS | Analysis | Fluids | Computational fluid dynamics | Discretization | Mathematical analysis | Continuums | Fluid flow | Mathematical models

Magnetohydrodynamics | Fluid dynamics | Complex fluids | Structure-preserving schemes | Geometric discretization | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | MESH | PHYSICS, MATHEMATICAL | GODUNOV METHOD | NUMERICAL-SOLUTION | LIE-GROUPS | MECHANICS | REDUCTION | CONSERVATION PROPERTIES | INTEGRATORS | SEMIDIRECT PRODUCTS | Analysis | Fluids | Computational fluid dynamics | Discretization | Mathematical analysis | Continuums | Fluid flow | Mathematical models

Journal Article

SIAM Review, ISSN 0036-1445, 3/2001, Volume 43, Issue 1, pp. 89 - 112

In this paper we review and further develop a class of strong stability-preserving (SSP) high-order time discretizations for semidiscrete method of lines...

Conservation laws | Approximation | Eulers method | Applied mathematics | Odes | Mathematics | Entropy | Problems and Techniques | Grants | Runge Kutta method | Coefficients | Strong stability preserving | Time discretization | Runge-Kutta methods | High-order accuracy | Multistep methods | MATHEMATICS, APPLIED | RUNGE-KUTTA SCHEMES | HIGH-RESOLUTION SCHEMES | APPROXIMATIONS | time discretization | multistep methods | high-order accuracy | strong stability preserving | HYPERBOLIC CONSERVATION-LAWS | FINITE-ELEMENT METHOD | Differential equations | Research

Conservation laws | Approximation | Eulers method | Applied mathematics | Odes | Mathematics | Entropy | Problems and Techniques | Grants | Runge Kutta method | Coefficients | Strong stability preserving | Time discretization | Runge-Kutta methods | High-order accuracy | Multistep methods | MATHEMATICS, APPLIED | RUNGE-KUTTA SCHEMES | HIGH-RESOLUTION SCHEMES | APPROXIMATIONS | time discretization | multistep methods | high-order accuracy | strong stability preserving | HYPERBOLIC CONSERVATION-LAWS | FINITE-ELEMENT METHOD | Differential equations | Research

Journal Article

Data Mining and Knowledge Discovery, ISSN 1384-5810, 9/2014, Volume 28, Issue 5, pp. 1366 - 1397

Discretization is the transformation of continuous data into discrete bins. It is an important and general pre-processing technique, and a critical element of...

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | Interaction preservation | Discretization | Computer Science | Data Mining and Knowledge Discovery | Information Storage and Retrieval | Classification | Artificial Intelligence (incl. Robotics) | Pattern mining | Outlier mining | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Data mining | Analysis | Information theory | Algorithms | Tasks | Exact solutions | Encoding | Transformations | Preserving

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | Interaction preservation | Discretization | Computer Science | Data Mining and Knowledge Discovery | Information Storage and Retrieval | Classification | Artificial Intelligence (incl. Robotics) | Pattern mining | Outlier mining | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Data mining | Analysis | Information theory | Algorithms | Tasks | Exact solutions | Encoding | Transformations | Preserving

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2017, Volume 339, Issue C, pp. 453 - 460

Here, the Fokker–Planck collision operator is an advection-diffusion operator which describe dynamical systems such as weakly coupled plasmas, photonics in...

Exact analytical equilibrium preserving | Rosenbluth potentials | Conservative discretization | Fokker–Planck | Multiple dimensions | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DIFFERENCE SCHEME | ALGORITHM | PHYSICS, MATHEMATICAL | Fokker-Planck | EQUATION | IMPLICIT | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | Mathematics

Exact analytical equilibrium preserving | Rosenbluth potentials | Conservative discretization | Fokker–Planck | Multiple dimensions | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DIFFERENCE SCHEME | ALGORITHM | PHYSICS, MATHEMATICAL | Fokker-Planck | EQUATION | IMPLICIT | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | Mathematics

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 3/2009, Volume 38, Issue 3, pp. 251 - 289

Strong stability preserving (SSP) high order time discretizations were developed to ensure nonlinear stability properties necessary in the numerical solution...

Spectral deferred correction methods | Computational Mathematics and Numerical Analysis | Algorithms | Runge–Kutta methods | Multistep methods | Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | High order accuracy | Strong stability preserving | Mathematics | Time discretization | Runge-Kutta methods | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | LOW-STORAGE | ABSOLUTE MONOTONICITY | CONTRACTIVITY | RUNGE-KUTTA SCHEMES | NUMERICAL-SOLUTION | HIGH-RESOLUTION SCHEMES | DISCONTINUOUS GALERKIN METHODS | CONSERVATION-LAWS | GENERAL MONOTONICITY | Universities and colleges | Stability | Discretization | Preserves | Norms | Nonlinearity | Mathematical models | Spectra | Preserving

Spectral deferred correction methods | Computational Mathematics and Numerical Analysis | Algorithms | Runge–Kutta methods | Multistep methods | Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | High order accuracy | Strong stability preserving | Mathematics | Time discretization | Runge-Kutta methods | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | LOW-STORAGE | ABSOLUTE MONOTONICITY | CONTRACTIVITY | RUNGE-KUTTA SCHEMES | NUMERICAL-SOLUTION | HIGH-RESOLUTION SCHEMES | DISCONTINUOUS GALERKIN METHODS | CONSERVATION-LAWS | GENERAL MONOTONICITY | Universities and colleges | Stability | Discretization | Preserves | Norms | Nonlinearity | Mathematical models | Spectra | Preserving

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 02/2015, Volume 48, Issue 5, pp. 55201 - 25

The Korteweg-de Vries equation is one of the most important nonlinear evolution equations in the mathematical sciences. In this article invariant...

Korteweg-de Vries equation | invariant discretization | moving meshes | HEAT-TRANSFER | PHYSICS, MULTIDISCIPLINARY | PARTIAL-DIFFERENTIAL-EQUATIONS | LIE SYMMETRIES | PHYSICS, MATHEMATICAL | GEOMETRIC INTEGRATION | SCHEMES | Discretization | Mathematical analysis | Preserves | Nonlinear evolution equations | Mathematical models | Transformations | Invariants | Standards | Preserving

Korteweg-de Vries equation | invariant discretization | moving meshes | HEAT-TRANSFER | PHYSICS, MULTIDISCIPLINARY | PARTIAL-DIFFERENTIAL-EQUATIONS | LIE SYMMETRIES | PHYSICS, MATHEMATICAL | GEOMETRIC INTEGRATION | SCHEMES | Discretization | Mathematical analysis | Preserves | Nonlinear evolution equations | Mathematical models | Transformations | Invariants | Standards | Preserving

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 09/2015, Volume 296, pp. 369 - 381

The numerical simulation of the discharge inception is an active field of applied physics with many industrial applications. In this work we focus on the...

Streamer | Reaction | Advection | STREAMER SIMULATION | FIELD | ASYMPTOTIC PRESERVING SCHEME | POSITIVE STREAMER | EQUATIONS | AIR | PHYSICS, MATHEMATICAL | DISCHARGES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-ELEMENT | Avalanches | Analysis | Stability | Computer simulation | Discretization | Mathematical analysis | Mathematical models | Electron avalanche | Discharge | Convergence | ELECTRIC FIELDS | NUMERICAL ANALYSIS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ELECTRONS | AVALANCHE QUENCHING | ADVECTION | CONVERGENCE | MATHEMATICAL METHODS AND COMPUTING | COMPUTERIZED SIMULATION

Streamer | Reaction | Advection | STREAMER SIMULATION | FIELD | ASYMPTOTIC PRESERVING SCHEME | POSITIVE STREAMER | EQUATIONS | AIR | PHYSICS, MATHEMATICAL | DISCHARGES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-ELEMENT | Avalanches | Analysis | Stability | Computer simulation | Discretization | Mathematical analysis | Mathematical models | Electron avalanche | Discharge | Convergence | ELECTRIC FIELDS | NUMERICAL ANALYSIS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ELECTRONS | AVALANCHE QUENCHING | ADVECTION | CONVERGENCE | MATHEMATICAL METHODS AND COMPUTING | COMPUTERIZED SIMULATION

Journal Article

Nonlinearity, ISSN 0951-7715, 03/2018, Volume 31, Issue 4, pp. 1673 - 1705

In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a...

entropy | nonequilibrium thermodynamics | variational integrators | discrete Lagrangian formulation | structure preserving discretization | MATHEMATICS, APPLIED | FACTORIZATION | MECHANICS | INTEGRATORS | FORMULATION | PHYSICS, MATHEMATICAL | Mathematics - Numerical Analysis

entropy | nonequilibrium thermodynamics | variational integrators | discrete Lagrangian formulation | structure preserving discretization | MATHEMATICS, APPLIED | FACTORIZATION | MECHANICS | INTEGRATORS | FORMULATION | PHYSICS, MATHEMATICAL | Mathematics - Numerical Analysis

Journal Article

Ocean Modelling, ISSN 1463-5003, 12/2018, Volume 132, pp. 73 - 90

•New discretization of isoneutral diffusion and eddy parametrization on unstructured grids is introduced•Essential mathematical/physical properties are...

ocean parametrization | isoneutral diffusion | eddy advection | structure-preserving discretization | skew diffusion | CIRCULATION | OCEANOGRAPHY | ROTATED DIFFUSION OPERATORS | MODEL | FORMULATION | METEOROLOGY & ATMOSPHERIC SCIENCES

ocean parametrization | isoneutral diffusion | eddy advection | structure-preserving discretization | skew diffusion | CIRCULATION | OCEANOGRAPHY | ROTATED DIFFUSION OPERATORS | MODEL | FORMULATION | METEOROLOGY & ATMOSPHERIC SCIENCES

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2014, Volume 258, pp. 118 - 136

We present an artificial viscous force for two-dimensional axi-symmetric r–z geometry and logically rectangular grids that is dissipative, conserves the...

Spherical symmetry | Staggered grid Lagrangian | Artificial viscosity | Axi-symmetric | Dissipative | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ERRORS | PHYSICS, MATHEMATICAL | Viscosity | Discretization | Computation | Dissipation | Preserves | Two dimensional | Preserving | Symmetry

Spherical symmetry | Staggered grid Lagrangian | Artificial viscosity | Axi-symmetric | Dissipative | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ERRORS | PHYSICS, MATHEMATICAL | Viscosity | Discretization | Computation | Dissipation | Preserves | Two dimensional | Preserving | Symmetry

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 05/2016, Volume 81, Issue 3, pp. 131 - 150

Summary This paper introduces a vertex‐centered linearity‐preserving finite volume scheme for the heterogeneous anisotropic diffusion equations on general...

linearity preserving | vertex‐centered scheme | diffusion equation | Vertex-centered scheme | Linearity preserving | Diffusion equation | vertex-centered scheme | FINITE-VOLUME METHOD | DIFFERENCE-METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ELEMENT METHOD | PHYSICS, FLUIDS & PLASMAS | SCHEMES | FAMILY | Mathematical analysis | Linearity | Coercive force | Preserves | Coercivity | Mathematical models | Diffusion | Symmetry

linearity preserving | vertex‐centered scheme | diffusion equation | Vertex-centered scheme | Linearity preserving | Diffusion equation | vertex-centered scheme | FINITE-VOLUME METHOD | DIFFERENCE-METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ELEMENT METHOD | PHYSICS, FLUIDS & PLASMAS | SCHEMES | FAMILY | Mathematical analysis | Linearity | Coercive force | Preserves | Coercivity | Mathematical models | Diffusion | Symmetry

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 10/2014, Volume 78, Issue 1, pp. 329 - 339

In this paper, we derive a variational characterization of constrained Birkhoffian dynamics in both continuous and discrete settings. When additional algebraic...

Engineering | Vibration, Dynamical Systems, Control | Birkhoffian dynamics | Variational discretization | Mechanics | Automotive Engineering | Discrete constrained Birkhoffian equations | Mechanical Engineering | Constrained Birkhoffian system | MECHANICS | STRUCTURE-PRESERVING ALGORITHMS | INTEGRATORS | ENGINEERING, MECHANICAL | Algorithms | Aerospace engineering | Constraints | Computer simulation | Configurations | Mathematical analysis | Pendulums | Nonlinear dynamics | Derivation | Mathematical models | Dynamical systems | Three dimensional

Engineering | Vibration, Dynamical Systems, Control | Birkhoffian dynamics | Variational discretization | Mechanics | Automotive Engineering | Discrete constrained Birkhoffian equations | Mechanical Engineering | Constrained Birkhoffian system | MECHANICS | STRUCTURE-PRESERVING ALGORITHMS | INTEGRATORS | ENGINEERING, MECHANICAL | Algorithms | Aerospace engineering | Constraints | Computer simulation | Configurations | Mathematical analysis | Pendulums | Nonlinear dynamics | Derivation | Mathematical models | Dynamical systems | Three dimensional

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 1/2018, Volume 74, Issue 1, pp. 244 - 266

We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and...

Computational Mathematics and Numerical Analysis | Runge–Kutta | Algorithms | Theoretical, Mathematical and Computational Physics | Total variation diminishing | Mathematical and Computational Engineering | Positivity | Strong stability preserving | Mathematics | MATHEMATICS, APPLIED | CONSERVATION | RUNGE-KUTTA METHODS | Runge-Kutta | CONTRACTIVITY | SCHEMES | Environmental law

Computational Mathematics and Numerical Analysis | Runge–Kutta | Algorithms | Theoretical, Mathematical and Computational Physics | Total variation diminishing | Mathematical and Computational Engineering | Positivity | Strong stability preserving | Mathematics | MATHEMATICS, APPLIED | CONSERVATION | RUNGE-KUTTA METHODS | Runge-Kutta | CONTRACTIVITY | SCHEMES | Environmental law

Journal Article