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

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An energy‐momentum‐conserving temporal discretization scheme for adhesive contact problems

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 03/2013, Volume 93, Issue 10, pp. 1057 - 1081

SUMMARYNumerical solution of dynamic problems requires accurate temporal discretization schemes. So far, to the best of the authors’ knowledge, none have been...

temporal integration schemes | nonlinear finite element methods | adhesion | energy‐momentum conserving schemes | computational contact mechanics | nonlinear dynamics | Nonlinear dynamics | Computational contact mechanics | Nonlinear finite element methods | Adhesion | Energy-momentum conserving schemes | Temporal integration schemes | TIME INTEGRATION | ALGORITHMS | MODEL | energy-momentum conserving schemes | MECHANICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | ENGINEERING, MULTIDISCIPLINARY | NONLINEAR ELASTODYNAMICS | Energy conservation | Analysis | Finite element method | Reproduction | Adhesives | Discretization | Mathematical models | Temporal logic | Contact

temporal integration schemes | nonlinear finite element methods | adhesion | energy‐momentum conserving schemes | computational contact mechanics | nonlinear dynamics | Nonlinear dynamics | Computational contact mechanics | Nonlinear finite element methods | Adhesion | Energy-momentum conserving schemes | Temporal integration schemes | TIME INTEGRATION | ALGORITHMS | MODEL | energy-momentum conserving schemes | MECHANICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | ENGINEERING, MULTIDISCIPLINARY | NONLINEAR ELASTODYNAMICS | Energy conservation | Analysis | Finite element method | Reproduction | Adhesives | Discretization | Mathematical models | Temporal logic | Contact

Journal Article

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

International Journal for Multiscale Computational Engineering, ISSN 1543-1649, 2012, Volume 10, Issue 2, pp. 189 - 211

In this paper, we propose a muscle tissue model valid for striated muscles, in general, and for the myocardium, in particular based on a multiscale...

Myocardium | Energy balance | Time and space discretizations | Muscle tissue modeling | Multiscale | HEART | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | muscle tissue modeling | time and space discretizations | FRAMEWORK | EQUATIONS | myocardium | energy balance | multiscale | MECHANICAL-PROPERTIES

Myocardium | Energy balance | Time and space discretizations | Muscle tissue modeling | Multiscale | HEART | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | muscle tissue modeling | time and space discretizations | FRAMEWORK | EQUATIONS | myocardium | energy balance | multiscale | MECHANICAL-PROPERTIES

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 05/2012, Volume 231, Issue 14, pp. 4723 - 4744

The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation...

CFD | Staggered grid | Shallow water equations | Energy conserving discretization | Compressible Euler equations | INCOMPRESSIBLE-FLOW | FINITE-DIFFERENCE SCHEMES | MESH SCHEMES | NONUNIFORM GRIDS | CONVECTION | SYMMETRY | CONSERVATION PROPERTIES | NUMERICAL-SIMULATION | Compressible euler equations | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MESHES | PHYSICS, MATHEMATICAL | Thermodynamics

CFD | Staggered grid | Shallow water equations | Energy conserving discretization | Compressible Euler equations | INCOMPRESSIBLE-FLOW | FINITE-DIFFERENCE SCHEMES | MESH SCHEMES | NONUNIFORM GRIDS | CONVECTION | SYMMETRY | CONSERVATION PROPERTIES | NUMERICAL-SIMULATION | Compressible euler equations | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MESHES | PHYSICS, MATHEMATICAL | Thermodynamics

Journal Article

Journal of Computational Science, ISSN 1877-7503, 09/2019, Volume 36, p. 101008

•A new finite-difference symmetry-preserving discretization is presented.•It allows shallow-water simulations with mass, momentum and energy preserved.•Any...

Symmetry-preserving discretizations | Curvilinear staggered grid | Mimetic methods | Finite-difference methods | Mass, momentum and energy conservation | MIMETIC DISCRETIZATIONS | ENERGY | MESHES | DISCONTINUOUS GALERKIN METHOD | FORMULATION | COMPRESSIBLE EULER | SHALLOW-WATER EQUATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | COMPUTER SCIENCE, THEORY & METHODS | GRADIENTS | SCHEMES | Convergence (Mathematics) | Differential equations | Research

Symmetry-preserving discretizations | Curvilinear staggered grid | Mimetic methods | Finite-difference methods | Mass, momentum and energy conservation | MIMETIC DISCRETIZATIONS | ENERGY | MESHES | DISCONTINUOUS GALERKIN METHOD | FORMULATION | COMPRESSIBLE EULER | SHALLOW-WATER EQUATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | COMPUTER SCIENCE, THEORY & METHODS | GRADIENTS | SCHEMES | Convergence (Mathematics) | Differential equations | Research

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2018, Volume 355, Issue C, pp. 492 - 533

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as...

Reconstruction | Bounds-preserving | ALE | Remap | Energy-conserving | ARBITRARY | COMPRESSION | INTEGRAL PROPERTIES | SIMULATION | PHYSICS, MATHEMATICAL | GAS-DYNAMICS | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | SYSTEMS | REZONING ALGORITHM | Energy conservation | Force and energy | Beer | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | Lagrangian,hydrodynamics,remap,mimetic,cell-centered,ALE,exactintersection,KEfixup, finite-volume

Reconstruction | Bounds-preserving | ALE | Remap | Energy-conserving | ARBITRARY | COMPRESSION | INTEGRAL PROPERTIES | SIMULATION | PHYSICS, MATHEMATICAL | GAS-DYNAMICS | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | SYSTEMS | REZONING ALGORITHM | Energy conservation | Force and energy | Beer | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | Lagrangian,hydrodynamics,remap,mimetic,cell-centered,ALE,exactintersection,KEfixup, finite-volume

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2019, Volume 57, Issue 2, pp. 875 - 898

The nonlocal Allen-Cahn equation, a generalization of the classic Allen-Cahn equation by replacing the Laplacian with a parameterized nonlocal diffusion...

Energy stability | Discrete maximum principle | Exponential time differencing | Asymptotic compatibility | Nonlocal Allen-Cahn equation | MATHEMATICS, APPLIED | discrete maximum principle | 2ND-ORDER | RUNGE-KUTTA METHODS | APPROXIMATIONS | NUMERICAL-ANALYSIS | DISCRETIZATION | 1ST | energy stability | nonlocal Allen-Cahn equation | PERIDYNAMIC MODELS | DIFFUSION | asymptotic compatibility | exponential time differencing

Energy stability | Discrete maximum principle | Exponential time differencing | Asymptotic compatibility | Nonlocal Allen-Cahn equation | MATHEMATICS, APPLIED | discrete maximum principle | 2ND-ORDER | RUNGE-KUTTA METHODS | APPROXIMATIONS | NUMERICAL-ANALYSIS | DISCRETIZATION | 1ST | energy stability | nonlocal Allen-Cahn equation | PERIDYNAMIC MODELS | DIFFUSION | asymptotic compatibility | exponential time differencing

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2014, Volume 256, pp. 630 - 655

In this paper, we propose energy-conserving numerical schemes for the Vlasov–Ampère (VA) systems. The VA system is a model used to describe the evolution of...

Two-stream instability | Discontinuous Galerkin methods | Landau damping | Energy conservation | Bump-on-tail instability | Vlasov–Ampère system | Vlasov-Ampère system | IN-CELL METHOD | COLLISIONLESS PLASMA | Vlasov-Ampere system | POISSON SYSTEM | SIMULATION | PHYSICS, MATHEMATICAL | MAXWELL SYSTEM | IMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | RF GLOW-DISCHARGES | EQUATION | FINITE-ELEMENT CODE | Finite element method | Analysis | Methods | Computer simulation | Discretization | Mathematical analysis | Instability | Mathematical models | Plasmas | Galerkin methods

Two-stream instability | Discontinuous Galerkin methods | Landau damping | Energy conservation | Bump-on-tail instability | Vlasov–Ampère system | Vlasov-Ampère system | IN-CELL METHOD | COLLISIONLESS PLASMA | Vlasov-Ampere system | POISSON SYSTEM | SIMULATION | PHYSICS, MATHEMATICAL | MAXWELL SYSTEM | IMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | RF GLOW-DISCHARGES | EQUATION | FINITE-ELEMENT CODE | Finite element method | Analysis | Methods | Computer simulation | Discretization | Mathematical analysis | Instability | Mathematical models | Plasmas | Galerkin methods

Journal Article

ASTROPHYSICAL JOURNAL, ISSN 0004-637X, 12/2019, Volume 887, Issue 2, p. 191

We design a novel, exact energy-conserving implicit nonsymplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom....

ORDER | COMPUTATION | INTEGRATION | ASTRONOMY & ASTROPHYSICS | Circular orbits | Numerical simulations | Computer simulation | Gravitational waves | Binary systems | Integrators | Electromagnetic fields | Time dependence | Accuracy | Algorithms | Discretization | Energy conservation | Runge-Kutta method | Mathematical models | Hamiltonian functions | Gravity waves

ORDER | COMPUTATION | INTEGRATION | ASTRONOMY & ASTROPHYSICS | Circular orbits | Numerical simulations | Computer simulation | Gravitational waves | Binary systems | Integrators | Electromagnetic fields | Time dependence | Accuracy | Algorithms | Discretization | Energy conservation | Runge-Kutta method | Mathematical models | Hamiltonian functions | Gravity waves

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2020, Volume 400, p. 108991

The computation of multiphase flows presents a subtle energetic equilibrium between potential (i.e., surface) and kinetic energies. The use of traditional...

Conservative level set | Symmetry-preserving | Multiphase flow | Energy-preserving | Mimetic | EQUATIONS | FORMULATION | SIMULATION | PHYSICS, MATHEMATICAL | SURFACE-TENSION | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | FLUID | FRAMEWORK | COMPUTATION | SCHEMES | Robustness (mathematics) | Computer simulation | Energy conservation | Energia mecànica | Power transmission | Termodinàmica | Flux multifàsic | Corbes de nivell, Mètodes de | Física | Level set methods | Transmissió | Àrees temàtiques de la UPC

Conservative level set | Symmetry-preserving | Multiphase flow | Energy-preserving | Mimetic | EQUATIONS | FORMULATION | SIMULATION | PHYSICS, MATHEMATICAL | SURFACE-TENSION | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | FLUID | FRAMEWORK | COMPUTATION | SCHEMES | Robustness (mathematics) | Computer simulation | Energy conservation | Energia mecànica | Power transmission | Termodinàmica | Flux multifàsic | Corbes de nivell, Mètodes de | Física | Level set methods | Transmissió | Àrees temàtiques de la UPC

Journal Article

Physics Letters A, ISSN 0375-9601, 2007, Volume 370, Issue 1, pp. 8 - 12

We present a remarkable discretization of the 3-dimensional classical Kepler problem which preserves its trajectories and all integrals of motion. The points...

Kepler motion | Simulation by difference equations | Integrals of motion | Energy preserving discretization | Harmonic oscillator | MOTION | CONSTANTS | PHYSICS, MULTIDISCIPLINARY | integrals of motion | SYSTEMS | harmonic oscillator | simulation by difference equations | REGULARIZATION | energy preserving discretization | NUMERICAL INTEGRATOR

Kepler motion | Simulation by difference equations | Integrals of motion | Energy preserving discretization | Harmonic oscillator | MOTION | CONSTANTS | PHYSICS, MULTIDISCIPLINARY | integrals of motion | SYSTEMS | harmonic oscillator | simulation by difference equations | REGULARIZATION | energy preserving discretization | NUMERICAL INTEGRATOR

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2017, Volume 350, pp. 782 - 795

Recently, element based high order methods such as Discontinuous Galerkin (DG) methods and the closely related flux reconstruction (FR) schemes have become...

Discontinuous Galerkin method | Turbulence | De-aliasing | Large eddy simulation | Kinetic energy preserving | Split form | Kennedy and Gruber | FINITE-DIFFERENCE SCHEMES | ERRORS | PHYSICS, MATHEMATICAL | DIRECT NUMERICAL-SIMULATION | IMPLICIT LES | SUITABILITY | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | HIGH-RESOLUTION | SPECTRAL ELEMENT METHODS | TURBULENT FLOWS | Usage | Analysis | Force and energy | Mathematics - Numerical Analysis

Discontinuous Galerkin method | Turbulence | De-aliasing | Large eddy simulation | Kinetic energy preserving | Split form | Kennedy and Gruber | FINITE-DIFFERENCE SCHEMES | ERRORS | PHYSICS, MATHEMATICAL | DIRECT NUMERICAL-SIMULATION | IMPLICIT LES | SUITABILITY | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | HIGH-RESOLUTION | SPECTRAL ELEMENT METHODS | TURBULENT FLOWS | Usage | Analysis | Force and energy | Mathematics - Numerical Analysis

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 07/2016, Volume 316, Issue C, pp. 218 - 242

We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage...

Magnetohydrodynamics | Constrained transport | Lax–Wendroff | Finite difference WENO | Positivity preserving | High order | Lax-Wendroff | WEIGHTED ENO SCHEMES | EFFICIENT IMPLEMENTATION | TIME DISCRETIZATIONS | ESSENTIALLY NONOSCILLATORY SCHEMES | HAMILTON-JACOBI EQUATIONS | MHD EQUATIONS | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE SCHEME | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSTRAINED-TRANSPORT METHOD | HYPERBOLIC CONSERVATION-LAWS | Magnetic fields | Energy conservation | Methods | Accuracy | Discretization | Mathematical analysis | Evolution | Mathematical models | Fluxes

Magnetohydrodynamics | Constrained transport | Lax–Wendroff | Finite difference WENO | Positivity preserving | High order | Lax-Wendroff | WEIGHTED ENO SCHEMES | EFFICIENT IMPLEMENTATION | TIME DISCRETIZATIONS | ESSENTIALLY NONOSCILLATORY SCHEMES | HAMILTON-JACOBI EQUATIONS | MHD EQUATIONS | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE SCHEME | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSTRAINED-TRANSPORT METHOD | HYPERBOLIC CONSERVATION-LAWS | Magnetic fields | Energy conservation | Methods | Accuracy | Discretization | Mathematical analysis | Evolution | Mathematical models | Fluxes

Journal Article

Quarterly Journal of the Royal Meteorological Society, ISSN 0035-9009, 10/2014, Volume 140, Issue 684, pp. 2223 - 2234

This article presents families of spatial discretizations of the nonlinear rotating shallow‐water equations that conserve both energy and potential enstrophy....

energy conservation | shallow‐water equations | mixed finite element | Mixed finite element | Energy conservation | Shallow-water equations | POTENTIAL-ENSTROPHY | GRIDS | CIRCULATION | NUMERICALLY INDUCED OSCILLATIONS | EXTERIOR CALCULUS | shallow-water equations | VORTICITY | GENERAL-METHOD | DISCRETIZATIONS | WAVES | MODELS | METEOROLOGY & ATMOSPHERIC SCIENCES | Finite element analysis | Finite element method | Discretization | Mathematical analysis | Nonlinearity | Rotating | Two dimensional | Finite difference method

energy conservation | shallow‐water equations | mixed finite element | Mixed finite element | Energy conservation | Shallow-water equations | POTENTIAL-ENSTROPHY | GRIDS | CIRCULATION | NUMERICALLY INDUCED OSCILLATIONS | EXTERIOR CALCULUS | shallow-water equations | VORTICITY | GENERAL-METHOD | DISCRETIZATIONS | WAVES | MODELS | METEOROLOGY & ATMOSPHERIC SCIENCES | Finite element analysis | Finite element method | Discretization | Mathematical analysis | Nonlinearity | Rotating | Two dimensional | Finite difference method

Journal Article