Journal of Scientific Computing, ISSN 0885-7474, 12/2019, Volume 81, Issue 3, pp. 1732 - 1766

First this paper analyzes the reason for the accuracy losing of the third-order weighted essentially non-oscillatory (WENO) scheme. It is shown that one reason...

Third-order WENO scheme | Computational Mathematics and Numerical Analysis | 76L05 | Algorithms | Hybrid-WENO scheme | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics | Non-nodal critical point | 76M20 | Discontinuity-detecting method

Third-order WENO scheme | Computational Mathematics and Numerical Analysis | 76L05 | Algorithms | Hybrid-WENO scheme | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics | Non-nodal critical point | 76M20 | Discontinuity-detecting method

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 08/2012, Volume 231, Issue 20, pp. 6861 - 6906

Shallow water flows are found in a variety of engineering problems always dominated by the presence of bed friction and irregular bathymetry. These source...

Source terms | Augmented solver | 65M06 | HLL | Roe | Stability region | 76M20 | Shallow water | 35L65 | 76M12 | Wet/dry front | Weak solutions | HLLC | Well-balanced approach | 65M12 | TOPOGRAPHY | SIMULATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GODUNOV-TYPE METHODS | HYPERBOLIC CONSERVATION-LAWS | WATER EQUATIONS | SCHEMES | GEOMETRY | Elevation | Approximation | Friction | Mathematical analysis | Solvers | Mathematical models | Two dimensional | Riemann solver

Source terms | Augmented solver | 65M06 | HLL | Roe | Stability region | 76M20 | Shallow water | 35L65 | 76M12 | Wet/dry front | Weak solutions | HLLC | Well-balanced approach | 65M12 | TOPOGRAPHY | SIMULATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GODUNOV-TYPE METHODS | HYPERBOLIC CONSERVATION-LAWS | WATER EQUATIONS | SCHEMES | GEOMETRY | Elevation | Approximation | Friction | Mathematical analysis | Solvers | Mathematical models | Two dimensional | Riemann solver

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 12/2019, Volume 81, Issue 3, pp. 1963 - 1986

A second order interface anchoring method has been developed and used with fast sweeping algorithm for reinitialization of a level set function. The algebraic...

Reinitialization | Computational Mathematics and Numerical Analysis | Algorithms | Level set | Interface tracking | 76T99 | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics | 76M20 | 65Y05 | Fast sweeping method

Reinitialization | Computational Mathematics and Numerical Analysis | Algorithms | Level set | Interface tracking | 76T99 | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics | 76M20 | 65Y05 | Fast sweeping method

Journal Article

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Error estimates for the implicit MAC scheme for the compressible Navierâ€“Stokes equations

Numerische Mathematik, ISSN 0029-599X, 2/2019, Volume 141, Issue 2, pp. 495 - 567

We prove existence of a solution to the implicit MAC scheme for the compressible Navierâ€“Stokes equations. We derive error estimates for this scheme on two and...

65N12 | Theoretical, Mathematical and Computational Physics | Mathematics | 35Q30 | 76M20 | 76N10 | 76M12 | Mathematical Methods in Physics | 76N15 | Numerical Analysis | Mathematical and Computational Engineering | Mathematics, general | Numerical and Computational Physics, Simulation | NUMERICAL APPROXIMATION | SYSTEM | MATHEMATICS, APPLIED | FLUID | OPERATOR | SUITABLE WEAK SOLUTIONS | CONVERGENCE | FINITE-VOLUME SCHEME | FLOW | Classical Analysis and ODEs

65N12 | Theoretical, Mathematical and Computational Physics | Mathematics | 35Q30 | 76M20 | 76N10 | 76M12 | Mathematical Methods in Physics | 76N15 | Numerical Analysis | Mathematical and Computational Engineering | Mathematics, general | Numerical and Computational Physics, Simulation | NUMERICAL APPROXIMATION | SYSTEM | MATHEMATICS, APPLIED | FLUID | OPERATOR | SUITABLE WEAK SOLUTIONS | CONVERGENCE | FINITE-VOLUME SCHEME | FLOW | Classical Analysis and ODEs

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2018, Volume 340, pp. 122 - 150

The method presented below focuses on the numerical approximation of the Euler compressible system. It pursues a two-fold objective: being able to accurately...

Implicitâ€“explicit schemes | Hyperbolic equations | Multi-scale flows | Low Mach number | Relaxation schemes | Fractional step | UPWIND SCHEMES | MATHEMATICS, APPLIED | Implicit-explicit schemes | ACCURATE | NUMBER LIMIT | BEHAVIOR | EQUATIONS | PROJECTION LIKE SCHEME | ISENTROPIC EULER | NUMERICAL-SIMULATION | Mathematical Physics | Numerical Analysis | Mathematics

Implicitâ€“explicit schemes | Hyperbolic equations | Multi-scale flows | Low Mach number | Relaxation schemes | Fractional step | UPWIND SCHEMES | MATHEMATICS, APPLIED | Implicit-explicit schemes | ACCURATE | NUMBER LIMIT | BEHAVIOR | EQUATIONS | PROJECTION LIKE SCHEME | ISENTROPIC EULER | NUMERICAL-SIMULATION | Mathematical Physics | Numerical Analysis | Mathematics

Journal Article

Journal de mathÃ©matiques pures et appliquÃ©es, ISSN 0021-7824, 05/2019, Volume 125, pp. 189 - 208

We prove that weak solutions obtained as limits of certain numerical spaceâ€“time discretizations are suitable in the sense of Scheffer and...

Navierâ€“Stokes equations | Numerical schemes | Î¸-method | Finite element and finite difference methods | Local energy inequality | MATHEMATICS | MATHEMATICS, APPLIED | theta-method | SLIP BOUNDARY-CONDITIONS | SEMI-DISCRETIZATION | Navier-Stokes equations | PARTIAL REGULARITY

Navierâ€“Stokes equations | Numerical schemes | Î¸-method | Finite element and finite difference methods | Local energy inequality | MATHEMATICS | MATHEMATICS, APPLIED | theta-method | SLIP BOUNDARY-CONDITIONS | SEMI-DISCRETIZATION | Navier-Stokes equations | PARTIAL REGULARITY

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 6/2019, Volume 79, Issue 3, pp. 1936 - 1980

Hysteresis phenomenon plays an important role in fluid flow through porous media and exhibits convoluted behavior that are often poorly understood and that is...

Hysteretic two-phase flow | Computational Mathematics and Numerical Analysis | Riemann problem | Theoretical, Mathematical and Computational Physics | Mathematics | Finite volume/element | 76M20 | 76M10 | Hyperbolic conservation laws | Projection method | Relaxation | Algorithms | Mathematical and Computational Engineering | 76S05 | MATHEMATICS, APPLIED | BEHAVIOR | EQUATIONS | Finite volume | MODEL | RELATIVE PERMEABILITIES | DOMAIN DECOMPOSITION | 3-PHASE FLOW | TRANSPORT PHENOMENA | CAPILLARY-PRESSURE | CONSERVATION-LAWS | DISPLACEMENT | element | Environmental law | Analysis | Numerical analysis

Hysteretic two-phase flow | Computational Mathematics and Numerical Analysis | Riemann problem | Theoretical, Mathematical and Computational Physics | Mathematics | Finite volume/element | 76M20 | 76M10 | Hyperbolic conservation laws | Projection method | Relaxation | Algorithms | Mathematical and Computational Engineering | 76S05 | MATHEMATICS, APPLIED | BEHAVIOR | EQUATIONS | Finite volume | MODEL | RELATIVE PERMEABILITIES | DOMAIN DECOMPOSITION | 3-PHASE FLOW | TRANSPORT PHENOMENA | CAPILLARY-PRESSURE | CONSERVATION-LAWS | DISPLACEMENT | element | Environmental law | Analysis | Numerical analysis

Journal Article

Applied Mathematics and Mechanics, ISSN 0253-4827, 11/2019, Volume 40, Issue 11, pp. 1647 - 1656

A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure...

rectangular duct | Fluid- and Aerodynamics | Classical Mechanics | Maxwell fluid | 76A05 | Mathematics | 76M20 | finite difference method | O351.2 | oscillatory flow | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | Partial Differential Equations | Fluid dynamics | Analysis

rectangular duct | Fluid- and Aerodynamics | Classical Mechanics | Maxwell fluid | 76A05 | Mathematics | 76M20 | finite difference method | O351.2 | oscillatory flow | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | Partial Differential Equations | Fluid dynamics | Analysis

Journal Article

Numerische Mathematik, ISSN 0029-599X, 6/2018, Volume 139, Issue 2, pp. 281 - 314

We consider various approximations of artificial boundary conditions for linearized Benjaminâ€“Bonaâ€“Mahony BBM equation. Continuous (respectively discrete)...

Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65M06 | Mathematical and Computational Engineering | Mathematics, general | 65M85 | Mathematics | Numerical and Computational Physics, Simulation | 76M20 | 65M12 | MATHEMATICS, APPLIED | WAVE-EQUATION | TRANSPARENT | DISPERSION | BBM EQUATION | SCHEMES | Analysis of PDEs

Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65M06 | Mathematical and Computational Engineering | Mathematics, general | 65M85 | Mathematics | Numerical and Computational Physics, Simulation | 76M20 | 65M12 | MATHEMATICS, APPLIED | WAVE-EQUATION | TRANSPARENT | DISPERSION | BBM EQUATION | SCHEMES | Analysis of PDEs

Journal Article

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Numerical Methods for Euler Equations with Self-similar and Quasi Self-similar Solutions

Journal of Scientific Computing, ISSN 0885-7474, 11/2018, Volume 77, Issue 2, pp. 726 - 754

Some problems of Euler equations have self-similar solutions which can be solved by more accurate method. The current paper proposes two new numerical methods...

Computational Mathematics and Numerical Analysis | Shock reflection | Theoretical, Mathematical and Computational Physics | 65M06 | Mathematics | Euler equations | 76M20 | Shock tube problem | 2D Riemann problem | 35L65 | 76M22 | Algorithms | Mathematical and Computational Engineering | Quasi self-similar | Self-similar | POSITIVE SCHEMES | MATHEMATICS, APPLIED | SYSTEMS | CONSERVATION-LAWS | 2-DIMENSIONAL GAS-DYNAMICS | RIEMANN PROBLEM | Environmental law | Methods | Numerical analysis

Computational Mathematics and Numerical Analysis | Shock reflection | Theoretical, Mathematical and Computational Physics | 65M06 | Mathematics | Euler equations | 76M20 | Shock tube problem | 2D Riemann problem | 35L65 | 76M22 | Algorithms | Mathematical and Computational Engineering | Quasi self-similar | Self-similar | POSITIVE SCHEMES | MATHEMATICS, APPLIED | SYSTEMS | CONSERVATION-LAWS | 2-DIMENSIONAL GAS-DYNAMICS | RIEMANN PROBLEM | Environmental law | Methods | Numerical analysis

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 11/2018, Volume 77, Issue 2, pp. 1084 - 1114

We present a new, formally third order, implicit Weighted Essentially Non-Oscillatory (iWENO3) finite volume scheme for solving systems of nonlinear...

Computational Mathematics and Numerical Analysis | 65M25 | Eulerianâ€“Lagrangian | Theoretical, Mathematical and Computational Physics | Semi-Lagrangian | 65M06 | Mathematics | Finite volume | 76M20 | Traceline | Algorithms | Locally frozen | Mathematical and Computational Engineering | Hyperbolic | Roe solver | WENO reconstruction | 76X05 | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | RUNGE-KUTTA METHODS | ESSENTIALLY NONOSCILLATORY SCHEMES | NAVIER-STOKES EQUATIONS | Eulerian-Lagrangian | ADVECTION | FINITE-ELEMENT | TRANSPORT PROBLEMS | Environmental law

Computational Mathematics and Numerical Analysis | 65M25 | Eulerianâ€“Lagrangian | Theoretical, Mathematical and Computational Physics | Semi-Lagrangian | 65M06 | Mathematics | Finite volume | 76M20 | Traceline | Algorithms | Locally frozen | Mathematical and Computational Engineering | Hyperbolic | Roe solver | WENO reconstruction | 76X05 | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | RUNGE-KUTTA METHODS | ESSENTIALLY NONOSCILLATORY SCHEMES | NAVIER-STOKES EQUATIONS | Eulerian-Lagrangian | ADVECTION | FINITE-ELEMENT | TRANSPORT PROBLEMS | Environmental law

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 8/2018, Volume 76, Issue 2, pp. 727 - 758

Fluidâ€“solid interaction has been a challenging subject due to their strong nonlinearity and multidisciplinary nature. Many of the numerical methods for solving...

Computational Mathematics and Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65N06 | Helmholtzâ€“Hodge decomposition | Mathematics | Primary 76D03 | 76M20 | 35J25 | Extended Hodge decomposition | Algorithms | Numerical analysis | Secondary 35Q30 | Mathematical and Computational Engineering | Fluidâ€“solid interaction | FREE-SURFACE | Fluid-solid interaction | MATHEMATICS, APPLIED | MONOLITHIC APPROACH | FLOWS | SOLVERS | IMMERSED BOUNDARY METHOD | Helmholtz-Hodge decomposition | SCHEMES | Analysis | Methods | Force and energy

Computational Mathematics and Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65N06 | Helmholtzâ€“Hodge decomposition | Mathematics | Primary 76D03 | 76M20 | 35J25 | Extended Hodge decomposition | Algorithms | Numerical analysis | Secondary 35Q30 | Mathematical and Computational Engineering | Fluidâ€“solid interaction | FREE-SURFACE | Fluid-solid interaction | MATHEMATICS, APPLIED | MONOLITHIC APPROACH | FLOWS | SOLVERS | IMMERSED BOUNDARY METHOD | Helmholtz-Hodge decomposition | SCHEMES | Analysis | Methods | Force and energy

Journal Article

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Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms

Applied Mathematics and Mechanics, ISSN 0253-4827, 6/2019, Volume 40, Issue 6, pp. 823 - 836

To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries...

compact scheme | Fluid- and Aerodynamics | O241 | Classical Mechanics | Mathematics | simultaneous approximation term (SAT) | 76M20 | 93D20 | time stability | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | Partial Differential Equations | high-order scheme | Eigenvalues | Boundary value problems | Approximation theory | Research | Mathematical research

compact scheme | Fluid- and Aerodynamics | O241 | Classical Mechanics | Mathematics | simultaneous approximation term (SAT) | 76M20 | 93D20 | time stability | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | Partial Differential Equations | high-order scheme | Eigenvalues | Boundary value problems | Approximation theory | Research | Mathematical research

Journal Article

Russian Journal of Numerical Analysis and Mathematical Modelling, ISSN 0927-6467, 02/2020, Volume 35, Issue 1, pp. 21 - 35

In the present work the possibility of turbulence closure applying to improve barotropic jet instability simulation at coarse grid resolutions is considered....

kinetic energy backscatter | 76E20 | 76F65 | 65L07 | subgrid scale modelling | 76M20 | 76F06 | 76M55 | normal modes | 76M35 | Two-dimensional turbulence | scale-similarity | barotropic instability | stochastic parameterization | 81T80 | Damping | Turbulence | Turbulent flow | Computer simulation | Structural stability | Backscattering | Eddy viscosity | Ocean models | Vortices | Spectrum analysis | Computational grids | Kinetic energy | Closures

kinetic energy backscatter | 76E20 | 76F65 | 65L07 | subgrid scale modelling | 76M20 | 76F06 | 76M55 | normal modes | 76M35 | Two-dimensional turbulence | scale-similarity | barotropic instability | stochastic parameterization | 81T80 | Damping | Turbulence | Turbulent flow | Computer simulation | Structural stability | Backscattering | Eddy viscosity | Ocean models | Vortices | Spectrum analysis | Computational grids | Kinetic energy | Closures

Journal Article

Environmental Earth Sciences, ISSN 1866-6280, 12/2015, Volume 74, Issue 11, pp. 7387 - 7405

An algorithm is presented for numerical modelling of impulse water waves generated by submarine landslides moving along irregular bottom profiles. A spatially...

Shallow water equations | Earth Sciences | Hydrology/Water Resources | Biogeosciences | Geology | 76B15 | Geochemistry | Terrestrial Pollution | Adaptive grid | 76M20 | Submarine landslide | Surface waves | Finite-difference scheme | Irregular bottom | Environmental Science and Engineering | ENVIRONMENTAL SCIENCES | GEOSCIENCES, MULTIDISCIPLINARY | TSUNAMI GENERATION | WATER RESOURCES | SIMULATION | UNDERWATER LANDSLIDE | Water waves | Submarine boats | Landslides | Algorithms | Analysis | Reservoirs | Models | Landslides & mudslides | Geophysics

Shallow water equations | Earth Sciences | Hydrology/Water Resources | Biogeosciences | Geology | 76B15 | Geochemistry | Terrestrial Pollution | Adaptive grid | 76M20 | Submarine landslide | Surface waves | Finite-difference scheme | Irregular bottom | Environmental Science and Engineering | ENVIRONMENTAL SCIENCES | GEOSCIENCES, MULTIDISCIPLINARY | TSUNAMI GENERATION | WATER RESOURCES | SIMULATION | UNDERWATER LANDSLIDE | Water waves | Submarine boats | Landslides | Algorithms | Analysis | Reservoirs | Models | Landslides & mudslides | Geophysics

Journal Article

Applied Mathematics and Mechanics, ISSN 0253-4827, 11/2018, Volume 39, Issue 11, pp. 1679 - 1690

A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the...

genetic algorithm | time stable | 93D20 | dissipative compact | O241 | Classical Mechanics | high-order | finite-difference scheme | Mathematics | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | 76M20 | MATHEMATICS, APPLIED | MECHANICS | LARGE-EDDY SIMULATION | STABILITY | Finite element method | Research | Mathematical research | Genetic algorithms

genetic algorithm | time stable | 93D20 | dissipative compact | O241 | Classical Mechanics | high-order | finite-difference scheme | Mathematics | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | 76M20 | MATHEMATICS, APPLIED | MECHANICS | LARGE-EDDY SIMULATION | STABILITY | Finite element method | Research | Mathematical research | Genetic algorithms

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2011, Volume 200, Issue 23, pp. 2083 - 2093

We introduce in this paper a new direction splitting algorithm for solving the incompressible Navierâ€“Stokes equations. The main originality of the method...

Pressure Poisson equation | 76D30 | 65N35 | Direction splitting | ADI | Incompressible flows | Navierâ€“Stokes | 35J05 | 76M20 | Time splitting | 65F05 | Navier-Stokes | NUMERICAL SOLUTION | CORRECTION PROJECTION METHODS | FICTITIOUS DOMAIN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | DRIVEN CAVITY FLOW | Operators | Splitting | Algorithms | Mathematical analysis | Projection | Mathematical models | Convergence | Navier-Stokes equations

Pressure Poisson equation | 76D30 | 65N35 | Direction splitting | ADI | Incompressible flows | Navierâ€“Stokes | 35J05 | 76M20 | Time splitting | 65F05 | Navier-Stokes | NUMERICAL SOLUTION | CORRECTION PROJECTION METHODS | FICTITIOUS DOMAIN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | DRIVEN CAVITY FLOW | Operators | Splitting | Algorithms | Mathematical analysis | Projection | Mathematical models | Convergence | Navier-Stokes equations

Journal Article

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Numerical modeling of tsunamis and tsunami vulnerability analysis for Heraklion, Crete

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 02/2018, Volume 41, Issue 3, pp. 1068 - 1073

Tsunamis are rare events compared with other extreme natural hazards, but the growth of population along coastlines has increased their potential impact....

subclass 76B15 | tsunami | 86A15 | tsunami vulnerability of Heraklion | 76M20 | shallow water equations | WAVE | MATHEMATICS, APPLIED | HAZARD | RISK | Models | Tsunamis | Seismology | Analysis | Shallow water equations | Nonlinear equations | Computer simulation | Seismic engineering | Software reliability | Population statistics | Remote sensing | Inundation | Dislocations | Windows (intervals) | Wave propagation | Earthquakes | Probabilistic analysis | Mathematical models | Hazard assessment | Seismic response | Finite difference method | Geographic information systems

subclass 76B15 | tsunami | 86A15 | tsunami vulnerability of Heraklion | 76M20 | shallow water equations | WAVE | MATHEMATICS, APPLIED | HAZARD | RISK | Models | Tsunamis | Seismology | Analysis | Shallow water equations | Nonlinear equations | Computer simulation | Seismic engineering | Software reliability | Population statistics | Remote sensing | Inundation | Dislocations | Windows (intervals) | Wave propagation | Earthquakes | Probabilistic analysis | Mathematical models | Hazard assessment | Seismic response | Finite difference method | Geographic information systems

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 8/2015, Volume 64, Issue 2, pp. 289 - 316

In this paper, a novel penalty method based on the immersed boundary formulation is proposed for simulating the transient Stokes flow with an inextensible...

Computational Mathematics and Numerical Analysis | Stability | Theoretical, Mathematical and Computational Physics | 65M06 | Mathematics | Solid particle | Immersed boundary method | 76D07 | 76M20 | Penalty method | Algorithms | Appl.Mathematics/Computational Methods of Engineering | Inextensible interface | 65M12 | Stokes flow | STOKES-FLOW | MATHEMATICS, APPLIED | FLUID | VESICLES | SHEAR-FLOW

Computational Mathematics and Numerical Analysis | Stability | Theoretical, Mathematical and Computational Physics | 65M06 | Mathematics | Solid particle | Immersed boundary method | 76D07 | 76M20 | Penalty method | Algorithms | Appl.Mathematics/Computational Methods of Engineering | Inextensible interface | 65M12 | Stokes flow | STOKES-FLOW | MATHEMATICS, APPLIED | FLUID | VESICLES | SHEAR-FLOW

Journal Article