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User:Ddcampayo/SPH a la 2005

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This is a modified version of Smoothed-particle hydrodynamics, started on Nov 6th 2017.


Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the dynamics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan (1977) and Lucy (1977) initially for astrophysical problems. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography. It is a mesh-free Lagrangian method (where the coordinates move with the fluid), and the resolution of the method can easily be adjusted with respect to variables such as the density.

Interpolation

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Integral and summation interpolants and their kernels

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Derivatives

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Errors in the interpolants

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Errors when the particles are disordered

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SPH Euler equations

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The SPH acceleration equation

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The energy equations

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Resolution varying in space and time

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Lagrangian equations

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Conservation laws

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The Lagrangian with constraints

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Time integration in the absence of dissipation

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Applications of the Euler equations

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Dispersion relation for an infinite one-dimensional gas

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Toy star oscillations

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Toy stars in one dimension

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Heat conduction and matter diffusion

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The SPH heat conduction equation

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Diffusion, increase of entropy

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Boundary and interface conditions. The Stefan problem

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Viscosity

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Artificial viscosity

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Viscous heating and the energy equations

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Dissipation and the thermokinetic energy equation

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Reducing artificial dissipation

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Applications to shock and rarefaction problems

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Applications of SPH to liquids

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Boundaries

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Motion of a rigid body interacting with a liquid

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The boundary force

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Applications to rigid bodies in water

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Turbulence

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Multiphase flow

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Elasticity and fracture

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Special and general relativistic SPH

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Prospects for the future

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