This lesson covers the concept of Smoothed Particle Hydrodynamics (SPH), a Lagrangian methodology used in two-phase flow and heat transfer. The lesson explains the algorithm for solving multi-phase flow in SPH, including the use of freeware for simulation. It delves into the equations used in SPH, such as the Navier-Stokes equation and energy equations, and how they transform in a Lagrangian framework. The lesson also discusses how the domain is discretized using Lagrangian particles in SPH, and how to deal with Lagrangian equations. It further explains how to tackle equations for two-phase flow using SPH, and how to use the Von Neumann-Richtmyer artificial viscosity to regain the continuum nature of the fluid. The lesson concludes with a demonstration of a case study using the LAMMPS SPH multiphase software.

- Smoothed Particle Hydrodynamics (SPH) is a Lagrangian methodology used in two-phase flow and heat transfer.
- In SPH, the domain is discretized using Lagrangian particles, and Lagrangian equations are used.
- The Von Neumann-Richtmyer artificial viscosity is used in SPH to regain the continuum nature of the fluid.
- The LAMMPS SPH multiphase software can be used to simulate SPH, as demonstrated in a case study.

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