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Extreme Physics by Jon Larsen, Jeff Colvin

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4 Hydrodynamic motion

4.1 Derivation of Navier–Stokes equations

4.1.1 Continuum flux

Our goal in this chapter is to provide a complete mathematical description of plasmas in motion, and to describe how the motion changes with time in response to applied forces. The equations of motion are the central and most essential part of all simulation computer codes. All the other physical processes operative in matter at extreme conditions – thermal energy transport, radiation energy transport, ionization – affect the motion, and in the simulation code are added as source terms to the basic hydrodynamic equations.

We begin by considering motion in one dimension only. We also start with the simplest case of plasma that is a non-viscous and non-conducting fluid. ...

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