Bagaimana Persamaan Navier-Stokes dapat mensimulasikan sistem udara di suatu daerah?
Atau bisakah persamaan ini memodelkan suatu badai seperti Tornado dan El-Nino?
Penurunan Persamaan Navier-Stokes
The derivation of the Navier–Stokes equations begins with an application of Newton's second law: conservation of momentum (often alongside mass and energy conservation) being written for an arbitrary portion of the fluid. In an inertial frame of reference, the general form of the equations of fluid motion is:
Navier–Stokes equations (general)
where v is the flow velocity, ρ is the fluid density, p is the pressure, is the (deviatoric) component of the total stress tensor, and f represents body forces (per unit volume) acting on the fluid and ∇ is the del operator. This is a statement of the conservation of momentum in a fluid and it is an application of Newton's second law to a continuum; in fact this equation is applicable to any non-relativistic continuum and is known as the Cauchy momentum equation.
This equation is often written using the material derivative Dv/Dt, making it more apparent that this is a statement of Newton's second law:
The left side of the equation describes acceleration, and may be composed of time dependent or convective effects (also the effects of non-inertial coordinates if present). The right side of the equation is in effect a summation of body forces (such as gravity) and divergence of stress (pressure and shear stress).
Arip Nurahman Notes
Jani Suhamjani, S.Si.
NASA Glenn Research Center