Incompressible Navier-Stokes Equations

The incompressible Navier-Stokes equations solved in NekRS are conservation of mass,

(1)

conservation of momentum,

(2)

and conservation of energy,

(3)

where is the velocity, is the pressure, is the fluid density, is the fluid temperature, is the viscous stress tensor, is a force vector, is a volumetric heat source in the fluid, is the fluid isobaric specific heat capacity, and is the fluid thermal conductivity.

Passive Scalars

A passive scalar is any quantity which satisfies an equation of the form

where and are coefficients. For instance, temperature is a passive scalar if and . Other quantities which obey passive scalar equations include many aspects of mass transport.