Fluid Mechanics : Numerical Methods

where σ is the stress tensor, ǫ = 12 (∇u +∇u) T is the strain tensor, f is a body force per unit mass (gravity is a typical example), qT is a volume source (it may model chemical reactions, Joule effects, radioactive decay, etc.), and jT is the heat flux. In addition to the above three fundamental conservation equations, one may also have to add L equations that accounts for the conservation of other quantities, say φl, 1 ≤ l ≤ L. These quantities may be the concentration of constituents in an alloy, the turbulent kinetic energy, the mass fractions of various chemical species by unit volume, etc. All these conservation equations take the following form