Mathematics of advection Advection
1 mathematics of advection 1.1 advection equation 1.2 solving equation 1.3 treatment of advection operator in incompressible navier stokes equations mathematics of advection the advection equation partial differential equation governs motion of conserved scalar field advected known velocity vector field. derived using scalar field s conservation law, gauss s theorem, , taking infinitesimal limit. one visualized example of advection transport of ink dumped river. river flows, ink move downstream in pulse via advection, water s movement transports ink. if added lake without significant bulk water flow, ink disperse outwards source in diffusive manner, not advection. note moves downstream, pulse of ink spread via diffusion. sum of these processes called convection. the advection equation in cartesian coordinates advection operator is u ⋅ ∇ = u x ...