Introduction to Computational Fluid Dynamics
                              Dmitri Kuzmin
                       Institute of Applied Mathematics (LS III)
          partial differential equation (PDE) models of fluid flows
          numerical solution methods and their properties
         https://www.mathematik.tu-dortmund.de/sites/cfdintro
   Examples of fluid flows
   Fluids (gases and liquids) are flowing
     around us: rains, winds, floods, hurricanes
     in our body: blood flow, breathing, drinking
     in our homes: heating and air conditioning
     around cars, planes, buildings, wind turbines
     in automobile engines and propulsion systems
     in furnaces, heat exchangers, chemical reactors
     in geophysical porous media (rock, sand, soil)
   Experimental fluid dynamics
     Experimental studies are performed with laboratory-scale models
     The amount of information is limited and the costs are very high
     There are measurement errors and disturbances caused by probes
       Theoretical fluid dynamics
        Generic conservation law
          ∂ Z udx+Z f ·nds=Z gdx,                       ∀V ⊂Ω                 n  f
          ∂t V             S              V
                                                                                V
                   ∂u +∇·f =g            in Ω×(0,T)                      S
                   ∂t
        Convection - diffusion equation
                         ∂u +∇·(vu−d∇u)=g                   in Ω×(0,T)
                         ∂t