## More on Body - Computation

A Real World Simulation is performed by solving an appropriate equation, such as the Navier-Stokes equation for fluid flow.

A Dual World Simulation is performed by solving a corresponding Dual Linearized Equations which gives information on sensitivities in the original Real World Simulation.

### Computational Simulations from the Real World

#### Movies

Transition to turbulence in a jet flow (blowing out a candle?)
(Navier-Stokes equations).

(Created by: Johan
Hoffman)

Transition to turbulence in a shear flow (Navier-Stokes equations).

(Created by: Johan
Hoffman)

Turbulent flow around a surface mounted cube at Reynolds number 40.000
(pressure in the left column, velocity in the right, viewed from the
side in the top row and from above in the bottom row) (Navier-Stokes
equations).

(Created by: Johan Hoffman)

Channel flow with four square inlets (Navier-Stokes equations).

(Created by: Johan Hoffman)

Flying circus cow (physical and geometric representation) (Lagrange equations).

(Created by: Johan Jansson)

#### Still Images

Fluid flow around a train. (Navier-Stokes equations).

Magnetic field around a coil. (Maxwell equations).

### Computational Simulations from the Dual World

Dual solution for turbulent shear flow (see above): spread of initial
disturbance in the middle. (Navier-Stokes equations).

(Created by: Johan
Hoffman)

Dual solution for the surface mounted cube (see above): sensitivity
for computation of drag (pressure to the left, velocity to the right).
(Navier-Stokes equations).

(Created by: Johan Hoffman)