advance fluid

tn -> tn+1

advance solid

tn -> tn+1

input
- vorticity @tn+1
- angle, velangle @tn-1, tn
output
- angle @tn+1, velangle @tn+1
- char fn @tn+1, u_fluid, u_beam @tn+1
kill vorticity @tn+1 at the boundary
vorticity -> u_fluid @tn+1
u_fluid @tn+1 -> pressure @tn+1
use secant method: angle, velangle @tn-1, @tn -> angle, velangle @tn+1
- estimate value for angle, velangle @tn+1;
- beam.update(), beam.update_pressure -> pressureOnBody @tn+1
- solve for T @tn+1
- solve for g, g is a funtion of angle, velangle @tn-1, tn, tn+1

(currPressure, oldAngle, oldVelAngle, currAngle, currVelAngle, currT, newAngle, newVelAngle, newT)

member variable
- currPressure
- oldAngle, oldVelAngle, currAngle, currVelAngle, currT
- newAngle, newVelAngle, newT
member function
- operator()
  - the main flow of the program
  - broyden(computeF, currangel, newangle, newvelangle)
- computeF(estimatedAngle, estimatedVelAngle)
  - beam(currangle, currvelangle)
  - pressureOnBody = vector{..}
  - beam.update_pressure(pressureOnBody)
  - broygen(computeG, estimatedT, tempT)
  - return ----
- computeG(estimatedT)
  - return ----
- broyden(estimated, result)
mistake
- I think I should combine class advanceBeam and class beam together.
  - they two are both properties of beam.
  - advance need to use member function of class beam: updatePressure.

input
- goemetry: width, length, locHead, velHead
- computational setting: epsilon, numofElem
- fluid knowledge: pressure
- dynamic knowledge: oldAngle, oldVelAngle, currAngle, currVelAngle, currT
internal variable
- deltaFunc
- pressureOnBody
output
- charFunc
- velBeam
- newangle, newvelangle, newT

public
- constructor(geometry and computational setting)
- advance(pressure, 3 angle, 3 velAngle, 2 T, velBeam, charFunc)
  - Broyden()
private
- update(angle, velangle)
  - update_pressure