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COMPUTATIONAL MARINE HYDRODYNAMICS (NA40020)

Ritwik Ghoshal

Spring 2025

Contact:

ritwik@naval.iitkgp.ac.in

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Wave Equation (1D)

The wave equation (with source) in one space dimension can be written as

Finite-difference discretization

Rearranging

CFL-condition

Wall boundary

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Grid and boundary condition

CFL= 2

Wall

Wall

Total Time, T=20

​

dx=0.1, nx=100

​

c=1;

​

@ x=4.9 and 5.1 δ= 0.1, 0.1

@x=5.0 δ =0.2

​

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Wave Equation (2D)

The wave equation (with source) in two space dimension can be written as

Finite-difference discretization

Boundary conditions (Wall)

Source

 

T=time-period

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Absorbing boundary

For 1D

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Grid and boundary condition

Wall

Wall

Wall

Wall

Time period, T=20

​

dx=dy=0.1

nx=ny=100

​

c=1;

​

CFL<c*dt/dx = 0.5

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Finite Difference Method

Wall boundary

Absorbing boundary

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Assignment

  • Solve the following problem using FDM

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  • Convert the boundary condition to absorbing boundary.
  • Rewrite the code considering absorbing boundary.
  • Create animation.
  • Submit/print code and contour plots.
  • Use any input signal.