wave-simulator 0.0.2

wave simulator

Wave Simulator

中文

This project is for wave simulation.

Please do not use this project for any purpose other than learning, as the author does not guarantee its rigor.

Installation

pip install wave-simulator

Examples

The following is a simple example. You can find more examples here.

from wave_simulator import OneDimensionSimulator, FixedBoundary

def my_initial_wave(x):
    if x < 4:
        return 0.5*x
    return -x + 6

s = OneDimensionSimulator()
s.set_simulation_range(6, 0.01, 16, 0.001)
s.set_initial_wave(my_initial_wave)
s.set_left_boundary(FixedBoundary())
s.set_right_boundary(FixedBoundary())
s.simulate()
s.animate_result_1D(ylim=(-4, 4), down_sampling_rate=20)

Detailed Guide

You can set the simulation's spatial and temporal ranges. This setting should be done before other configurations.

s.set_simulation_range(6, 0.01, 16, 0.001)

Set the initial waveform

def my_initial_wave(x):
    if x < 4:
        return 0.5*x
    return -x + 6

s.set_initial_wave(my_initial_wave)

Set the initial speed of the particles

def my_initial_speed(x):
    if x > 0.1 and x < np.pi/4+0.1:
        return -8*np.cos(8*(x-0.1))
    return 0

s.set_initial_point_speed(my_initial_speed)

Set the wave speed

def my_wave_speed(x):
    if x > 1.5:
        return 0.5
    return 1

s.set_wave_speed(my_wave_speed)

Set boundary conditions

s.set_left_boundary(FixedBoundary())
s.set_right_boundary(FixedBoundary())
s.set_up_boundary(UnlimitedBoundary())
s.set_down_boundary(NeumannBoundary())

To save the simulation result as a video, just add a save_path parameter

s.animate_result_3D(save_path="your_path.mp4")

Correspondence between Mathematical Symbols and Code Variables

Variable Name	Meaning
L_x	Simulation range for x
dx	Spatial step for x
X	Discrete values for x
c	Wave speed
c2	$c^2$
C	$c\frac{dt}{dx}$
C2	$(c\frac{dt}{dx})^2 $
c2_i_sub_1	$c_{i-1}^2$
c2_i	$c_i^2$
c2_i_add_1	$c_{i+1}^2$
u_i_sub_1	$u_{i-1}$
u_i	$u_{i}$
u_i_add_1	$u_{i+1}$
u_i_j	$u_{i,j}$
u_ip1_j	$u_{i+1,j}$
u_is1_j	$u_{i-1,j}$
u_i_ja1	$u_{i,j+1}$
u_i_js1	$u_{i,j-1}$

Related Formulas

1d reference 2d reference