All Questions
Tagged with finite-difference wave-propagation
32
questions
3
votes
1
answer
270
views
Why does the FDM give a correct solution to a PDE with a discontinuous initial condition?
I was solving the dimensionless wave equation:
$$ u_{xx} = u_{tt} \tag 1$$
with the initial conditions:
$$ u(x,0) = 0 \tag 2 $$
$$ u_t(x=0,0) = v_0 \tag 2 $$
$$ u_t(x>0,0) = 0 \tag 3 $$
and the ...
2
votes
0
answers
112
views
Finite difference scheme to 1D wave equation with Dirac Delta forcing term
I am trying to simulate the following 1-dimensional wave equation with trivial initial conditions and a inhomogeneous Dirac delta function:
$u_{tt} - c^2 u_{xx} = \delta(x - x')\delta(t - t'), \ u(0, ...
- 121
2
votes
1
answer
132
views
Can the Runge-Kuta algorithm help in reducing numerical dispersion and anisotropy when using the FDM to solve the 2D wave equation? [closed]
I am currently studying the effects of group velocity on the finite difference solution of the wave equation. Most of what I learned is from this source. I understand that high frequency components in ...
- 45
0
votes
0
answers
45
views
Which numerical method can I use to solve this system of hyperbolic PDEs?
Backround
The mathematical model I am trying to numerically solve models wave propagation inside a cylinder with specific material properties suited for dynamic loading. The cylinder's upper base is ...
2
votes
1
answer
146
views
Can this finite difference dispersion be eliminated somehow?
I am trying to solve the wave equation
$$ {\partial ^2u(t,x) \over \partial x^2} = {\partial ^2u(t,x) \over \partial t^2} \tag1 $$
with the following boundary and initial conditions:
$$ {\partial u \...
0
votes
1
answer
211
views
Solving the wave equation for a circular membrane in polar cordinates
As you see this mode is not right, unless for what i understand
And the initial conditions were
...
- 31
2
votes
1
answer
579
views
Numerical solution of 2D wave equation using Fourier transform and finite differences
This is the $2$-dimensional wave equation
$$ u_{tt} = u_{xx} + u_{yy} $$
with initial condition $u(x,y,0)=f(x,y)$ and $u_{t}(x,y,0) = 0$.
The inverse Fourier transform used is
$$ u(x,y,t) = \iint \hat{...
- 121
1
vote
0
answers
280
views
Open boundary condition for 1d wave equation with variable wave speed using finite differences
I have implemented a finite difference solver for the 1d wave equation with variable wave speed:
$$ u_{tt} = c(x)u_{xx}, \hspace{10mm}c(x) = \dfrac{6 -x^2}{2} \hspace{5mm} $$
on $-2 \leq x \leq 2, t &...
- 11
0
votes
0
answers
51
views
How do I identify negative group speeds?
This question is a continuation of one of my other questions.
I've been trying to show that collocated (non-staggered) grids can suffer from negative group speeds in the linearized shallow water ...
- 105
0
votes
1
answer
166
views
A simple wave for the linear shallow water equations
I'm looking for a simple, right-traveling wave for the linear shallow water equations (1D). My question: what are the initial conditions (velocity $U_0(x)$ and/or average water height, average ...
- 105
2
votes
0
answers
161
views
Divergence on wave equation simulation
I'm currenly working on my own PDE solver for non-linear simulations in python. I've done succesfully simulations for KdV and Fisher's equation, but now I'm playing with second order derivatives in ...
1
vote
0
answers
60
views
Results blow up when number of intervals is increases (Yee algorithm FDTD, dielectric sphere)
I have been trying to write a program that analyses EM wave scattering by a dielectric sphere for a project.
The reference is Sadiku's book Numerical Methods in electromagnetics Edition 3.
Now the ...
- 41
1
vote
2
answers
491
views
Solve wave equation with discontinuous coefficients numerically?
I would like to solve the following equation
$$\frac{\partial^2 y}{\partial t^2} - c^2(x,t)\frac{\partial^2 y}{\partial x^2}=0,$$
for $y=y(x,t)$ numerically. The wave speed, $c(x,t)$, is of the form
$$...
- 219
5
votes
2
answers
843
views
Numerical solution of zero-potential time-dependent Schrödinger equation in 1D
I want to solve numerically the one-dimensional time-dependent Schrödinger equation $$i \psi_t(x,t)=-\frac{\hbar}{2m} \psi''(x,t)$$
My issue is that I don't have the physical background to understand ...
- 560
2
votes
1
answer
643
views
Modified Equation and Stability for Centred Finite Differences for Wave Equation
I am trying to use the modified equation to derive the stability condition for the finite difference approximation
$$
\frac{u(x,t+\Delta t) - 2 u(x, t) + u(x, t -\Delta t)}{\Delta t^2} = c^2 \frac{...
- 1,273