Questions tagged [wave-propagation]
The wave-propagation tag has no usage guidance.
31
questions with no upvoted or accepted answers
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Sound Waves Simulation in 3D Environment
I want to do a simulation of sound waves including wave propagation, absorption, and reflection in 3D space.
I did some research and I found this question in stackoverflow but it talks about ...
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297
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How can I solve the wave equation for a circular rod in cylindrical coordinates using finite differences?
I have a problem with the stability of finite difference method for the wave equation in cylindrical coordinates.
the equation is:
$$
\frac{\partial^2 \omega_n}{\partial r^2}+\frac{1}{r}\frac{\...
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2D wave equation with Mur boundary condition - setting up the RHS and solving (time-steps)
I am trying to solve a 2D wave equation implicitly using FD with central approximations with the following boundary conditions
$$\begin{align}
&u=2\sin\left(\frac{2\pi}{5}t\right)\quad \text{at }...
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Looking for non-trivial examples of solutions to 3D wave equations?
We have developed a (new) numerical scheme to solve the classical wave equation in 3 dimensions and we aim to publish the results.
We can read in the aim and scope of the journal of computational and ...
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My discretization of a wave equation in first-order form does not give correct solutions. What should I do?
I haven't much experience with conservation laws, shocks, etc. After reformulating my wave equation to 1st order system (velocity-stress):
$$
\frac{\partial v}{\partial t} + A \frac{\partial v}{\...
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3
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76
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Absorbing BC's / PML on a graph
The wave equation,
$$\ddot{u} = c^2 \Delta u,$$
can be generalized to abstract graphs by using the negative graph Laplacian in place of the physical Laplacian.
Is there a graph-theoretic analog of ...
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398
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Euler Equation Eigensystem with Gravity in the Energy Flux
I am modifying a conservative form of the Euler equations with gravity in the energy flux (see previous question: Energy Conservation in Conservation Laws with Source Terms) for use in a Riemann ...
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2
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Divergence on wave equation simulation
I'm currenly working on my own PDE solver for non-linear simulations in python. I've done succesfully simulations for KdV and Fisher's equation, but now I'm playing with second order derivatives in ...
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Resolving a stiff hyperbolic problem with Neumann boundary conditions
I am trying to numerically resolve the equation for an Euler-Bernoulli beam that is inextensible, unshearable, and subject to planar deformations:
$$\rho I(s) \frac{\partial^2 \theta}{\partial t^2}(s,...
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Time discretization of wave equation
I am trying to model the seismic wave equation and have therefore been reading about discretization schemes and their stability. I recently came across an insightful paper on 'Galerkin FEM methods for ...
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Solving nonlinear wave equation in a dispersive infinite waveguide
I would like to solve a three-dimensional nonlinear wave equation in an infinite cylindrical waveguide numerically. Since the waveguide is dispersive, shocks are less likely to form. Both the ...
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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 &...
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56
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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 ...
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223
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shallow water equation maccormack method
I am trying to make a code for 1D shallow water equation (nonlinear without source terms) using the MacCormack method for sinusoidal wave propagation. My issue is that the wave fluctuates and does not ...
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Simulation of a lens, insufficient points
I am simulating the propagation of a light pulse using the equation
$$\frac{\partial}{\partial z}A=\frac{1}{2\cdot k_0}\nabla^2_rA$$
with
$$k_0=\frac{2\pi}{\lambda_0}$$
The propagation with a step ...
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How do we implement Parameter free generalised Moment limiter in 1D Case in Discontinuous Galerkin methods?
I am referring to this paper:-
"A Parameter-Free Generalized Moment Limiter for High-
Order Methods on Unstructured Grids " by Michael Yang and Z.J. Wang.
http://dept.ku.edu/~cfdku/papers/AIAA-2009-...
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Degree of freedom for elastic wave propagation problem
I am solving a elastodynamics (vector valued elastic wave) equation.
I create the 2D mesh in Gmsh discretised into triangular elements of second order. Therefore, it is my understanding that the ...
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882
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Seismic Wave modelling: Elastic Wave or Acoustic Wave?
I am modelling a seismic wave equation using FEM. In the few papers that I read, I understand the following: (Kindly correct me if you disagree)
A shear (secondary wave - no change of volume) is more ...
- 347
1
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0
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397
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How to add a Ricker Wavelet (Mexican Hat) to a 2D/ 3D fem mesh?
I have a 2D square mesh and a 3D beam shaped mesh and I want to propagate a seismic wave in them. I am trying to simulate them using Open source FEM codes (fenics). I have left the top surface to be ...
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Weak form for elastoplastic wave propagation
I am trying to simulate elastoplastic seismic wave propagation using Fenics Solid Mechanics Application.
The app. provides some quasi-static demos to show elastoplastic behaviour in a cube/ beam/ ...
- 347
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0
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293
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Unwanted Oscillation in FDM simulation of elastic wave equation
I am using staggered grid FDTD for solving elastic wave equation. A description of which can be found at (geodynamics.usc.edu/~becker/teaching/557/reading/Virieux1987.pdf). I have generated a ...
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Numerically evaluate 1D inhomogeneous wave equation solution
I am trying to solve the following 1D inhomogeneous wave equation.
Forgive me if I a miss any rigorous mathematical concept.
$$ \frac{\partial^2 u}{\partial x^2} - \frac{1}{c^2}\frac{\partial^2 u}{\...
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Which numerical method can I use to solve this system of hyperbolic PDEs?
Backround
The mathematical model I am trying to numerically solve models wave propagation inside a cylinder with specific material properties suited for dynamic loading. The cylinder's upper base is ...
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Analytical Equation of the gaussian 1D wave equation with periodic Boundary condition
I am trying to validate the 1D analytical wave equation with a numerical solution with periodic boundary conditions. I have implemented the periodic boundary condition for the numerically calculated ...
- 121
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Can you describe the Galerkin numerical method to solve the wave equation?
How would you describe the Galerkin method to solving the 3D wave equation
$$u_{tt}= c^2\Delta u$$
to someone who wants to implement it immediately?
More precisely, we want to solve the Cauchy problem
...
- 151
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62
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schrodinger eq time propagation with dissipation using split step operator
I am looking in ways to include energy dissipation while propagating a coherent wavepacket in a 1d TDSE. for example I use the split step method: exp[Δt(D+V)]≈exp[ΔtV/2]exp[ΔtD]exp[ΔtV/2], and ...
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49
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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 ...
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FEM port Boundary definition for electromagnetics and wave guides
We are currently in the process of implementing ports in our EM FEM simulation SW.
We have come across the definition of boundary conditions for the ports, and we do not understand the equation for ...
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Split of complex parts in weak form
I am working on a numerical model to simulate the acoustic and elastic wave propagation in frequency domain via the Finite Element Method. Basically, the problem is to solve the Helmholtz equation in ...
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What is the meaning of the Helmholtz wave equation?
I am trying to build understanding on the Helmholtz wave equation $\Delta p + k^2 p = 0$, where $p$ is the deviation from ambient pressure and $k$ the wave number, in order to use it in numerical ...
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Circumferencial waves on a cylinder/sphere
I was wondering how we can introduce $e^{ik.x}$ terms associated with circumferencially propagating waves? In this case $\hat{e}_\theta$ is the direction of wave propagation. However, I was not able ...
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