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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 ...
eyadof's user avatar
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4 votes
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313 views

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{\...
alireza's user avatar
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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 }...
user2579288's user avatar
3 votes
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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 ...
NotaChoice's user avatar
3 votes
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167 views

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}{\...
bjp's user avatar
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3 votes
0 answers
83 views

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 ...
Nick Alger's user avatar
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3 votes
0 answers
402 views

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 ...
Wes Lowrie's user avatar
2 votes
0 answers
111 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, ...
Rishi's user avatar
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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 ...
Rafael Riveros Ávila's user avatar
2 votes
0 answers
64 views

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,...
namu's user avatar
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2 votes
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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 ...
CRG's user avatar
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57 views

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 ...
vijay's user avatar
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278 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 &...
Adam Lau's user avatar
1 vote
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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 ...
Hridey's user avatar
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235 views

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 ...
babar's user avatar
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31 views

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 ...
arc_lupus's user avatar
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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-...
Manish's user avatar
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0 answers
71 views

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 ...
CRG's user avatar
  • 347
1 vote
0 answers
921 views

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 ...
CRG's user avatar
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1 vote
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423 views

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 ...
CRG's user avatar
  • 347
1 vote
0 answers
216 views

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/ ...
CRG's user avatar
  • 347
1 vote
0 answers
298 views

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 ...
Amartya's user avatar
  • 243
1 vote
0 answers
276 views

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}{\...
imbr's user avatar
  • 366
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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 ...
FriendlyNeighborhoodEngineer's user avatar
0 votes
0 answers
54 views

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 ...
NotaChoice's user avatar
0 votes
0 answers
65 views

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 ...
yourds's user avatar
  • 121
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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 ...
theWrongAlice's user avatar
0 votes
0 answers
301 views

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 ...
bbch's user avatar
  • 33
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52 views

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 ...
Lucas Vieira's user avatar
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0 answers
446 views

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 ...
Lucas Vieira's user avatar
0 votes
0 answers
30 views

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 ...
11235's user avatar
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