How to Approach Solving a 2D Damped Wave Equation?

In summary, the conversation discusses a damped wave on a two-dimensional plane and the equation needed to solve it. The equation involves a damping factor and wave speed, and the closest match is the Helmholtz equation. The person has tried to solve it using Mathematica but is unsure of how to proceed and is open to suggestions. One possible approach is to use separation of variables to turn it into ordinary differential equations.
  • #1
igor_b
1
0
Hi to all!

I need to solve following equation:
[tex]
\frac{\partial^2 u}{\partial t^2} + 2 \beta \frac{\partial u}{\partial t} -c^2\nabla^2u=0
[/tex]

It describes a damped wave on a x-y plane. [tex]2\beta[/tex] is damping factor and c is wave speed.

I haven't had any luck finding a PDE class that looks like this. Closest match is Helmholtz equation but it doesn't have [tex]\frac{\partial}{\partial t}[/tex] element.

Tried to solve it using Mathematica but didn't have any luck (but that is maybe because of the fact that I don't really know how to use Mathematica).

Any hints on how to proceed would be appreciated either on manual solving or by using Mathematica (or Matlab, for that matter).

Igor
 
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  • #2
Seperation of variables to turn it into ordinary differential equations. It looks like __ equation for spatial part, and __ for time part, but I won't fill in the blanks, that's cheating :)
 

FAQ: How to Approach Solving a 2D Damped Wave Equation?

What is the 2D damped wave equation?

The 2D damped wave equation is a partial differential equation that describes the propagation of a wave in a two-dimensional space while taking into account damping effects. It is typically used in fields such as acoustics, electromagnetics, and fluid dynamics.

How is the 2D damped wave equation derived?

The 2D damped wave equation is derived from the general wave equation by adding a damping term, which represents the dissipation of energy due to factors such as friction or viscosity. This term is typically denoted by a damping coefficient multiplied by the time derivative of the wave function.

What are the governing parameters of the 2D damped wave equation?

The governing parameters of the 2D damped wave equation include the damping coefficient, the wave speed, and the initial conditions of the wave. These parameters determine the behavior of the wave and can be adjusted to model different physical systems.

What are the applications of the 2D damped wave equation?

The 2D damped wave equation has many applications in various fields of science and engineering. It is commonly used in the study of sound and vibration, as well as in the analysis of electromagnetic waves and fluid flows. It is also used in image processing and signal analysis.

How is the 2D damped wave equation solved?

The 2D damped wave equation can be solved using various numerical methods, such as finite difference, finite element, and spectral methods. These methods involve discretizing the equation and solving it iteratively to obtain an approximate solution. Analytical solutions are also possible for simple cases with specific boundary and initial conditions.

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