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# Acoustic Scattering

Example files on this page

- full example — Salinas_rtest/training/exampleproblem/transient/acoustic/scattering/sphere_ps.inp

# 15. Acoustic Scattering

Acoustic analysis often includes the concepts of a “scattering” solution. By this, we mean an analysis where it is relatively easy to specify the incident wave at all points in space, and we solve for the reflected wave. Such analysis is seldom done for elasticity because the input medium is not usually homogeneous and an a priori specification of the incident wave is a challenge. Such scattering solutions are useful in a variety of contexts. A submarine in the ocean may be struck by an incident “ping” from a neighboring ship. Such a ping is nearly a plane wave, and calculation of the outbound wave is the item of interest. The total acoustic pressure (which is the sum of the incident and scattered components) may not be important. Because the incident wave is known, we do not need to model the vast region of space between the incident source and the scattering object. This greatly reduces the cost of the computation.

The theory manual details the formulation. There are several salient issues.

1. The same PDE is solved for scattering and full pressure solutions.

2. The acoustic scattering loads are applied analytically as a pressure on the wet surface of the structure.

3. A conjugate load is applied to the wet surface of acoustic medium. Thus, there are two loads applied: a pressure load, \(P\), on the elastic medium, and a velocity load on the acoustic medium. For a plane wave, \(v=\frac{P}{\rho c}\).

4. Because there are two such loads, we have designed a limited number of specialized functions for application of these loads. These functions ensure compatibility between the elastic and acoustic portions of the model.

5. The natural output quantity is the scattered pressure.

6. Typically, absorbing boundary conditions are applied to the exterior of the mesh to reduce reflection of the scattered wave.

Because scattering solutions use the same PDE as the full pressure calculation, the analyst could complete an analysis by applying these loads independently. Using the scattering loads and set up provides a more robust and simpler interface to scattering problems.

## 15.1. Scattering Sphere

The sample problem is an elastic sphere floating in an infinite acoustic medium. The meshes for the sphere and fluid do not match at the interface, so tied surface specifications must be used. The example problem is illustrated in Figure 15.1. A full example is attached, with geometry shown in Figure 15.2.

Figure 15.1 Elastic Sphere in Fluid Example.

Figure 15.2 Mesh Used in sphere_ps.inp

### 15.1.1. Solution

Within the solution section of the input, we specify the “scattering” keyword. This informs the solver that consistency must be maintained between loads, and output pressures will be scattered pressures.

### 15.1.2. Loads

The loads section should have a load applied to both the elastic and the fluid portions of the model. In the example input 15.1, sideset 1 is the surface of the elastic material, and sideset 2 is the corresponding surface of the fluid. Note that there are no checks made on this loading. However, if the loads are not applied in pairs, the analysis is meaningless.

While other structural loads can be applied in a scattering problem, it is incorrect to apply acoustic loads other than scattering loads. This is because we are redefining the acoustic variables to apply to incident pressures. We cannot define the variable as “incident” in one portion of the analysis and “total pressure” in another portion.

### 15.1.3. Functions

The functions referred to in the loads section must be capable of applying different functional responses to the elastic and acoustic regions. Specification of the “scattering” keyword in the solution section permits us to check this for consistency.

### 15.1.4. Tied Data

Because the elastic and acoustic regions of the model are not compatibly meshed, the surfaces must be tied together with a tied surface specification. Sidesets 1 and 2 are again applied. It is not necessary for the scattering problem to use tied data sections if the regions have compatible meshes.

### 15.1.5. Outputs

Specification of “apressure” outputs the scattered pressure.

Listing 15.1 Example Scattering Input

    Solution
      case out
        transient
        scattering
        nsteps=1000
        time_step=0.001
    end
    Loads
      sideset 1
        pressure=1
        function=1
      sideset 2
        acoustic_vel=1.
        function=1
    End
    Function 1
      type=Plane_Wave
      material=water
      k0=450.
      direction -1 0 0
    end
    Tied Data
      name surface1-2
      surface 1,2
    end
    Outputs
      apressure
      displacement
    end
    material water
      c0 = 5000
      density = 1