Sponge Layer Model

The Sponge Layer model provides a method for suppressing spurious reflective disturbances near exterior boundaries in direct noise simulations.

Direct noise simulations solve for time-dependent flow variations in compressible fluid flow. These flow variations convect with the flow (for vortical disturbances) or propagate at the speed of sound (for acoustic disturbances) towards the exterior boundaries of the flow domain. For high-quality aeroacoustics simulations, the numerical algorithm must allow these disturbances to smoothly travel through the exterior boundaries without reflecting inside.

Some boundaries, such as the pressure outlet boundary, provide non-reflective conditions. However, the efficiency of non-reflective boundary conditions depends on the inclination angle at which the disturbances reach the boundary—the larger the tangential component of the inclination angle, the less efficient the reflection suppression.

To overcome this dependency on the inclination angle, Simcenter STAR-CCM+ provides the Sponge Layer model, which achieves non-reflective conditions at the boundaries by suppressing unsteady flow variations within a layer of specified thickness—the sponge layer. This volumetric approach prevents the acoustic waves and vortical disturbances from reaching the boundaries and thereby eliminates spurious reflection.

The Sponge Layer model adds the following damping term to the right-hand sides of the continuity, momentum, and energy equations:

Figure 1. EQUATION_DISPLAY

S_{s l} = - σ_{s l} (ϕ - ϕ_{r e f})

(4744)

where:

$ϕ \in {ρ, ρ v, ρ E}$ represents the transported quantity. $ρ$ is the density, $v$ is the velocity vector, and $E$ is the total energy per unit mass.
$σ_{s l}$ is the Sponge Layer Damping Coefficient.
$ϕ_{r e f}$ is the Reference Solution.

Sponge Layer Damping Coefficient

The sponge layer damping coefficient $σ_{s l}$ allows a smooth transition of the amount of damping in the sponge zone. The coefficient is calculated as a function of the boundary distance $d$ as:

Figure 2. EQUATION_DISPLAY

σ_{s l} (d) = σ_{\max} {1 - \cos [2 π (1 - \frac{d}{w})]}

(4745)

where $w$ is the sponge layer thickness and a Model Coefficient.

$σ_{\max}$ is the maximum damping coefficient calculated as:

Figure 3. EQUATION_DISPLAY

σ_{\max} = - \frac{c}{w} \log (1 - \frac{α}{100})

(4746)

where $α$ is the relative amount of suppression and a Model Coefficient.

Reference Solution

The reference solution $ϕ_{r e f}$ is the solution towards which the model damps the fluctuations in the sponge zone. The reference solution is based on a moving time-average, given in explicit form as:

Figure 4. EQUATION_DISPLAY

ϕ_{r e f}^{n + 1} = ϕ_{r e f}^{n} + \frac{Δ t}{Δ T} (ϕ - ϕ_{r e f}^{n})

(4747)

where

$n + 1$ is the current time level and $n$ is the previous time level.
$Δ t$ is the time-step size.

$Δ T$ is the local time-filter width, calculated as:

Figure 5. EQUATION_DISPLAY

Δ T = \frac{w}{c}

(4748)

where $c$ is the speed of sound.

Model Coefficients


$α$	$w$
90.0	1.0 m