Particle Remediation

The Particle Remediation model excludes insignificant particles from the computation to optimize the computational resources and ensure robustness of the solver. The particle remediation shifting method applies an isotropic pattern for fluid particles to keep a uniform space discretization and avoid empty areas.

Removal

The Particle Remediation model provides the option to remove particles that exceed a specified maximum velocity or particles that are outside a specified geometry. The particles with irrelevant position or velocity are removed at the end of an iteration. The approach is useful, for example, for particles leaking from a reservoir or for particles that are trapped between the teeth of gears.

Shifting

In SPH simulations, the spatial derivation operators require a homogeneous particle distribution for accuracy. In some cases, the particle distribution can become inhomogeneous, leading to inaccuracies. The Skillen ([286]) shifting method includes a correction term to the SPH particle position equation for maintaining a near uniform particle distribution in the domain. The corrected particle position is then computed as:

Figure 1. EQUATION_DISPLAY
r i n + 1 ′ = r i n + 1 − χ R 2 Δ t ‖ v i n + 1 ‖ ∑ j ∈ P ( Ω ) V j ∇ W i j
(1126)
where:
  • n + 1 ′ is the updated value of a variable (position, velocity) at the next time-step after particle shifting.
  • R is the smoothing radius of the isotropic kernel function.
  • χ is the shifting coefficient that controls the correction term. χ = 0 indicates no shifting, while χ = 1 is recommended for simulations where shifting is required.

The correction term is deactivated for particles near the free surface to prevent any impact on the free surface condition.

The particle velocity correction based on the shift of particle position is:
Figure 2. EQUATION_DISPLAY
Δ v i = ( ∑ j ∈ P ( Ω ) V j ( v j n + 1 − v i n + 1 ) ⊗ ∇ W i j ) ( r i n + 1 ′ − r i n + 1 )
(1127)
The particle velocity is then modified to:
Figure 3. EQUATION_DISPLAY
v i n + 1 ′ = v i n + 1 + min ⁡ ( 1 , ξ ‖ v i n + 1 ‖ ‖ Δ v i ‖ ) Δ v i
(1128)
where ξ is the shifting limit. A recommended value for ξ is 0.1, which means that the maximum correction applied to the velocity is 0.1 times the magnitude of the current velocity.