Incompressible Flow (ISPH) Model Reference

The Incompressible Flow (ISPH) model is a mesh-free numerical method, which approximates values at points based on neighboring particle contributions, employing interpolation, gradient, divergence calculations, smoothing kernels, and time-stepping techniques to advance simulations. It can also incorporate boundary handling for accuracy and efficiency in complex scenarios.

表 1. Incompressible Flow (ISPH) Model Reference
Theory	See SPH Multiphase Flow Solver and SPH Boundary Conditions.
Provided By	[physics continuum] > Models > Multiphase Model > SPH Flow
Example Node Path	Continua > Physics 1 > Models > Incompressible Flow (ISPH)
Requires	Pre-requisite selections: Material: Multiphase Multiphase Model: Smoothed-Particle Hydrodynamics (SPH)
Properties	Key properties are: Pressure Stabilization Option, Pressure Stabilization Coefficient, Free Surface Stabilization Option, and Free Surface Stabilization Factor
Activates	Physics Models	Viscous Regime: Laminar Inviscid Optional models: Gravity Particle Remediation See Particle Remediation Model Reference.
	Initial Conditions	Velocity and Pressure See Initial Conditions.
	Boundary Inputs	Physics Conditions: No-Stick Processing Option, and Shear Stress Specification Physics Values: Relative Velocity Magnitude, Relative Mass Flux, and Relative Mass Flow Rate See Boundary Inputs.
	Field Functions	Sph Particle Size Sph Particle Volume Volume Fraction of [phase] See Field Functions.

Incompressible Flow (ISPH) Model Properties

Pressure Stabilization Option

When activated, applies a stabilization to the PPE source term to reduce checkerboard effects.

Pressure Stabilization Coefficient

Sets the coefficient $β$ for the pressure solver stabilization. The value can range from 0 (no stabilization) to 1 (high stabilization).

Free Surface Stabilization Option

Allows you to specify the method of stabilization to smooth the free surface shape.

Method	Corresponding Properties
None No stabilization to free surface is applied.	None.
Basic The basic method for standard fluid flow. This option is the default selection.	Free Surface Stabilization Factor Specifies the level of free-surface smoothing for the basic stabilization scheme.
Advanced This method is recommended for highly viscous flows (very low Reynolds numbers) or to prevent excessive dissipation for flows with fine discretization.	Free Surface Stabilization Factor Specifies the level of free-surface smoothing for the advanced stabilization scheme.

Initial Conditions

Lets you customize initial conditions for the simulation.

Velocity: Allows you to initialize the velocity of the fluid at the beginning of the simulation.

Pressure: Allows you to initialize the pressure of the fluid at the beginning of the simulation.

Boundary Settings

Wall

No-Stick Processing Option

Provides the option to disable the attractive forces between particles and the walls.

Enable No-Stick Processing Option: When activated, disables interaction between particles and walls by nullifying the attractive force in the pressure term of the momentum equation. This prevents particles from sticking to a wall.

Shear Stress Specification

Not available for inviscid flows. Selects whether the fluid sticks to the wall or slides along it. The following options are available:

No-slip wall—the fluid sticks to the wall and moves with the same velocity as the wall.
Slip wall—the fluid does not stick to the wall. No wall-induced shear stress is considered for the fluid.

Velocity Inlet

Relative Velocity Magnitude: Specifies the relative velocity for the velocity inlet boundary. This value must be positive.

Mass Flow Inlet

Mass Flow Option

Sets the mass flow rate option for the mass flow inlet boundary.

Specification Option	Corresponding Value Node
Mass Flux	Relative Mass Flux Specifies the relative mass flux for the mass flow inlet boundary. This value must be positive.
Mass Flow Rate	Relative Mass Flow Rate Specifies the relative mass flow rate for the mass flow inlet boundary. This value should be positive.

Field Functions

When the Incompressible Flow (ISPH) model is activated, the following field functions become available:

Sph Particle Size: The cubic square of the particle volume.

Sph Particle Volume: The volume of single particles, $V_{p} = m_{p} / ρ_{p}$ .

Volume Fraction of [phase]: This is the volume of material particles of the [phase] per unit volume of space. For individual particles, this value is 1 for the liquid particles and 0 for gas. On the boundary, the volume fraction of [phase] corresponds to the wetting area of the surface relative to the phase, using interpolation from fluid particles.