Multiphysics Coupling

MechanicsDSL supports coupling between different physics domains within a single simulation, enabling complex scenarios like floating objects in fluids.

Supported Couplings

Domain A	Domain B	Applications
Rigid Body	SPH Fluid	Floating objects, wave makers
Elastic Body	SPH Fluid	Flexible structures in flow
Particle System	Rigid Body	Granular materials, debris

Rigid Body + Fluid Coupling

Simulate a floating box in water:

source = r'''
\system{floating_box}

% Fluid setup
\fluid{water}
\region{rectangle}{x=0..2, y=0..0.5}
\parameter{h}{0.03}{m}
\parameter{rho_0}{1000}{kg/m^3}

% Rigid body (floating box)
\rigidbody{box}
\mass{5.0}{kg}
\geometry{rectangle}{width=0.3, height=0.2}
\initial_position{1.0, 0.6}
\initial_velocity{0, 0}

% Boundary container
\boundary{walls}
\region{line}{x=-0.1, y=0..1.2}
\region{line}{x=2.1, y=0..1.2}
\region{line}{x=-0.1..2.1, y=-0.1}
'''

Coupling Algorithm

The two-way coupling uses the following approach:

Fluid → Body: Sum pressure forces from nearby particles

\[\mathbf{F}_{fluid} = -\sum_i m_i \frac{P_i}{\rho_i^2} \nabla W(\mathbf{r} - \mathbf{r}_i)\]
Body → Fluid: Apply boundary conditions via ghost particles
Time stepping: Sub-cycle fluid (smaller dt) relative to rigid body

Force Computation

For each rigid body in contact with fluid:

# Pseudocode for coupling
for particle in fluid_particles:
    if particle.near(body):
        # Pressure force on body
        F_pressure = compute_pressure_force(particle, body)
        body.apply_force(F_pressure)

        # Reaction on particle
        particle.apply_force(-F_pressure)

# Update body with total forces
body.integrate(dt)

Buoyancy

Archimedes’ principle emerges naturally from the SPH pressure forces. A body will:

Float if body density < fluid density
Sink if body density > fluid density
Reach equilibrium with correct displaced volume

Example: Wave Maker

Create waves using a moving rigid body:

source = r'''
\system{wave_maker}

\fluid{water}
\region{rectangle}{x=0.5..3, y=0..0.4}

% Oscillating paddle
\rigidbody{paddle}
\geometry{rectangle}{width=0.05, height=0.5}
\motion{oscillate}{
    center=(0.2, 0.25),
    amplitude=0.1,
    frequency=1.0
}

\boundary{tank}
\region{line}{x=0, y=0..0.6}
\region{line}{x=3.5, y=0..0.6}
\region{line}{x=0..3.5, y=0}
'''

Limitations

Current multiphysics limitations:

2D only: 3D coupling is experimental
Simple geometries: Rectangles, circles, convex polygons
No deformation: Rigid bodies don’t deform
Explicit coupling: May require small time steps for stability

Future Work

Planned enhancements:

3D fluid-structure interaction
Deformable bodies (FEM)
Thermal coupling
Chemical reactions