Multiphysics Hub

A real-time, top-down driving application in which a single car couples three simulations, all computed live in the browser.

Live demonstration: https://bypire.github.io/multiphysics-hub/

• Vehicle dynamics. A double-track (four-wheel) model with Pacejka tyres, longitudinal and lateral load transfer, aerodynamic downforce, and a manual gearbox, handbrake and reverse.
• Aerodynamics. A two-dimensional fluid solver runs around the car outline every frame, showing the wake; the resulting drag and downforce feed back into the vehicle.
• Vehicle-bridge interaction. A modal moving-load beam deflects under the moving wheel load, coloured by bending moment, with the dynamic amplification factor.

The page opens in a self-driving demonstration loop; pressing any drive key hands over control.

A note on fidelity

The vehicle and bridge models are checked against analytical and finite-element references (py/verify_*.py, and web/xcheck.html for the JavaScript ports). The aerodynamics panel is a two-dimensional, low-Reynolds solver: it illustrates flow separation and the wake but is not a quantitative aerodynamic prediction. The drag and downforce used by the vehicle come from the standard coefficient relation F = 0.5 rho C A v^2; the Navier-Stokes solver is the separate vortex-street-cfd project.

Verification

The numerical models are written in Python (NumPy) and checked against ground truth; the JavaScript ports that run in the browser are then checked against those Python models on identical inputs. Both integrate at a fixed 250 Hz with RK4, decoupled from the render rate.

The checks that ship with the code:

• py/verify_car_dynamic.py and py/verify_doubletrack.py: the vehicle against static and steady-state references (static wheel loads, vertical equilibrium, load transfer against closed forms, low-speed Ackermann cornering, and the understeer balance trend).
• py/verify_bridge.py: the beam against the closed-form static deflection P L^3 / 48 E I and against the full Euler-Bernoulli FEM eigensolve from the VBI project.
• web/xcheck.html: the JavaScript ports against Python on identical inputs. The vehicle agrees to about 1e-13 over thousands of steps; the bridge crossing agrees to about 1e-9 metres against a 0.23 mm peak deflection.
• web/aero_test.html: the fluid solver's own properties (the projection reduces divergence, the integration is stable, and a wake is shed).

Controls

• Arrow keys or WASD: steer, throttle, brake.
• C and V: shift up and down. Space: handbrake. E: reverse (when stopped).
• T: toggle the force and velocity vectors and the driven line.
• R: reset. Edit track: reshape the circuit.

Implementation

The numerical models are written in Python and reimplemented in JavaScript for interactivity; the two are compared on identical inputs in web/xcheck.html. Vehicle and bridge states are integrated with RK4 at a fixed 250 Hz, decoupled from the render rate.

Running locally

Open web/index.html directly; there is no server or build step. To re-run the checks:

cd py
python verify_car_dynamic.py
python verify_doubletrack.py
python verify_bridge.py
python export_xcheck.py      # regenerates the JavaScript and Python reference data

Layout

index.html               redirect to web/ (for GitHub Pages)
py/   car_dynamic.py      vehicle models (bicycle, double-track, Pacejka)
      bridge_modal.py     modal moving-load beam
      verify_*.py         analytical checks
      export_xcheck.py    writes the JavaScript and Python reference data
web/  index.html          the application
      car.js bridge.js    physics (JavaScript ports)
      fluid.js aero.js    two-dimensional fluid and the aero panel
      render.js main.js   rendering and the input loop
      track.js bridge_render.js   track and bridge panels
      xcheck.html aero_test.html  verification pages

Limitations

Two-dimensional throughout. The aerodynamic field is qualitative. The bridge is a modal reduction of a simply-supported span rather than a continuous multi-span girder. The gearbox is a driver-input layer on top of the vehicle dynamics.