Buoyancy / Research

Research questions

01 / QUESTION

Why is our approach interesting enough to read about?

What happens when the movement of waiting orders in a market model is driven by an evolving fluid flow? Physics gives us a concrete mechanism for generating that flow: buoyant convection, where heat drives motion that then carries the heat, continually changing the flow. That is the meaning of buoyancy on our page. We use the resulting flow to drive movement in a simulated order book, then measure whether it adds behaviour that a well-calibrated stochastic model cannot explain. It is a testable idea, and we have built the computational machinery needed to investigate it.

Mathematical Foundation

The Boussinesq approximation is a specialisation of the Navier–Stokes equations where the fluid is treated as incompressible everywhere except in the buoyancy force.

Governing Equations

\nabla \cdot \mathbf{u} = 0

\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla)\mathbf{u} = -\frac{1}{\rho_0}\nabla p + \nu \nabla^2 \mathbf{u} + g \alpha \theta \, \hat{\mathbf{z}}

\frac{\partial \theta}{\partial t} + (\mathbf{u} \cdot \nabla)\theta = \kappa \nabla^2 \theta + Q

Symbol Definitions

$\mathbf{u}$: velocity field
$p$: fluid pressure
$\nu$: kinematic viscosity
$\rho_0$: reference density
$\theta$: temperature deviation from a reference state
$\alpha$: thermal expansion coefficient
$g$: gravitational acceleration
$\hat{\mathbf{z}}$: vertical direction
$\kappa$: thermal diffusivity
$Q$: internal heat source

02 / QUESTION

What are we really trying to solve, and has it been solved before?

The question is whether a changing drift, generated by fluid dynamics, produces order-book behaviour beyond what an established stochastic baseline captures. Existing research already connects fluid mathematics with financial markets. The specific gap identified in our literature review concerns replacing the constant drift in the models examined with a dynamically generated fluid flow. We found no study using this particular mechanism within that literature. The closest work discussed connects order-flow memory through the noise term rather than through fluid-driven drift.

On the computing side, investigating this requires repeated 3D convection simulations over long periods. Rayleigh provides an established starting point. Our C++/CUDA implementation adapts its numerical method for CPU and GPU execution, reducing the computational cost of generating those flows.

03 / QUESTION

What are we adding on top of the existing literature?

Three connected contributions:

(a) A specific hypothesis: using an evolving convection field to drive the transport of resting orders, and testing whether that mechanism adds anything beyond a well-calibrated stochastic model.

(b) A C++/CUDA port of Rayleigh whose hydrodynamic Case 0 benchmark report matches the original Fortran to every printed digit after 25,000 steps. At the larger tested grids, historical measurements show roughly 5.6–6.1× acceleration on one GPU against the fastest recorded repetition of the 16-rank Fortran baseline, with diagnostics disabled. The paper explains the conditions and limitations of those comparisons.

(c) A simulation study connecting fluid fields to order-book events, so the proposed mechanism can be tested and potentially falsified. The solver paper establishes the computational foundation; the market study evaluates what the coupling contributes.

This supports the case for simulation within the company: generating the fluid flow has a cost at every step. Reducing that cost allows longer experiments, more repetitions and a wider range of conditions within the same computing budget.