Computational Scaling Architecture & Numerical Validation

Computational Scaling Architecture & Numerical Validation

GPU-accelerated lattice Boltzmann simulation architecture, Reynolds-number scaling studies, and physics-based numerical validation framework.

Computational Hardware Configuration

The computational platform is designed for high-resolution lattice-based fluid simulation using distributed GPU acceleration.

The primary development configuration consists of:

8× V100
GPU Accelerators
256 GB
Aggregate HBM2 Memory
5.0 GLUPS
Target Throughput
FP64
Precision Mode

The primary performance metric is lattice updates per second rather than traditional mesh-cell throughput.

Lattice Boltzmann Solver Formulation

The solver evolves discrete distribution functions over a velocity lattice.

The lattice update equation is:

\begin{equation*} f_i(\mathbf{x}+\mathbf{c}_i\Delta t,t+\Delta t) = f_i(\mathbf{x},t) - \frac{1}{\tau} (f_i-f_i^{eq}) \end{equation*}

Macroscopic density:

\begin{equation*} \rho=\sum_i f_i \end{equation*}

Velocity:

\begin{equation*} \rho\mathbf{u} = \sum_i f_i\mathbf{c}_i \end{equation*}

The viscosity relationship is:

\begin{equation*} \nu = c_s^2 \left(\tau-\frac12\right) \Delta t \end{equation*}

The architecture supports D3Q19 and D3Q27 lattice models.

Reynolds Number Scaling Envelope

The achievable Reynolds number depends on lattice resolution, relaxation time, collision model, and physical scaling assumptions.

The Reynolds number is:

\begin{equation*} Re=\frac{UL}{\nu} \end{equation*}
DNS MFU Scaling on 8x V100 32GB (Rough Surfaces)

Friction Re (Re_tau)

Grid (Nx x Ny x Nz)

Total Points

Memory Req.

Run Time (8x V100)

Feasibility (256 GB Total VRAM)

Re_tau ~ 180 (Low)

256 x 192 x 128

~ 6.3 Million

~ 6.5 GB

~ 2 - 4 Hours

Safe; ultra-low memory usage

Re_tau ~ 395 (Mod)

512 x 384 x 256

~ 50 Million

~ 51 GB

~ 12 - 24 Hours

Safe; fits easily (~6.4 GB / GPU)

Re_tau ~ 590 (Std)

1024 x 512 x 512

~ 268 Million

~ 274 GB

~ 3 - 5 Days

Borderline; requires precision tuning or unified memory

Re_tau ~ 1000 (High)

2048 x 1024 x 1024

~ 2.1 Billion

~ 2.1 TB

Weeks (Infeasible)

Impossible; drastically exceeds system VRA

These values represent computational scaling estimates. Final results are validated through benchmark problems, conservation tests, and measured GPU performance.

Multi-GPU Domain Decomposition

The solver distributes lattice domains across multiple accelerators.

Configuration:

Accelerator Count: 8 × NVIDIA V100
Aggregate Memory: 256 GB HBM2
Precision: FP64
Parallel Strategy: Domain Decomposition
Scaling Metric: GLUPS

The objective is consistent numerical behavior from single GPU development cases through multi-GPU production simulations.

DNS and Turbulence Validation

Validation focuses on canonical turbulent flow problems where numerical behavior can be compared against established reference solutions.

Validation targets include:

  • conservation properties

  • turbulence decay

  • spectral energy distribution

  • wall-bounded turbulence statistics

  • multi-GPU reproducibility

Energy dissipation is calculated from:

\begin{equation*} \epsilon = 2\nu S_{ij}S_{ij} \end{equation*}

where:

\begin{equation*} S_{ij} = \frac12 \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} \right) \end{equation*}

Multiscale Analysis and Reduced Models

Large simulations generate high-dimensional data. The analysis framework extracts reduced representations of important flow structures.

Methods include:

  • Fourier analysis

  • wavelet decomposition

  • dynamic mode decomposition

  • reduced-order modeling

  • hierarchical correlation analysis

The energy spectrum is:

\begin{equation*} E(k)=\frac12|\hat{u}(k)|^2 \end{equation*}

The goal is to connect resolved turbulent structures with compact physics-informed models.

Validation Roadmap

The development sequence is:

Solver Verification
       |
       v
Single GPU Validation
       |
       v
Multi-GPU Scaling
       |
       v
DNS Benchmark Comparison
       |
       v
Surface Interaction Studies
       |
       v
Reduced Order Modeling

This architecture provides a foundation for studying complex fluid systems through high-performance simulation and multiscale analysis.

Back to Homepage