.. title: Computational Scaling Architecture & Numerical Validation
.. slug: specifications
.. date: 2026-08-05 12:00:00 UTC
.. type: text
.. has_math: true


.. raw:: html

   <div class="container mt-5">

   <div class="card p-5 border-0 shadow-sm mb-4">

   <h1 class="display-5 font-weight-bold text-primary">
   Computational Scaling Architecture & Numerical Validation
   </h1>

   <p class="lead text-secondary mt-3">
   GPU-accelerated lattice Boltzmann simulation architecture,
   Reynolds-number scaling studies, and physics-based numerical
   validation framework.
   </p>

   </div>

   </div>


Computational Hardware Configuration
------------------------------------

.. raw:: html

   <div class="card p-5 border-0 shadow-sm mb-4">


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

The primary development configuration consists of:

.. raw:: html

   <div class="row text-center my-4">

   <div class="col-md-3">
   <div class="p-3 bg-secondary text-white rounded">
   <h4>8× V100</h4>
   GPU Accelerators
   </div>
   </div>

   <div class="col-md-3">
   <div class="p-3 bg-secondary text-white rounded">
   <h4>256 GB</h4>
   Aggregate HBM2 Memory
   </div>
   </div>

   <div class="col-md-3">
   <div class="p-3 bg-secondary text-white rounded">
   <h4>5.0 GLUPS</h4>
   Target Throughput
   </div>
   </div>

   <div class="col-md-3">
   <div class="p-3 bg-secondary text-white rounded">
   <h4>FP64</h4>
   Precision Mode
   </div>
   </div>

   </div>


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

.. raw:: html

   </div>



Lattice Boltzmann Solver Formulation
------------------------------------

.. raw:: html

   <div class="card p-5 border-0 shadow-sm mb-4">


The solver evolves discrete distribution functions over a velocity lattice.

The lattice update equation is:

.. math::

   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})


Macroscopic density:

.. math::

   \rho=\sum_i f_i


Velocity:

.. math::

   \rho\mathbf{u}
   =
   \sum_i f_i\mathbf{c}_i


The viscosity relationship is:

.. math::

   \nu
   =
   c_s^2
   \left(\tau-\frac12\right)
   \Delta t


The architecture supports D3Q19 and D3Q27 lattice models.

.. raw:: html

   </div>



Reynolds Number Scaling Envelope
--------------------------------

.. raw:: html

   <div class="card p-5 border-0 shadow-sm mb-4">


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

The Reynolds number is:

.. math::

   Re=\frac{UL}{\nu}


.. list-table:: DNS MFU Scaling on 8x V100 32GB (Rough Surfaces)
   :widths: 20 25 15 15 20 25
   :header-rows: 1

   * - 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.

.. raw:: html

   </div>



Multi-GPU Domain Decomposition
------------------------------

.. raw:: html

   <div class="card p-5 border-0 shadow-sm mb-4">


The solver distributes lattice domains across multiple accelerators.

Configuration:

.. code-block:: text

   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.

.. raw:: html

   </div>



DNS and Turbulence Validation
-----------------------------

.. raw:: html

   <div class="card p-5 border-0 shadow-sm mb-4">


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:

.. math::

   \epsilon
   =
   2\nu S_{ij}S_{ij}


where:

.. math::

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


.. raw:: html

   </div>



Multiscale Analysis and Reduced Models
--------------------------------------

.. raw:: html

   <div class="card p-5 border-0 shadow-sm mb-4">


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:

.. math::

   E(k)=\frac12|\hat{u}(k)|^2


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

.. raw:: html

   </div>



Validation Roadmap
------------------

.. raw:: html

   <div class="card p-5 border-0 shadow-sm mb-5">


The development sequence is:

.. code-block:: text

   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.

.. raw:: html

   </div>


.. raw:: html

   <a href="/" class="btn btn-outline-primary font-weight-bold">
   Back to Homepage
   </a>