Why Lattice Boltzmann?
----------------------
The Lattice Boltzmann Method (LBM) provides a kinetic-based
computational approach for studying transient fluid systems.
Traditional computational fluid dynamics methods have demonstrated
excellent performance across many engineering applications. However,
complex transient flows, geometry-driven effects, and multiscale
turbulent structures remain active areas of research.
The LBM architecture explored here uses a different computational
representation. Instead of directly advancing macroscopic pressure
and velocity variables, the solver evolves discrete distribution
functions whose moments recover the macroscopic conservation laws.
The objective is not to replace established CFD methods universally,
but to develop a complementary high-performance framework for:
* transient flow simulation
* complex geometry interaction
* GPU-based acceleration
* multiscale turbulence analysis
* reduced-order modeling
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Computational Architecture
Geometry
→
Discrete Lattice Representation
→
Kinetic Evolution
→
Moment Recovery
→
Multiscale Analysis
Kinetic Formulation
-------------------
The solver advances discrete lattice populations rather than directly
solving for macroscopic fields.
The lattice evolution equation is:
.. math::
f_i(\mathbf{x}+\mathbf{c}_i\Delta t,t+\Delta t)
=
f_i(\mathbf{x},t)
-
\frac{1}{\tau}
\left(f_i-f_i^{eq}\right)
The macroscopic density is recovered through the zeroth moment:
.. math::
\rho=\sum_i f_i
The velocity field is obtained from:
.. 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
Solver Configuration
--------------------
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The simulation framework is designed around GPU-friendly lattice
operations and scalable domain decomposition.
Configuration:
.. code-block:: text
Lattice Models:
D3Q19 / D3Q27
Collision Models:
MRT / TRT / Cumulant LBM
Boundary Treatment:
Bounce-back and interpolated schemes
Precision:
FP64 numerical validation
Hardware:
Multi-GPU CUDA acceleration
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GPU Acceleration Strategy
-------------------------
The primary advantage of the lattice formulation is the locality of
the computational operations.
Each lattice update requires information from neighboring discrete
velocity states, allowing efficient parallel execution on modern GPU
architectures.
The computational strategy includes:
* domain decomposition across multiple GPUs
* memory-aware lattice partitioning
* CUDA accelerated collision and streaming kernels
* performance tracking using lattice updates per second
The target development platform is:
.. code-block:: text
8 × NVIDIA V100 GPUs
256 GB aggregate HBM2 memory
FP64 simulation capability
Distributed lattice domains
Multiscale Flow Analysis
========================
Large transient simulations generate high-dimensional flow data.
The challenge is not only producing accurate solutions, but extracting
the physical structures that govern aerodynamic behavior across
multiple length and time scales.
The Base Drag computational framework investigates methods for
transforming complex flow fields into compact, physically meaningful
representations. This includes analysis of turbulent structures,
energy transfer pathways, and hierarchical organization within the
flow.
Wavelet-Based Flow Decomposition
--------------------------------
Traditional spectral analysis methods describe turbulent behavior
primarily through frequency or wavenumber space. While powerful,
these approaches can be limited when analyzing localized transient
events, coherent structures, and geometry-driven flow interactions.
Wavelet analysis provides a complementary approach by decomposing
flow fields simultaneously in both spatial scale and location.
For a velocity or energy field, a wavelet transform can separate
features associated with different physical scales:
- large-scale coherent flow structures
- intermediate turbulent energy transfer
- small-scale dissipative features
- localized interactions near surfaces and wakes
This multiscale representation provides a framework for investigating
how aerodynamic losses emerge from interactions between geometry,
boundary layers, separation regions, and turbulent structures.
Hierarchical Flow Representation
--------------------------------
The objective is not simply to visualize turbulence, but to identify
relationships between structures at different scales.
The analysis framework investigates:
- wavelet decomposition of turbulent dissipation fields
- scale-dependent energy transfer
- hierarchical correlation structures
- reduced-order representations of transient flow behavior
- connections between geometric features and flow organization
These methods provide a pathway toward identifying the physically
relevant variables required for targeted aerodynamic optimization.
Energy Dissipation Analysis
---------------------------
The turbulent dissipation rate is evaluated through:
.. 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)
The resulting dissipation fields provide a measure of where kinetic
energy is converted into heat through viscous processes.
By analyzing these fields across multiple scales, the framework
investigates whether dominant aerodynamic loss mechanisms can be
identified and represented in a reduced computational form.
Research Direction
------------------
The long-term objective is to connect high-resolution kinetic
simulation with compact physics-informed models.
The LBM framework provides the numerical foundation for investigating:
* complex surface interactions
* turbulent energy transfer
* multiscale flow organization
* reduced computational representations
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