DRIP - Divergence-free Resolution with Iterative Poisson

A parallel CFD solver for 2D incompressible flow. It discretizes the Navier–Stokes equations on a staggered grid with finite differences, advances velocities in time, and enforces incompressibility via a pressure Poisson solve (SOR/CG), following the classic projection method. The discretization uses central differences with donor-cell stabilization for high Reynolds numbers.

Image Processing Pipeline

The graphic at the top summarizes how obstacle geometry is prepared before it enters the solver:

• A → B: A grayscale input image is converted to a clean binary mask (foreground vs. background).
• B → C: The binary mask is scaled to the target grid resolution, preserving aspect ratio.
• C → D: Small defects are corrected and boundaries are labeled to generate a simulation-ready obstacle map.

This pipeline ensures the obstacle field is well-defined on the staggered grid and matches the resolution used by the flow solver.

Highlights

• Incompressible Navier–Stokes via projection method (pressure Poisson equation).
• Finite differences on a staggered grid for velocity and pressure.
• Iterative solvers: SOR and Conjugate Gradient for the Poisson system.
• Stabilized convection using donor-cell blending for high-Re flows.
• Parallel execution with MPI + OpenMP and optional CUDA kernels.

Visuals & Results

Scenario	Preview	Notes
Tesla valve (Re = 100,000)		Forward flow forms a single fast stream, $\dot{V}=0.65$.
Tesla valve (Re = 100,000)		Backward flow splits into two slower streams, $\dot{V}=0.33$.
Maze		CG solves the maze efficiently; SOR would require impractical iterations.
Airfoil sweep		A340 airfoil, one simulation per angle of attack.

How it works (short version)

1. Spatial discretization: Finite differences on a staggered grid for $u$, $v$, and $p$.
2. Time stepping: Explicit update of momentum terms to get preliminary velocities $F$, $G$.
3. Projection: Enforce $\nabla \cdot \mathbf{u}=0$ via a pressure Poisson solve.
4. Pressure correction: Update velocities with the pressure gradient.

Build & Run

Requirements

• CMake 3.8+
• MPI (e.g., OpenMPI)
• CUDA toolkit (optional for GPU kernels)
• GCC/G++ (configured in CMakeLists.txt)

Build

Use the provided script to build the MPI/CUDA-enabled executable:

• build.sh

Run (example)

The default run script uses MPI and a sample settings file:

• run.sh

You can switch the input by editing the settings file path, for example:

• settings/a340.txt