# Turbulent Channel Flow with NekRS + Ginkgo

Simulates turbulent channel flow at $Re_\tau = 590$ using NekRS for the
spectral element discretization and time stepping, with Ginkgo replacing
NekRS's built-in PCG for the pressure Poisson solve at every time step.

Compatible with NekRS v26+.

## Integration Overview

This example extends the [NekRS Poisson example](../poisson/doc) to a
full time-dependent simulation. The Ginkgo solver is called at every time
step within NekRS's operator-splitting scheme. The same `NekRSOperator`
wrapper from `nekrs/nekrs_ginkgo.hpp` is reused.

## Key Integration Points

### Setup

```{literalinclude} turbulent_channel.cpp
:language: cpp
:start-after: [udf-setup-channel]
:end-before: [/udf-setup-channel]
```

### Per-Timestep Solve

Ginkgo's CG replaces NekRS's built-in PCG at every time step:

```{literalinclude} turbulent_channel.cpp
:language: cpp
:start-after: [udf-execute-channel]
:end-before: [/udf-execute-channel]
```

## Building

NekRS UDFs compile as shared libraries (plugins):

```bash
cmake -S . -B build --preset default \
  -DNEKRS_DIR=/path/to/nekrs \
  -DGinkgo_DIR=/path/to/ginkgo
cmake --build build
```

## Running

**Note:** Running has not been tested end-to-end. The code compiles
against the NekRS v26 API, validating the integration pattern, but
actually executing it requires a full NekRS case setup.

To run, copy the built shared library into a NekRS turbulent channel
case directory (e.g., the `channel` example bundled with NekRS):

```bash
cp -r /path/to/nekrs/examples/channel /tmp/test-channel
cp build/libturbulent_channel.so /tmp/test-channel/
cd /tmp/test-channel && mpirun -np 4 nekrs --setup channel
```

As with the Poisson example, a production integration would need to
disable NekRS's built-in pressure solve and route it through Ginkgo.

## Expected Output (approximate)

```text
[Ginkgo] Turbulent channel flow setup
[Ginkgo] Pressure DOFs: 262144
[Ginkgo] Step 500, time = 1.0, total Ginkgo solves: 500
[Ginkgo] Step 1000, time = 2.0, total Ginkgo solves: 1000
```