SPH

The smoothed particle hydrodynamics (SPH) technique is a purely Lagrangian method.
SPH discretizes a fluid in a series of interpolation points (SPH particles) whose distribution follows the mass density of the fluid and their evolution relies
on a weighted interpolation over close neighboring particles.

The parallelization of SPH codes is not trivial due to their boundless nature and the absence of a structured grid.

SPH-EXA

SPH-EXA is a C++20 simulation code for hydrodynamics simulations (with gravity and other physics), parallelized with MPI, OpenMP, CUDA, and HIP.

SPH-EXA is built with high performance, scalability, portability, and resilience in mind. Its SPH implementation is based on SPHYNX, ChaNGa, and SPH-flow, three SPH codes selected in the PASC SPH-EXA project to act as parent and reference codes to SPH-EXA.

The performance of standard codes is negatively impacted by factors such as imbalanced multi-scale physics, individual time-stepping, halos exchange, and long-range forces. Therefore, the goal is to extrapolate common basic SPH features, and consolidate them in a fully optimized, Exascale-ready, MPI+X, SPH code: SPH-EXA.

Check our wiki for more details

Folder structure

SPH-EXA
├── README.md
├── docs
├── domain                           - Cornerstone library: octree building and domain decomposition
│   ├── include
│   │   └── cstone
│   │       ├── CMakeLists.txt
│   │       ├── cuda
│   │       ├── domain
│   │       ├── findneighbors.hpp
│   │       ├── halos
│   │       ├── primitives
│   │       ├── sfc
│   │       ├── tree
│   │       └── util
│   └── test                        - Cornerstone unit- performance-
│       ├── integration_mpi           and integration tests
│       ├── performance
│       ├── unit
│       └── unit_cuda
├── ryoanji                         - Ryoanji: N-body solver for gravity
│   ├─── src
│   └─── test                       - demonstrator app and unit tests
│
├── sph                             - SPH implementation
│   ├─── include
│   │    └── sph
│   └─── test                       - SPH kernel unit tests
│
└── main/src
    ├── init                        - initial conditions for test cases
    ├── io                          - file output functionality
    └── sphexa                      - SPH main application front-end

Toolchain requirements

The code requires a C++20 compiler for both the CPU and GPU parts.

GCC 12 and later
Clang 16 and later
CUDA 12 and later
ROCm 6 and later. ROCm 5 compiles, but has bugs preventing the reliable use of GPU-aware-MPI

Check your GPU compute capability

In you need to specify the compute capability of your GPUs, you can look them up here: https://developer.nvidia.com/cuda-gpus

Compilation

Minimal CMake configuration:

shell
mkdir build
cd build
cmake <GIT_SOURCE_DIR>

Compilation at sciCORE (UniBas):

shell
ml HDF5/1.14.6-gompi-2025a
ml CMake/3.31.3-GCCcore-14.2.0
ml CUDA/12.8.0

mkdir build
cd build
cmake -DCMAKE_CUDA_ARCHITECTURES="80;90" <GIT_SOURCE_DIR>

CMake configuration on Daint on Alps:
CUDA 12.6 + GCC 13.3:

shell
uenv image pull prgenv-gnu/24.11:v1
uenv start prgenv-gnu/24.11:v1 --view=default

mkdir build
cd build

CC=mpicc CXX=mpicxx cmake -DCMAKE_CUDA_ARCHITECTURES=90 -DCSTONE_WITH_GPU_AWARE_MPI=ON -DCMAKE_CUDA_FLAGS=-ccbin=mpicxx -S <GIT_SOURCE_DIR

Module and CMake configuration on LUMI (ROCm 6.2.2)

shell
module swap PrgEnv-cray PrgEnv-gnu
module load CrayEnv buildtools craype-accel-amd-gfx90a rocm cray-hdf5-parallel
export MPICH_GPU_SUPPORT_ENABLED=1
cmake -DCMAKE_CXX_COMPILER=CC -DCMAKE_HIP_ARCHITECTURES=gfx90a -DCSTONE_WITH_GPU_AWARE_MPI=ON -S <GIT_SOURCE_DIR>

Build everything: make -j

Running the main application

The main sphexa (and sphexa-cuda, if GPUs are available) application can either start a simulation by reading initial conditions
from a file or generate an initial configuration for a named test case.
Self-gravity will be activated automatically based on named test-case choice or if the HDF5 initial
configuration file has an HDF5 attribute with a non-zero value for the gravitational constant.

Arguments:

--init CASE/FILE: use the case name as seen below or provide an HDF5 file with initial conditions
--glass FILE: template glass block for IC generation avaiable from
-n NUM : Run the simulation with NUM^3 (NUM to the cube) number of particles (for named test cases). [NOTE: This might vary with the test case]
-s NUM : Run the simulation with NUM of iterations (time-steps) if NUM is integer. Run until the specified physical time if NUM is real.
-w NUM : Dump particle data every NUM iterations (time-steps) if NUM is integer. Dump data at the specified physical time if NUM is real.
-f FIELDS: Comma separated list of particle fields for file output dumps. See a list of common ouput fields below.
--quiet : Do not print any output to stdout

Implemented cases:

--sedov: spherical blast wave
--noh: spherical implosion
--evrard: gravitational collapse of an isothermal cloud
--turbulence: subsonic turbulence in a box
--kelvin-helmholtz: development of the subsonic Kelvin-Helmholtz instability in a thin slice

Only the Sedov test case supports running without providing a glass block (--glass), but for accurate simulation
results, a glass block is nevertheless strongly recommended.

Common output fields:

x, y, z: position
vx, vy, vz: velocity
h: smoothing length
rho: density
c: speed of sound
p: pressure
temp: temperature
u: internal energy
nc: number of neighbors
divv: Module of the divergence of the velocity field
curlv: Module of the curl of the velocity field

Example usage:

OMP_NUM_THREADS=4 ./sphexa --init sedov -n 100 -s 1000 -w 10 -f x,y,z,rho,p
Runs Sedov with 100^3 particles for 1000 iterations (time-steps) with 4 OpenMP
threads and dumps particle xyz-coordinates, density and pressure data every 10 iterations
OMP_NUM_THREADS=4 ./sphexa-cuda --init sedov -n 100 -s 1000 -w 10 -f x,y,z,rho,p
Runs Sedov with 100^3 particles for 1000 iterations (time-steps) with 4 OpenMP
threads. Uses the GPU for most of the compute work.
OMP_NUM_THREADS=4 mpiexec -np 2 ./sphexa --init noh -n 100 -s 1000 -w 10
Runs Noh with 100^3 particles for 1000 iterations (time-steps) with 2 MPI ranks of 4 OpenMP
threads each. Works when using MPICH. For OpenMPI, use mpirun instead.
OMP_NUM_THREADS=12 srun -Cgpu -A<your account> -n<nnodes> -c12 --hint=nomultithread ./sphexa-cuda --init sedov -n 100 -s 1000 -w 10
Optimal runtime configuration on Piz Daint for nnodes GPU compute nodes. Launches 1 MPI rank with
12 OpenMP threads per node.
./sphexa-cuda --init evrard --glass 50c.h5 -s 2000 -w 100 -f x,y,z,rho,p,vx,vy,vz
Run SPH-EXA, initializing particle data from an input file (e.g. for the Evrard collapse). Includes
gravitational forces between particles. The angle dependent accuracy parameter theta can be specificed
with --theta <value>, the default is 0.5.

Restarting from checkpoint files

If output to file is enabled and if the -f option is not provided, sphexa will output all conserved particle
fields which allows restoring the simulation to the exact state at the time of writing the output.
This includes the following fields x_m1, y_m1, z_m1, du_m1.
In order to save diskspace, sphexa can be instructed to omit these fields by setting the -f option, e.g.
-f x,y,z,m,h,temp,alpha,vx,vy,vz. If one wants to restart the simulation from an output file containing
these fields, it is necessary to add the _m1. We provide an example script that can be used to achieve this:

bash
./scripts/add_m1.py <hdf5-output-file>

Unit, integration and regression tests

Cornerstone octree comes with an extensive suite of unit, integration and regression tests, see README.

SPH kernel unit tests:

shell
./sph/test/hydro_ve
./sph/test/hydro_std

Input data

Some tests require template blocks with glass-like (Voronoi tesselated) particle distributions, these can be obtained here:

Ryoanji GPU N-body solver

Ryoanji is a high-performance GPU N-body solver for gravity. It relies on the cornerstone octree framework
for tree construction, EXAFMM multipole kernels,
and a warp-aware tree-traversal inspired by the
Bonsai GPU tree-code.