Header-only C++20 multiscale water simulation for MuJoCo. Five concurrent LOD levels span roughly 10 orders of magnitude: spectral ocean (km) down to cellular-scale Stokes flow (um). The water surface renders as a single solid hfield volume. Forces apply via data->xfrc_applied; disable MuJoCo's built-in fluid model (opt.density = 0; opt.viscosity = 0;) to avoid double-counting.
MIT licensed.
| LOD | Method | Scale | Timestep | Physics |
|---|---|---|---|---|
| 0 | Spectral Ocean | km, wavelength 1-300 m | master dt | Gerstner waves, Phillips/JONSWAP spectrum |
| 1 | Shallow Water (SWE) | pools to 1 km, dx 10 cm to 10 m | ~10 ms | HLL Riemann solver, MUSCL reconstruction, Manning friction |
| 2 | Smoothed Particle Hydrodynamics (SPH) | splashes, waves, ~cm | ~1 ms | WCSPH, Wendland C2 kernel, Tait EOS, XSPH, CSF surface tension |
| 3 | Lattice Boltzmann (LBM) | microfluidics, dx ~1 mm | ~0.01 ms | D3Q19 TRT collision, Guo forcing, bounce-back BCs |
| 4 | Stokes Flow | cellular/capillary, dx ~10 um | ~1 us | Creeping flow (Re << 1), concentration diffusion with source terms |
Ocean provides the far-field background. SWE covers the near field. SPH, LBM, and Stokes activate in progressively smaller focus zones and substep within their parent.
| LOD | Zone radius |
|---|---|
| 4 Stokes | 5 mm |
| 3 LBM | 5 cm |
| 2 SPH | 50 cm |
| 1 SWE | 50 m |
| 0 Ocean | beyond SWE |
The Step() pipeline runs the full hierarchy each frame:
Step(master_dt):
0. RepositionGrids() move LBM/Stokes grids if focus has drifted
1. UpdateLOD() 5-level zone check; fire escalation/de-escalation
2. Ocean step advance spectral waves; couple to SWE boundary edges
3. SWE step (MUSCL) 2nd-order TVD step at master_dt
4. SPH substeps N_sph steps per master step
a. SWE->SPH coupling ghost zone velocity nudging
b. SPH step neighbor search, density, Tait pressure,
forces + surface tension, XSPH leapfrog
c. LBM substeps N_lbm steps per SPH step
i. SPH->LBM coupling ghost cell equilibrium nudging
ii. LBM step collide (+ bounce-back) + stream
iii. Stokes substeps N_stokes steps per LBM step
- LBM->Stokes coupling boundary velocity nudging
- Stokes step diffuse, pressure project,
advect-diffuse concentration
5. MuJoCo coupling buoyancy + drag + added mass -> xfrc_applied
The water surface is rendered as a single solid hfield volume (z_bottom = 50; no separate box). Wireframe overlay uses chunk-based LOD: coarse everywhere, fine near the focus point.
All headers live in include/mjwater/. Include via #include "mjwater/<header>.h".
| Header | Description |
|---|---|
mjwater.h |
Convenience umbrella: includes the entire library |
types.h |
Vec3, AABB, LODLevel enum (5 levels), physical constants |
spectral_ocean.h |
Gerstner waves, Phillips/JONSWAP spectrum, orbital velocity |
shallow_water.h |
HLL Riemann solver, MUSCL reconstruction, Manning friction |
sph.h |
WCSPH: Tait EOS, XSPH smoothing, CSF surface tension, Shepard density reinitialization, adaptive splitting |
lbm.h |
D3Q19 TRT collision, Guo body forcing, bounce-back boundary conditions |
stokes.h |
Stokes creeping flow, Red-Black Gauss-Seidel pressure projection, scalar concentration field |
water_grid.h |
HeightField (2D) and LatticeGrid (3D D3Q19) |
water_sdf.h |
Volume definition via SDF primitives |
lod_manager.h |
Distance-based 5-level zone assignment with hysteresis |
lod_transition.h |
Bidirectional state transfer across all LOD pairs with mass and momentum conservation |
coupling.h |
MuJoCo body-fluid coupling: buoyancy, drag, added mass |
water_engine.h |
Top-level orchestrator |
mujoco_utils.h |
MuJoCo helpers: hfield update, force application |
cmake -B build -DMJWATER_TESTS_ONLY=ON
cmake --build build --config Release
ctest --test-dir build -C Releasemujoco-game is fetched automatically via CMake FetchContent (or used from a sibling directory if present):
cmake -B build -DMJWATER_TESTS=ON
cmake --build build --config ReleaseInteractive 1 km x 1 km ocean with all 5 LOD levels running simultaneously. Scroll from ocean scale (km) down to Stokes scale (um). Dear ImGui is fetched automatically via CMake FetchContent and is linked only to demo targets.
cmake -B build -DMJWATER_DEMO=ON -DMUJOCO_DIR=<path-to-mujoco>
cmake --build build --config Release --target multiscale_demo
./build/Release/multiscale_demoCamera controls:
- Left drag: orbit
- Right drag: pan (XY)
- Shift + right drag: adjust height
- Scroll: zoom
The ImGui panel provides:
- Simulation: play/pause, sim time, reset, wireframe overlay with edge sensitivity
- Camera: distance, look-at position, elevation, azimuth
- LOD Layers: per-layer enable/disable, cell count, compute cost bars
- Ocean: wind speed, choppiness, JONSWAP gamma sliders
- Zone Radii: live adjustment of LOD activation distances
- Export To Project: 5 presets (swimming robot, pool/tank, ocean vehicle, microfluidics, full multiscale), feature toggles (surface tension, chemotaxis, body coupling, Python bindings), and export to a ready-to-compile folder
The library is header-only with no rendering or GUI code. Only the headers in include/mjwater/ are needed.
add_subdirectory(path/to/mujoco-water)
target_link_libraries(my_app PRIVATE mujoco-water)cmake -B build && cmake --install build --prefix /usr/localfind_package(mujoco-water REQUIRED)
target_link_libraries(my_app PRIVATE mjwater::mujoco-water)Copy include/mjwater/ into your project. No build system integration needed.
An interactive CLI wizard that generates a ready-to-compile project folder. Run python configure.py and follow the prompts: select a backend (MuJoCo, Chrono, Standalone), choose a preset, and toggle features. The output folder contains only the headers and CMake config you selected.
#include <mujoco/mujoco.h>
#include "mjwater/mjwater.h"
#include "mjwater/mujoco_utils.h"
// Disable MuJoCo's built-in fluid model to avoid double-counting.
// m->opt.density = 0; m->opt.viscosity = 0;
mjwater::WaterEngineConfig cfg;
cfg.swe_nx = 40; cfg.swe_ny = 40; cfg.swe_dx = 0.1f;
cfg.initial_surface_z = 0.5f;
cfg.domain = {{-2, -2, -1}, {2, 2, 2}};
mjwater::WaterEngine water;
water.Init(cfg);
// Register each MuJoCo body to couple with fluid.
int hull_id = mj_name2id(m, mjOBJ_BODY, "hull");
mjwater::BodyCoupling hull;
hull.volume = 0.05f; // displaced volume (m^3)
hull.cross_section = 0.1f; // reference area (m^2)
hull.drag_coeff = 0.8f; // Cd
hull.added_mass_coeff = 0.5f; // Ca (0.5 for sphere)
size_t hull_idx = water.AddBody(hull);
// In the simulation loop:
water.SetFocus({d->xpos[3*hull_id], d->xpos[3*hull_id+1],
d->xpos[3*hull_id+2]});
water.Step();
mjwater::Vec3 body_pos = {d->xpos[3*hull_id], d->xpos[3*hull_id+1],
d->xpos[3*hull_id+2]};
mjwater::Vec3 body_vel = {d->cvel[6*hull_id+3], d->cvel[6*hull_id+4],
d->cvel[6*hull_id+5]};
auto force = water.ComputeBodyForce(hull_idx, body_pos, body_vel,
m->opt.timestep);
mjwater::ApplyFluidForces(d, hull_id, force);
// Update hfield for rendering (requires render context).
int hfield_id = mj_name2id(m, mjOBJ_HFIELD, "water_surface");
mjwater::UpdateMuJoCoHField(m, &con, water, hfield_id, max_water_z);
mj_step(m, d);mjwater::WaterEngineConfig cfg;
cfg.ocean_enabled = true;
cfg.ocean.wind_speed = 15.0f; // m/s
cfg.ocean.jonswap_gamma = 3.3f;
cfg.ocean_mean_depth = 50.0f; // m
mjwater::WaterEngine water;
water.Init(cfg);
// LOD zones activate around the focus point.
// Moving the focus inward activates finer layers (SPH, LBM, Stokes).
water.SetFocus(camera_position);
water.Step();
// Query fluid state at any point (highest active LOD used).
auto state = water.Query({1.0f, 0.0f, 0.0f});
// state.velocity, state.density, state.depth, state.submerged#include "mjwater/stokes.h"
mjwater::StokesSolver solver;
mjwater::StokesParams p;
p.dx = 5e-6f; // 5 um grid spacing
p.viscosity = 3.5e-3f; // blood plasma (Pa*s)
p.diffusivity = 1e-10f; // protein diffusion coefficient
solver.Init(40, 40, 40, p);
solver.SetSource({20, 20, 20}, 1e3f);
solver.SetBodyForce({100.0f, 0.0f, 0.0f});
float dt = p.StableDt();
for (int i = 0; i < 1000; ++i) solver.Step(dt);
float c = solver.Concentration({100e-6f, 100e-6f, 100e-6f});7 suites, 63 tests. All pass without MuJoCo.
| Suite | File | Coverage |
|---|---|---|
| Shallow water | test_shallow_water.cc |
Mass conservation, dam break shock, Ritter analytical validation, quiescent stability, velocity query |
| SPH | test_sph.cc |
Kernel normalization, mass conservation, density estimation |
| LBM | test_lbm.cc |
Equilibrium distributions, mass/momentum conservation, bounce-back validation |
| LOD transitions | test_lod.cc |
5-level zone assignment, hysteresis, SWE/SPH/LBM state transfer, mass/momentum conservation round-trips, dynamic grid repositioning |
| Integration | test_lod.cc |
Multi-level engine init/step/query, 5-level LOD activation from focus, submerged/dry query, LOD round-trip mass conservation |
| Coupling | test_coupling.cc |
Buoyancy force, drag force, submerged body detection |
| Ocean | test_ocean.cc |
Phillips spectrum, JONSWAP enhancement, dispersion relation (deep and shallow), Gerstner displacement, orbital velocity decay, circular orbits, energy, significant wave height |
| Stokes | test_stokes.cc |
Poiseuille flow validation, divergence-free projection, concentration diffusion/source, Reynolds number, no-slip boundaries, velocity queries |
mujoco-water/
include/mjwater/ Library headers (header-only; ship these)
tests/ Standalone test suites (no MuJoCo needed)
demo/ MuJoCo demos with Dear ImGui (separate consumers)
configure.py Interactive project generator (5 presets, 3 backends)
CMakeLists.txt Build config: MJWATER_TESTS_ONLY, MJWATER_TESTS, MJWATER_DEMO
build.sh Linux/macOS helper: build, test, demo, clean
launch.bat Windows helper: kill, rebuild, launch demo
docs/Screenshot.png Demo screenshot
LICENSE MIT
- C++20 compiler: MSVC 19.30+, GCC 11+, or Clang 14+
- CMake 3.20+
- MuJoCo 3.0+ (required only for coupling and demos, not for tests or standalone use)
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