A high-performance 3D compressible Euler solver implemented in NVIDIA Warp, based on the wave-appropriate reconstruction framework of Chamarthi et al. (2023–2026). Initially, it was a fun project, but I realized it has significant potential and will develop it into a fully functional code.
Q-criterion isosurface (Q=4.0) coloured by vorticity magnitude |ω| for the inviscid Taylor-Green Vortex at t=10, N=512³.
- Wave-appropriate reconstruction — each characteristic wave family (acoustic, entropy, vortical) is treated with its physically appropriate scheme
- SoA memory layout
cons[var, ix, iy, iz]for coalesced GPU memory access. Needed several modifications from the FORTRAN code (column and row major). - SSP-RK3 time integration
- Ducros sensor for shock detection and for the contact discontinuity rank-1 correction is used.
| Region | Acoustic waves | Entropy wave | Vortical waves |
|---|---|---|---|
| Smooth | Upwind (eta=0.6) |
MP5 | Central-6 (kai=0.5) |
| Shock | WENO-Z/MP | WENO-Z/MP | WENO-Z/MP |
Or corresponding conservative variables, depending on the direction, will have appropriate values of \eta and kai (kai, a random name I used during development).
In regions of shock waves, one can also perform wave-appropriate centralization. However, this is not included in the current Python code. There are many possible choices. :)
The wave-appropriate framework decomposes the flow into its five characteristic families and applies the minimum necessary dissipation to each:
-
Acoustic waves — upwind-biased (η = 0.6) for stability near shocks and in general. See double shear layer case in paper 5, 3, 2 and 1, please.
-
Entropy wave — MP5 in smooth regions, WENO-Z (or MP5 or MUSCL) near shocks; rank-1 correction from WA-CR
-
Vortical waves — central (η = 0.5) to preserve turbulent structures
-
For more details see please see the References, mainly 2 and 3.
pip install warp-lang numpy matplotlib# Inviscid Taylor-Green Vortex, 64³
python 3D_TGV_WA.py
# 128³
python 3D_TGV_WA.py --n 128
# 512³ (A100 or better)
python 3D_TGV_WA.py --n 512
# CPU mode
python 3D_TGV_WA.py --n 64 --cpuEach snapshot is saved as a compressed .npz file containing:
time, x, y, z, rho, p, u, v, w
Change to Tecplot or VTK files if necessary.
Can use Python scripts for plotting, but the code does periodically plot the output. Can disable it if not required. Pyvista or Paraview.
| Grid | Memory | Time/step | Steps (t=10) | Wall time |
|---|---|---|---|---|
| 64³ | ~0.5 GB | ~5 ms | ~1,500 | ~2 min |
| 512³ | ~49 GB | ~1.2 s | ~28,000 | ~9 hr |
Could run 200M for inviscid case and 150M for viscous case in 3D on one GPU with 80 GB VRAM.
The other two codes in the repository simulate the 2D Riemann problem by using WA-3 or WA-WENO-CR. Both of them work with NVIDIA Warp
![2D Riemann Problem — WA-3 scheme]
Density contours for the 2D Riemann problem using the WA-3 approach, 512² grid, t=1.1. Wall time: 11s on A100 (WA-WENO-CR).
Two solvers are included:
MUSCL_WA.py— WA-3 approachWENO_PNG_Cheap.py— WA-WENO-CR approach (11s on A100 at 512², an hour and few minutes for 2048²)
I’ll add the multicomponent and multiphase codes later, and I might even add geometries like curvilinear or immersed boundary.
It was enjoyable. It was faster than nvFORTRAN for reasons I don’t understand. For instance, the Riemann problem took about 24 seconds with FORTRAN code. I like the CUDA code I get. :). It matches really well for the viscous TGV, which is not included in this code. This is a comparsion against the FORTRAN code.
- Chamarthi, Hoffmann, Frankel — A wave appropriate discontinuity sensor approach for compressible flows, Phys. Fluids 35, 066107 (2023)
- Hoffmann, Chamarthi, Frankel — Centralized gradient-based reconstruction for wall modeled large eddy simulations of hypersonic boundary layer transition, J. Comput. Phys. (2024)
- Chamarthi — Wave-appropriate multidimensional upwinding approach for compressible multiphase flows, J. Comput. Phys. 538, 114157 (2025)
- Chamarthi — Physics appropriate interface capturing reconstruction approach for viscous compressible multicomponent flows, Comput. Fluids 303, 106858 (2025)
- Chamarthi — Wave-appropriate reconstruction of compressible flows: physics-constrained acoustic dissipation and rank-1 entropy wave correction, preprint (2026)
Amareshwara Sainadh Chamarthi sainath@caltech.edu