Seunghyun Joo

Seunghyun Joo

Research Associate at Seoul National University | Looking for a PhD position

CuDAFLOW: CUDA Discrete-Adjoint CFD

GitHub

🔍 Project Overview

CuDAFLOW is a single-precision GPU finite-volume compressible RANS/LES solver built around an exact discrete adjoint. Its distinguishing piece is CuAD, a Tapenade-style source-to-source automatic-differentiation compiler for CUDA (Clang LibTooling): CuAD differentiates the actual GPU residual kernels, so every derivative in the adjoint chain is exact rather than finite difference.

  • Flow solver (GPU, FP32) — structured multiblock, overset/chimera, AUSMPW+ with up to 5th-order MUSCL / eMLP-VC reconstruction, full viscous fluxes, Spalart–Allmaras (RANS) and SA-DDES/IDDES/Vreman (LES), implicit red-black / line (DADI) smoothing and pseudo-time multigrid, dual-time unsteady.
  • CuAD — CUDA AD compiler (now a separate open-source repository) — forward (tangent) and reverse (adjoint) mode; handles arrays, structs, cross-call, atomicAdd, ternaries and 2-D array access. It differentiates the heavy flux/viscous/turbulence kernels exactly.
  • Exact discrete adjoint — the stiff RANS adjoint amplifies any finite-difference term by the condition number, so all four amplified derivatives — the Jacobian ∂R/∂Q, the objective seed ∂J/∂Q, the mesh sensitivity ∂R/∂X and the wall-distance term ∂R/∂wd — are produced by CuAD AD. A 6.85%-accurate FP32 finite-difference Jacobian gave a shape gradient 233× too large and the wrong sign; the full-AD chain recovers the correct sign and magnitude.
  • Optimization from Python — objectives cd, cl, cf, cp, qw and design variables (FFD control points or the SA field β), driven by pyOptSparse. Objective and constraints are plain Python callables of the CFD functionals.
  • PETSc adjoint solve — the assembled block Jacobian is solved in double precision with GMRES + ILU (the only FP64 part; the flow stays FP32).

✅ Validation Status

CaseConfigurationResult
Schubauer–Klebanoff flat plateSA-BCM transition, M = 0.3, LE-refined gridSkin friction matches the S&K transitional experiment
Axisymmetric Mach-7 SWBLI (Kussoy)Spalart–Allmaras, Re = 57 000 / cmWall pressure / heating within ~1–2% of the reference WIND-SA solution
ONERA M6 transonic wingM = 0.84, α = 3.06°, multiblock, eMLP-VCλ-shock captured; surface pressure in line with experiment
Exact-AD shape adjoint (NACA 0012)order 3, viscous, CuAD AD Jacobian + PETScAssembly consistency ‖gJac·q − dR‖ ≈ 3.6e-4; shape gradient right-sign, usable
Schubauer–Klebanoff transitional flat plate skin friction
Schubauer–Klebanoff transitional flat plate — CuDAFLOW SA-BCM skin friction tracks the transitional experiment through laminar, transition onset and the turbulent branch.
Mach-7 axisymmetric shock/boundary-layer interaction wall pressure and heating
Kussoy Mach-7 axisymmetric SWBLI (20° flare) — CuDAFLOW (SA) wall pressure and heat transfer against the WIND-US SA reference and experiment.
ONERA M6 chordwise pressure at seven span stations
ONERA M6 transonic wing (M = 0.84, α = 3.06°) — CuDAFLOW chordwise Cp at seven span stations captures the λ-shock, in line with CFL3D and FUN3D.

🔧 Engineering Notes

The core finding is that for the stiff RANS discrete adjoint exact AD is not a luxury: an ill-conditioned adjoint amplifies a 6.85%-accurate finite-difference Jacobian into a 233× gradient error with the wrong sign. CuAD makes every residual derivative exact, and because the amplified terms (∂R/∂Q, ∂R/∂X, ∂R/∂wd) are objective-independent, the same machinery serves shape optimization, Cf/Cp inverse design and Spalart–Allmaras field inversion (FIML) alike — the choice of objective only enters through the (un-amplified) ∂J/∂Q. A regression harness checks the AD-Jacobian assembly consistency, the adjoint convergence, and that the FIML loss actually descends.

GPL-3.0.