Trimmed shape optimization driver: max L/D at fixed CL with CMy = 0 (discrete adjoint, FFD)

[nikita-ageev]

I have published a small Python driver around SU2 8.5 for trimmed shape optimization with the discrete adjoint: https://github.com/nikita-ageev/su2-trimmed-shape-optimization

What it does:

• maximizes L/D at fixed CL: every flow solution uses FIXED_CL_MODE= YES, and the adjoint gradients are taken at constant CL through dCD/dCL and dCMy/dCL;
• keeps the configuration trimmed: CMy = 0 about the CG is an equality constraint with its own discrete-adjoint gradient;
• keeps fuselage volume (V >= 0.995 V0, volume and its analytic gradient computed from the surface mesh through a Python re-implementation of the SU2 FFD map) and length (FFD points move only in y and z);
• FFD parameterization (11 × 3 × 2 Bernstein box, 66 variables, or a 15 × 5 × 5 cubic B-spline box, 450 variables), SLSQP from SciPy; one design iteration costs one direct run, two adjoint runs and two SU2_DOT_AD projections.

Results on a supersonic wing-body model (Sears-Haack fuselage, L = 60 m, fixed thin 62° swept wing, M = 1.7, Euler, CL = 0.10, half model 347k tetrahedra):

	baseline	66 variables	450 variables
L/D	15.91 (untrimmed, CMy = −3.6e-3)	18.37 (+15.4 %)	21.49 (+35 %)
CMy about CG	−3.6e-3	−1e-6	−3e-7
fuselage volume	100 %	99.50 %	99.50 %

The trim comes from the fuselage camber alone, without a control surface. Gradient check against central finite differences (baseline of the 66-variable case, every point a fixed-CL solution): dCD/dp within 0.02 %, dCMy/dp within 0.001 %. On a finer mesh (0.8–1M cells) the gains are +14.1 % and +30.9 %. There is also a 10-minute axisymmetric Sears-Haack benchmark at M = 1.8 (adjoint vs finite differences 1.5e-5).

Limitations: inviscid only, only the fuselage is shaped, the coarse mesh is not grid-converged in absolute CD (about 6 % between meshes, the relative gain carries over).

Things found on the way:

• Fixed-CL mode: dCD/dCL, dCMy/dCL in flow.meta are stale when the finite-difference phase does not end on a screen-output iteration #2937: in fixed-CL mode DCD_DCL_VALUE / DCMY_DCL_VALUE in flow.meta can be stale when the finite-difference phase ends on the ITER_DCL_DALPHA limit on a non-screen-output iteration. In my runs dCMy/dCL jumped from about −0.04 to +0.85, which broke the trim constraint gradient; the 450-variable run therefore computes dCD/dCL and dCMy/dCL with a separate run at AoA + 0.1°.
• Fix STATION function names in SU2_PY: SU2_GEO numbers stations from 1 #2934 (SU2_PY station names for SU2_GEO constraints) and Quote the SU2 executable path in SU2_PY on Linux/macOS (SU2_RUN with spaces) #2935 (quoting the SU2 executable path in SU2_PY), both open.

Feedback is welcome, in particular on the fixed-CL gradient handling, on whether a trim constraint like this would be useful in the SU2_PY optimization scripts, and on the next step to RANS.

[bigfooted]

I've seen it, a very useful tool for airfoil shape optimization and visualization. Is it configurable? Thanks for the contribution!

[nikita-ageev]

Thanks, Nijso! Yes, it is configurable from the command line; nothing is hard-wired to this particular body:

• Mesh and flow case: --mesh takes any SU2 mesh with the markers aircraft, symmetry, farfield; --template takes your own SU2 config (Mach, altitude, solver settings), config/wing_body.cfg is only the default.
• Trim and constraints: --target-cl, --xcg (reference point for CMy = 0), --vol-frac (minimum volume ratio).
• Parameterisation: --ffd bezier|bspline presets plus the move bounds --bnd-z, --bnd-y; the FFD box itself is generated from the mesh bounding box.
• Optimiser: built-in SLSQP (driver.py) and a trust-region SQP (trsqp.py: --delta0, --nu, --kkt-tol, --budget-hours), or DAKOTA through dakota_driver.py with analytic adjoint gradients (optpp_q_newton, rol, conmin_mfd).
• dJ/dCL: --dcx alpha|su2 (finite step in AoA, or SU2's EVAL_DOF_DCX; see Fixed-CL mode: dCD/dCL, dCMy/dCL in flow.meta are stale when the finite-difference phase does not end on a screen-output iteration #2937 for why the default is alpha).

The full option list is in the README: https://github.com/nikita-ageev/su2-trimmed-shape-optimization#readme . What is not configurable yet: the FFD layout is one box around the fuselage (a multi-box layout for wing + tail exists in my working copy and will go into the next release), and the objective is fixed to CD at fixed CL. If a config-file interface (one YAML instead of flags) would be more useful for the tutorials side, I am happy to add it.