[PhaGe8539]

Proposed Changes

A dual-time run started from a steady solution, or restarted, loses the LM transition state. CFVMFlowSolverBase::LoadRestart's dual-time handling covers FLOW and TURB but not TRANS, and the time levels in CTransLMVariable start at zero. The first physical step then sees a wrong Solution_time_n / Solution_time_n1 for the LM equations.

This PR:

• pushes TRANS_SOL to time levels n and n-1 alongside FLOW and TURB;
• loads the second restart file for the transition model on 2nd-order restarts, and pushes it to level n;
• initialises Solution_time_n and Solution_time_n1 from the initial state in CTransLMVariable when dual time stepping is on.

Test

2-D RG14 airfoil, Re 2e5, alpha 1.97 deg, SST + LM, DUAL_TIME_STEPPING-2ND_ORDER, no multigrid. I ran 10 physical steps continuously and compared them with 9 steps + restart + 1 step, using the same steady seed for both.

Values at step 10, continuous vs restarted:

Binary	rms[LM_1]	rms[LM_2]	CD
8.5.0 release	-3.8146 vs -0.3549	-0.8087 vs 0.3235	0.00975976 vs 0.00975678
develop f4b67d2 + this PR	-6.9209 vs -6.9209	-1.5798 vs -1.5798	0.00975914 vs 0.00975914

With this PR, all residuals, CL and CD at step 10 match to the printed digits, for both WRT_RESTART_COMPACT YES and NO.

Limits of this test:

• The "before" row is the 8.5.0 release, not unpatched develop. I read the develop code and the same gaps are there, but I did not run an unpatched develop build.
• Not tested with multigrid, compressible cases other than this one, or MPI (OpenMP build only).
• No regression case added yet. I am happy to add one if you can suggest the right place.

Related Work

Fixes #2993.

PR Checklist

• I am submitting my contribution to the develop branch.
• My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
• My contribution is commented and consistent with SU2 style (https://su2code.github.io/docs_v7/Style-Guide/).
• I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
• I have added a test case that demonstrates my contribution, if necessary.
• I have updated appropriate documentation (Tutorials, Docs Page, config_template.cpp), if necessary.

This fix was written with AI assistance (Claude) and tested by running the case above.

🤖 Generated with Claude Code