`advance_particles` mutates FillPatch density in-place across grown tiles, risking overlap corruption

Summary

Castro::advance_particles() inverts density in S[mfi] in-place over mfi.growntilebox(), then reuses S to compute velocities. With tiled iteration and ng > 0, grown tile regions can overlap, so cells in overlap are inverted multiple times (rho -> 1/rho -> rho ...), producing incorrect Ucc values.

Location

• Source/particles/CastroParticles.cpp:267
• Source/particles/CastroParticles.cpp:270

Problem Details

Current code mutates shared FillPatch data per tile:

const Box& bx = mfi.growntilebox();
S[mfi].invert(1.0, bx, 0, 1);
for (int dir=0; dir < AMREX_SPACEDIM; ++dir) {
    Ucc[mfi].copy(S[mfi], bx, dir+1, bx, dir, 1);
    Ucc[mfi].mult(S[mfi], bx, 0, dir);
}

Because S[mfi] is reused across tiles, overlap makes the result order-dependent.

Impact

• Wrong particle advection velocities near tile boundaries when ghost grows are nonzero.
• Non-deterministic behavior under tiling/OpenMP depending on tile decomposition.

Suggested Patch

Compute Ucc = momentum / rho without mutating S:

diff --git a/Source/particles/CastroParticles.cpp b/Source/particles/CastroParticles.cpp
--- a/Source/particles/CastroParticles.cpp
+++ b/Source/particles/CastroParticles.cpp
@@
             for (MFIter mfi(Ucc,true); mfi.isValid(); ++mfi)
             {   
                 const Box& bx = mfi.growntilebox();
-                S[mfi].invert(1.0, bx, 0, 1);
                 for (int dir=0; dir < AMREX_SPACEDIM; ++dir) {
                     Ucc[mfi].copy(S[mfi], bx, dir+1, bx, dir, 1);
-                    Ucc[mfi].mult(S[mfi], bx, 0, dir);
+                    Ucc[mfi].divide(S[mfi], bx, 0, dir, 1);
                 }
             }

Prepared by Codex

Read Source/particles/CastroParticles.cpp around lines 267-270 and inspect how advance_particles uses S and Ucc during tiled iteration. Verify the fix avoids mutating shared FillPatch density over mfi.growntilebox() while preserving momentum-to-density velocity calculation across overlapping grown tiles.