`define_new_center` can divide by zero when parabola fit curvature is zero

Summary

Castro::define_new_center computes subcell center shift via parabola fit and uses x = -b / (2a) (and similarly y, z) without guarding a == 0 (or near zero). Flat/near-flat local maxima can produce NaN/Inf center updates.

Location

• Source/driver/Castro.cpp:4366
• Source/driver/Castro.cpp:4372
• Source/driver/Castro.cpp:4379

Problem Details

For each direction:

• a = 0.5 * (f(+1) + f(-1))
• b = 0.5 * (f(+1) - f(-1))
• shift = -b / (2a)

If a is zero or tiny, this division is unstable and can corrupt problem::center.

Impact

• NaN/Inf moving center values in symmetric or plateau-like density peaks.
• Follow-on failures in any center-relative diagnostics/source terms.

Suggested Patch

diff --git a/Source/driver/Castro.cpp b/Source/driver/Castro.cpp
--- a/Source/driver/Castro.cpp
+++ b/Source/driver/Castro.cpp
@@
         Real a = 0.5_rt * (data(mi[0]+1, mi[1], mi[2]) + data(mi[0]-1, mi[1], mi[2]));
         Real b = 0.5_rt * (data(mi[0]+1, mi[1], mi[2]) - data(mi[0]-1, mi[1], mi[2]));
-        Real x = -b / (2.0_rt * a);
+        Real x = 0.0_rt;
+        if (std::abs(a) > std::numeric_limits<Real>::epsilon()) {
+            x = -b / (2.0_rt * a);
+        }
         problem::center[0] = new_center[0] + x * dx[0];
@@
-        Real y = -b / (2.0_rt * a);
+        Real y = 0.0_rt;
+        if (std::abs(a) > std::numeric_limits<Real>::epsilon()) {
+            y = -b / (2.0_rt * a);
+        }
         problem::center[1] = new_center[1] + y * dx[1];
@@
-        Real z = -b / (2.0_rt * a);
+        Real z = 0.0_rt;
+        if (std::abs(a) > std::numeric_limits<Real>::epsilon()) {
+            z = -b / (2.0_rt * a);
+        }
         problem::center[2] = new_center[2] + z * dx[2];

Notes

Choosing zero shift when the local quadratic is singular is a safe fallback that preserves the cell-center location.

Prepared by Codex

Start in Source/driver/Castro.cpp at the define_new_center locations around lines 4366, 4372, and 4379, and review how the parabola-fit coefficients determine each center shift. Verify the zero-curvature fallback for x, y, and z prevents NaN or Inf center values while preserving the cell-center location.