AMReX Level-set Redistancing

Block-structured adaptive-mesh (AMR) reinitialization ("redistancing") of an advected level-set scalar, built on the AMReX framework.

The library restores the signed-distance property $|\nabla\phi| = 1$ of a level set after advection without moving its zero contour. It provides two independent redistancing algorithms — a PDE-based Sussman driver and a geometric mass-preserving driver — plus a validation suite (unit, convergence, volume-conservation, geometric-corner, and Zalesak rotation tests), a combined regression driver that emits a JUnit-style XML report, standalone rotation executables, and a Jupyter harness for running, visualising, and animating the tests.

---

Features

Capability	Options
Redistancing algorithm	LevelSetRedistance (Sussman PDE) and GeometricRedistance (Ausas–Dari–Buscaglia geometric, mass-preserving)
PDE spatial discretization	First-order Godunov upwind Hamiltonian, fifth-order HJ-WENO5
PDE pseudo-time integration	TVD-RK2, TVD-RK3 (SSP, Shu–Osher)
PDE interface preservation	Russo–Smereka subcell constraint
PDE mass/volume control	Sussman–Fatemi volume-conserving correction (multi-level FillPatch)
Geometric reconstruction	Bounded-facet (segment/disc) reconstruction with $\mathbf n = \nabla\phi/
Geometric propagation	Parallel Rouy–Tourin (Jacobi) eikonal sweeps
Geometric mass control	Band-local per-neighbourhood volume correction (feature-safe)
AMR	Multi-level FillPatchTwoLevels, average_down, dynamic regridding
Advection (tests)	Godunov / WENO5 upwind, TVD-RK3, Berger–Colella time subcycling, smoothed conservative coarse-band sync
Configuration	Runtime ParmParse control of scheme, integrator, and all physical parameters
CI	Combined regression driver → JUnit XML; standalone rotation executables; Doxygen docs
Tooling	Jupyter harness: run, parse, plot, animate, and mass-conservation comparison

---

Governing equations

PDE redistancing (LevelSetRedistance)

Reinitialization integrates the Hamilton–Jacobi PDE to steady state in a pseudo-time $\tau$:

$$ \frac{\partial \phi}{\partial \tau} = \operatorname{sgn}(\phi_0)\bigl(1 - |\nabla\phi|\bigr), \qquad \operatorname{sgn}(\phi_0) \approx \frac{\phi_0}{\sqrt{\phi_0^2 + \epsilon^2}}, $$

with $\epsilon = \texttt{sign_eps}\cdot\Delta x$. The gradient magnitude uses a sign-dependent Godunov Hamiltonian; the one-sided derivatives are either first-order differences or HJ-WENO5 reconstructions.

Geometric redistancing (GeometricRedistance)

A four-stage geometric scheme that computes distances directly from a reconstructed interface:

1. Bounded-facet reconstruction — each cut cell yields a segment (2D) / disc (3D) of half-extent $L$ through the crossing centroid, normal $\mathbf n = \nabla\phi_0/|\nabla\phi_0|$. Bounding the facet prevents an unbounded plane from chamfering convex corners.
2. First-band distances — minimum bounded-facet distance over the $3^d$ neighbourhood, frozen as Dirichlet data.
3. Propagation — parallel Rouy–Tourin (Jacobi) eikonal sweeps solve $|\nabla d| = 1$; the band is then clamped and $\operatorname{sgn}(\phi_0)$ reapplied.
4. Band-local mass preservation — a per-neighbourhood normal shift $$ \delta_{ij} = \frac{\sum_{\Omega_{ij}}\bigl(H_\epsilon(\phi_0)-H_\epsilon(\phi)\bigr)} {\sum_{\Omega_{ij}} \delta_\epsilon(\phi)}, \qquad \phi \mathrel{-}= \delta_{ij}, $$ restores volume where a corner lost area without translating intact thin features (so it does not close the Zalesak slot).

---

Directory layout

amrex_levelset_redistance/
├── CMakeLists.txt              # root build (adds Source, Test, Docs)
├── README.md  LICENSE  CITATION.cff
├── CONTRIBUTING.md  CODE_OF_CONDUCT.md  .clang-format  .gitignore
├── .github/workflows/          # ci.yml, docs.yml
├── inputs/
│   ├── inputs.regression       # combined regression driver (all namespaces)
│   ├── inputs.zdisk2d          # standalone 2D Zalesak disk
│   └── inputs.zsphere3d        # standalone 3D Zalesak sphere
├── Source/
│   ├── RedistanceUtil.H             # shared host/device helpers (redist_detail)
│   ├── LevelSetRedistance.H / .cpp  # Sussman PDE driver (Godunov/WENO5,
│   │                                #   RK2/RK3, Russo–Smereka, Sussman–Fatemi)
│   ├── GeometricRedistance.H / .cpp # geometric mass-preserving driver (ADB 2011)
│   ├── AdvectionSolver.H   / .cpp   # subcycling advection integrator + sync
│   └── ZalesakProblem.H    / .cpp   # Zalesak IC, tagging, metrics, I/O
├── Test/
│   ├── RegressionMain.cpp   RegressionTests.H   # combined driver + registry
│   ├── JUnitReport.H / .cpp                     # JUnit XML writer + msg hook
│   ├── UnitTest.cpp         ConvergenceTest.cpp
│   ├── VolumeTest.cpp       GeometricTest.cpp
│   ├── ZalesakTest.cpp      ZalesakSyncTest.cpp
│   ├── GeometricCornerTest.cpp                  # static slot/corner unit test
│   ├── ZalesakDisk2D.cpp                        # standalone 2D (own main)
│   └── ZalesakSphere3D.cpp                      # standalone 3D (own main)
├── Docs/
│   ├── index.html            # user guide (tracked)  ->  site root on Pages
│   ├── main_page.md          # Doxygen API landing page (tracked)
│   ├── Doxyfile.in           # CMake-configured Doxygen template (tracked)
│   ├── CMakeLists.txt        # `docs` target (tracked)
│   └── api/                  # generated Doxygen HTML (git-ignored)  ->  /api/
└── zalesak_harness.py        # Jupyter/Jupytext harness (run, plot, animate)

---

Building

Prerequisites

• CMake ≥ 3.20, a C++17 compiler
• Git (AMReX is fetched automatically if not already installed)
• Optional: MPI, and CUDA / HIP / SYCL for GPU builds

Configure and build

The 2D and 3D executables require separate builds (AMREX_SPACEDIM is compile-time):

# 2D, CPU + MPI
cmake -S . -B build   -DREDIST_DIM=2 -DREDIST_MPI=ON
cmake --build build   -j

# 3D
cmake -S . -B build3d -DREDIST_DIM=3
cmake --build build3d -j

# CUDA GPU (3D)
cmake -S . -B buildcuda -DREDIST_DIM=3 -DREDIST_GPU_BACKEND=CUDA
cmake --build buildcuda -j

CMake option	Default	Meaning
REDIST_DIM	2	Spatial dimension (2 or 3)
REDIST_MPI	ON	Enable MPI
REDIST_OMP	OFF	Enable OpenMP
REDIST_GPU_BACKEND	NONE	NONE, CUDA, HIP, or SYCL

Documentation

cmake --build build --target docs      # HTML in build/Docs/html/index.html

---

Running the tests

Combined regression driver (JUnit XML)

cd build/Test

# Full suite → single JUnit report
./regression inputs.regression --output regression_results.xml

# A single test
./regression inputs.regression --only geometric_test

# Via CTest (each case also emits its own XML)
ctest --output-on-failure

The driver exits non-zero if any case fails, so it doubles as a single pass/fail gate. The XML is ingestible by GitHub Actions (mikepenz/action-junit-report), GitLab (artifacts:reports:junit), and Jenkins.

Test	Verifies	Metric
unit_test	$	\nabla\phi
convergence_test	Reinitialization convergence rate	value error vs exact signed distance (order ≈ 2)
volume_test	Sussman–Fatemi reduces enclosed-volume drift	smoothed-Heaviside volume A/B
geometric_test	Geometric driver restores $	\nabla\phi
zalesak_test	Shape/area error after rotating the slotted disk	finest-data masked sym. difference
zalesak_sync_test	Conservative coarse-band sync reduces coarse–fine mismatch	smoothed coarse–fine volume A/B

Metric note. Several metrics use a smoothed Heaviside rather than a sharp cell count, and the convergence test measures the value error against the exact signed distance. These choices measure exactly the quantity each mechanism controls and are robust to sub-cell interface motion and MPI decomposition (verified rank-invariant on 1–8 ranks, 2D and 3D).

Standalone rotation executables (own main)

These select the redistancing algorithm at runtime via redist.method, support time-series animation, and (2D) log per-step volume to volume.txt for mass-conservation studies.

# 2D disk — level-set vs geometric
cd build/Test
./test_zdisk2d inputs.zdisk2d redist.method=levelset
./test_zdisk2d inputs.zdisk2d redist.method=geometric

# 3D slotted sphere
cd build3d/Test
./test_zsphere3d inputs.zsphere3d redist.method=geometric

# Static slot/corner unit test (2D)
cd build/Test
./test_geom_corner

---

Configuration reference (ParmParse)

Redist.* — PDE redistancing driver:

Key	Default	Meaning
scheme	godunov1	godunov1 | weno5
integrator	rk3	rk2 | rk3
subcell_fix	1	Russo–Smereka interface constraint
volume_fix	0	Sussman–Fatemi volume conservation
cfl	0.5	$\Delta\tau = \texttt{cfl}\cdot\Delta x$
sign_eps	1.0	Sign-smoothing width (cells)
weno_eps	1e-6	WENO5 regularization
vc_eps, vc_radius	1.5, 1	Volume-fix delta width / neighbourhood radius
n_iter	5	Default pseudo-time iterations

Geom.* — geometric redistancing driver:

Key	Default	Meaning
mass_preserving	1	Band-local volume-conserving correction
band	5.0 (6.0 for Zalesak)	Narrow-band half-width (cells)
prop_iters	0	Eikonal propagation iterations (0 → auto)
mass_eps	1.5	Smoothed-Heaviside width (cells) for the correction
vc_radius	2	Local mass-correction neighbourhood radius (cells)

redist.method — levelset | geometric (standalone executables).

Test namespaces (tst.*, conv.*, vol.*, zalesak.*, sync.*, geom.*, zd2d.*, zs3d.*) are documented in the corresponding inputs/* files.

---

Minimal usage

#include "LevelSetRedistance.H"    // PDE driver
#include "GeometricRedistance.H"   // geometric driver

amrex::Vector<amrex::MultiFab*> phi = /* per-level level-set pointers */;

// PDE (Sussman) redistancing:
LevelSetRedistance ls(&amrcore, /*nghost=*/3);
ls.setScheme(RedistScheme::WENO5);
ls.setIntegrator(RedistIntegrator::RK3);
ls.setInterfaceConstraint(true);       // Russo–Smereka
ls.setVolumeConservation(false);       // Sussman–Fatemi (optional)
ls.readParameters();                   // "Redist" inputs override
ls.redistance(phi, /*n_iter=*/5);

// Geometric (Ausas–Dari–Buscaglia) redistancing:
GeometricRedistance geo(&amrcore, /*nghost=*/3);
geo.setMassPreserving(true);           // band-local correction
geo.readParameters();                  // "Geom" inputs override
geo.redistance(phi, /*n_iter=*/0);     // 0 => auto propagation iterations

---

Python / Jupyter harness

zalesak_harness.py (Jupytext-compatible; jupytext --to notebook zalesak_harness.py) provides:

• Build / run / parse helpers for both the combined driver and the standalone executables.
• Static visualisation — 2D contour + symmetric-difference maps; 3D orthogonal slices + phi = 0 marching-cubes isosurface.
• Time-series animation — drives the plot_int frame output and animates the rotating slot (2D contours, 3D slices) with in-notebook playback and GIF/MP4 export.
• Method comparison — level-set vs geometric shape-error / drift bar charts and interface overlays.
• Mass-conservation comparison — loads the per-step volume.txt logs and plots volume-vs-time, relative-drift-vs-time, and the instantaneous drift rate (exposing per-reinit mass "kicks").

Requirements:

pip install numpy matplotlib yt scikit-image jupytext   # + system ffmpeg for MP4

---

Numerical methods and citations

The algorithms implemented here draw on the following literature. If you use this code in academic work, please cite the relevant methods below alongside AMReX.

Level-set method and PDE reinitialization

• Osher, S. and Sethian, J. A. (1988). Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys., 79(1), 12–49. doi:10.1016/0021-9991(88)90002-2
• Sussman, M., Smereka, P. and Osher, S. (1994). A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys., 114(1), 146–159. doi:10.1006/jcph.1994.1155

Godunov Hamiltonian for the eikonal/HJ equation

• Rouy, E. and Tourin, A. (1992). A viscosity solutions approach to shape-from-shading. SIAM J. Numer. Anal., 29(3), 867–884. doi:10.1137/0729053
• Bardi, M. and Osher, S. (1991). The nonconvex multidimensional Riemann problem for Hamilton–Jacobi equations. SIAM J. Math. Anal., 22(2), 344–351. doi:10.1137/0522022

High-order WENO reconstruction

• Liu, X.-D., Osher, S. and Chan, T. (1994). Weighted essentially non-oscillatory schemes. J. Comput. Phys., 115(1), 200–212. doi:10.1006/jcph.1994.1187
• Jiang, G.-S. and Shu, C.-W. (1996). Efficient implementation of weighted ENO schemes. J. Comput. Phys., 126(1), 202–228. doi:10.1006/jcph.1996.0130
• Jiang, G.-S. and Peng, D. (2000). Weighted ENO schemes for Hamilton–Jacobi equations. SIAM J. Sci. Comput., 21(6), 2126–2143. doi:10.1137/S106482759732455X

Strong-stability-preserving (TVD) Runge–Kutta

• Shu, C.-W. and Osher, S. (1988). Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys., 77(2), 439–471. doi:10.1016/0021-9991(88)90177-5
• Gottlieb, S., Shu, C.-W. and Tadmor, E. (2001). Strong stability-preserving high-order time discretization methods. SIAM Review, 43(1), 89–112. doi:10.1137/S003614450036757X

Interface-preserving reinitialization (subcell fix)

• Russo, G. and Smereka, P. (2000). A remark on computing distance functions. J. Comput. Phys., 163(1), 51–67. doi:10.1006/jcph.2000.6553

Higher-order subcell distance (context for the interface-layer accuracy)

• du Chéné, A., Min, C. and Gibou, F. (2008). Second-order accurate computation of curvatures in a level set framework using novel high-order reinitialization schemes. J. Sci. Comput., 35(2–3), 114–131. doi:10.1007/s10915-007-9177-1
• Min, C. (2010). On reinitializing level set functions. J. Comput. Phys., 229(8), 2764–2772. doi:10.1016/j.jcp.2009.12.032

Volume/mass-conserving reinitialization

• Sussman, M. and Fatemi, E. (1999). An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM J. Sci. Comput., 20(4), 1165–1191. doi:10.1137/S1064827596298245

Geometric mass-preserving redistancing

• Ausas, R. F., Dari, E. A. and Buscaglia, G. C. (2011). A geometric mass-preserving redistancing scheme for the level set function. Int. J. Numer. Methods Fluids, 65(8), 989–1010. doi:10.1002/fld.2227 — the geometric driver implemented in GeometricRedistance.

Eikonal solvers (propagation)

• Sethian, J. A. (1996). A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. USA, 93(4), 1591–1595. doi:10.1073/pnas.93.4.1591 — the sequential alternative to the parallel Jacobi Rouy–Tourin sweep used here.

Adaptive mesh refinement and time subcycling

• Berger, M. J. and Oliger, J. (1984). Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys., 53(3), 484–512. doi:10.1016/0021-9991(84)90073-1
• Berger, M. J. and Colella, P. (1989). Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys., 82(1), 64–84. doi:10.1016/0021-9991(89)90035-1

Benchmark test problem

• Zalesak, S. T. (1979). Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys., 31(3), 335–362. doi:10.1016/0021-9991(79)90051-2

Framework

• Zhang, W., Almgren, A., Beckner, V., Bell, J., et al. (2019). AMReX: A framework for block-structured adaptive mesh refinement. J. Open Source Softw., 4(37), 1370. doi:10.21105/joss.01370
• AMReX-Codes. AMReX [software]. https://github.com/AMReX-Codes/amrex

---

BibTeX

@article{OsherSethian1988,
  author  = {Osher, Stanley and Sethian, James A.},
  title   = {Fronts propagating with curvature-dependent speed:
             Algorithms based on {Hamilton--Jacobi} formulations},
  journal = {Journal of Computational Physics},
  volume  = {79}, number = {1}, pages = {12--49}, year = {1988},
  doi     = {10.1016/0021-9991(88)90002-2}
}

@article{SussmanSmerekaOsher1994,
  author  = {Sussman, Mark and Smereka, Peter and Osher, Stanley},
  title   = {A level set approach for computing solutions to
             incompressible two-phase flow},
  journal = {Journal of Computational Physics},
  volume  = {114}, number = {1}, pages = {146--159}, year = {1994},
  doi     = {10.1006/jcph.1994.1155}
}

@article{RouyTourin1992,
  author  = {Rouy, Elisabeth and Tourin, Agn\`{e}s},
  title   = {A viscosity solutions approach to shape-from-shading},
  journal = {SIAM Journal on Numerical Analysis},
  volume  = {29}, number = {3}, pages = {867--884}, year = {1992},
  doi     = {10.1137/0729053}
}

@article{JiangShu1996,
  author  = {Jiang, Guang-Shan and Shu, Chi-Wang},
  title   = {Efficient implementation of weighted {ENO} schemes},
  journal = {Journal of Computational Physics},
  volume  = {126}, number = {1}, pages = {202--228}, year = {1996},
  doi     = {10.1006/jcph.1996.0130}
}

@article{JiangPeng2000,
  author  = {Jiang, Guang-Shan and Peng, Danping},
  title   = {Weighted {ENO} schemes for {Hamilton--Jacobi} equations},
  journal = {SIAM Journal on Scientific Computing},
  volume  = {21}, number = {6}, pages = {2126--2143}, year = {2000},
  doi     = {10.1137/S106482759732455X}
}

@article{ShuOsher1988,
  author  = {Shu, Chi-Wang and Osher, Stanley},
  title   = {Efficient implementation of essentially non-oscillatory
             shock-capturing schemes},
  journal = {Journal of Computational Physics},
  volume  = {77}, number = {2}, pages = {439--471}, year = {1988},
  doi     = {10.1016/0021-9991(88)90177-5}
}

@article{GottliebShuTadmor2001,
  author  = {Gottlieb, Sigal and Shu, Chi-Wang and Tadmor, Eitan},
  title   = {Strong stability-preserving high-order time
             discretization methods},
  journal = {SIAM Review},
  volume  = {43}, number = {1}, pages = {89--112}, year = {2001},
  doi     = {10.1137/S003614450036757X}
}

@article{RussoSmereka2000,
  author  = {Russo, Giovanni and Smereka, Peter},
  title   = {A remark on computing distance functions},
  journal = {Journal of Computational Physics},
  volume  = {163}, number = {1}, pages = {51--67}, year = {2000},
  doi     = {10.1006/jcph.2000.6553}
}

@article{duCheneMinGibou2008,
  author  = {du Ch\'{e}n\'{e}, Arthur and Min, Chohong and Gibou, Fr\'{e}d\'{e}ric},
  title   = {Second-order accurate computation of curvatures in a level set
             framework using novel high-order reinitialization schemes},
  journal = {Journal of Scientific Computing},
  volume  = {35}, number = {2--3}, pages = {114--131}, year = {2008},
  doi     = {10.1007/s10915-007-9177-1}
}

@article{Min2010,
  author  = {Min, Chohong},
  title   = {On reinitializing level set functions},
  journal = {Journal of Computational Physics},
  volume  = {229}, number = {8}, pages = {2764--2772}, year = {2010},
  doi     = {10.1016/j.jcp.2009.12.032}
}

@article{SussmanFatemi1999,
  author  = {Sussman, Mark and Fatemi, Emad},
  title   = {An efficient, interface-preserving level set redistancing
             algorithm and its application to interfacial incompressible
             fluid flow},
  journal = {SIAM Journal on Scientific Computing},
  volume  = {20}, number = {4}, pages = {1165--1191}, year = {1999},
  doi     = {10.1137/S1064827596298245}
}

@article{AusasDariBuscaglia2011,
  author  = {Ausas, Roberto F. and Dari, Enzo A. and Buscaglia, Gustavo C.},
  title   = {A geometric mass-preserving redistancing scheme for the
             level set function},
  journal = {International Journal for Numerical Methods in Fluids},
  volume  = {65}, number = {8}, pages = {989--1010}, year = {2011},
  doi     = {10.1002/fld.2227}
}

@article{Sethian1996,
  author  = {Sethian, James A.},
  title   = {A fast marching level set method for monotonically
             advancing fronts},
  journal = {Proceedings of the National Academy of Sciences},
  volume  = {93}, number = {4}, pages = {1591--1595}, year = {1996},
  doi     = {10.1073/pnas.93.4.1591}
}

@article{BergerColella1989,
  author  = {Berger, Marsha J. and Colella, Phillip},
  title   = {Local adaptive mesh refinement for shock hydrodynamics},
  journal = {Journal of Computational Physics},
  volume  = {82}, number = {1}, pages = {64--84}, year = {1989},
  doi     = {10.1016/0021-9991(89)90035-1}
}

@article{BergerOliger1984,
  author  = {Berger, Marsha J. and Oliger, Joseph},
  title   = {Adaptive mesh refinement for hyperbolic partial
             differential equations},
  journal = {Journal of Computational Physics},
  volume  = {53}, number = {3}, pages = {484--512}, year = {1984},
  doi     = {10.1016/0021-9991(84)90073-1}
}

@article{Zalesak1979,
  author  = {Zalesak, Steven T.},
  title   = {Fully multidimensional flux-corrected transport
             algorithms for fluids},
  journal = {Journal of Computational Physics},
  volume  = {31}, number = {3}, pages = {335--362}, year = {1979},
  doi     = {10.1016/0021-9991(79)90051-2}
}

@article{AMReX_JOSS,
  author  = {Zhang, Weiqun and Almgren, Ann and Beckner, Vince and
             Bell, John and others},
  title   = {{AMReX}: A framework for block-structured adaptive mesh
             refinement},
  journal = {Journal of Open Source Software},
  volume  = {4}, number = {37}, pages = {1370}, year = {2019},
  doi     = {10.21105/joss.01370}
}

---

Method-to-code map

Source component	Primary reference(s)
LevelSetRedistance (PDE)	Sussman, Smereka & Osher (1994); Osher & Sethian (1988)
Godunov Hamiltonian	Rouy & Tourin (1992); Bardi & Osher (1991)
RedistScheme::WENO5	Jiang & Peng (2000); Jiang & Shu (1996); Liu, Osher & Chan (1994)
RedistIntegrator::RK2/RK3	Shu & Osher (1988); Gottlieb, Shu & Tadmor (2001)
setInterfaceConstraint (subcell)	Russo & Smereka (2000); du Chéné, Min & Gibou (2008); Min (2010)
setVolumeConservation	Sussman & Fatemi (1999)
GeometricRedistance (bounded facet + local mass)	Ausas, Dari & Buscaglia (2011)
Geometric eikonal propagation	Rouy & Tourin (1992); Sethian (1996)
AdvectionSolver subcycling / sync	Berger & Colella (1989); Berger & Oliger (1984)
ZalesakProblem benchmark	Zalesak (1979)
AMR data structures / FillPatch	Zhang et al. (2019)

---

Method selection guidance

Both redistancing drivers pass the full suite in 2D and 3D. On the Zalesak benchmark (one revolution, 2 AMR levels):

Method	Shape error (sym.diff / A₀)	Area drift
LevelSetRedistance (WENO5 + RK3 + Russo–Smereka + Sussman–Fatemi)	~2.0×10⁻³	~2.0×10⁻⁴
GeometricRedistance (bounded facet + band-local mass)	~2.2×10⁻²	~−9.2×10⁻³

The PDE driver is the stronger choice for corner-heavy, thin-feature geometries like the Zalesak disk — it pins the contour cell-locally each reinit, whereas the geometric driver re-derives the interface. The geometric driver is a legitimate, feature-preserving option (its bounded-facet reconstruction keeps corners and the band-local correction keeps the slot open) and is the natural choice where a reconstruction-based distance is preferred over a PDE relaxation.

---

Validation status

• 2D and 3D suites pass on physically meaningful metrics (value-error convergence ≈ 2; smoothed-volume conservation; smoothed coarse–fine sync).
• MPI-invariant across 1–8 ranks (2D and 3D).
• Both redistancing methods exercised via the standalone rotation executables and the geometric_test regression case.

---

License

Distributed under the BSD 3-Clause License — see LICENSE. Copyright (c) 2026, The University of Edinburgh.

AMReX itself is distributed under the BSD-3-Clause license; retain its copyright and license notices when redistributing.

Authors and acknowledgements

• David Ingram, The University of Edinburgh — ORCID 0000-0002-8669-8942.
• Developed with assistance from ELM, the University of Edinburgh's secure generative-AI gateway.

Built on AMReX, developed at Lawrence Berkeley National Laboratory with U.S. Department of Energy support. The numerical methods are due to the authors cited above.

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Note on citations: DOIs and volume/page details have been provided to the best of accuracy; please verify each reference against the publisher of record before inclusion in a formal manuscript.