Independent CFD development

Adaptive flow,
resolved where
it matters.

OctFlux CFD explores a finite-volume solver built around block-structured octree adaptive mesh refinement: focused resolution for evolving flow features, guided by verification from the start.

Illustrative AMR hierarchy — refinement concentrates near a local feature.

Octree AMR Block-structured spatial adaptivity

Finite volume Conservative flow formulation

Verification-led Benchmarks guide development

The approach

Make resolution a decision, not a default.

The project focuses on the foundations that make adaptive simulation credible: hierarchy, conservative coupling, and transparent validation.

01 / HIERARCHY

Structured blocks

A quadtree in 2D and octree in 3D organize fixed-size Cartesian blocks into a hierarchy that is practical to refine, traverse, and visualize.

02 / CONSERVATION

Interfaces matter

Adaptive grids are only useful when transitions are treated carefully. The focus is consistent transfer and conservation across coarse-to-fine regions.

03 / EVIDENCE

Measure the basics

Known flows, mesh sensitivity, and observable physical quantities set a clear bar for each milestone.

Validation roadmap

Small cases, useful evidence.

The initial benchmark suite is designed to make progress measurable from the start.

AMR focus

Lid-driven cavity

A compact incompressible-flow reference for vortex placement, centreline profiles, and resolution sensitivity.

Compare: velocity profiles, primary vortex location, grid refinement behaviour.

CYLINDER WAKE

Flow past a cylinder

Use an unsteady wake to examine separation, force trends, and adaptive resolution around a moving flow feature.

Compare: wake structure and nondimensional shedding frequency.

CANONICAL FLOWS

Transport & shock cases

Simple manufactured and canonical problems help test accuracy, stability, and adaptation logic before complexity grows.

Compare: conservation, order trends, and feature capture.

02 / Validation record
AMR evidence

Results with a comparison basis.

Each result is framed around the same question: can resolution follow the important flow structure while a uniform mesh remains the fixed reference? The record below moves from centreline profiles, to a localized wake, to a moving multiphase interface.

FEATURED BENCHMARK / RE = 100

Lid-driven cavity

Gradient-based AMR is read against uniform-grid solutions and the Ghia, Ghia & Shin centreline reference data.

Comparison basisUniform 128² provides the fixed finest-grid reference; Ghia et al. (1982) provides the published centreline trace.

Lid-driven cavity centreline velocity profiles and error against a uniform 128 squared reference grid — Velocity profiles and error traces. AMR is shown alongside both uniform-grid and literature reference data.

5,824 AMR active cells

16,384 uniform 128² cells

4.7 × 10⁻⁴ RMS u error vs. 128²

2.7 × 10⁻⁴ RMS v error vs. 128²

CASE 01 / STATIC AMR

Cylinder wake

Body and near-wake resolution is fixed where the steady Re = 40 flow needs it.

Mesh record15,600 leaf cells · D/16 finest spacing

CASE 02 / DYNAMIC AMR

Vortex street

Re = 100 tagging tracks localized wake structures as they move downstream.

Mesh record21,184–32,128 active leaf cells · D/32 maximum

CASE 03 / MULTIPHASE

Rising interface

The hierarchy follows a deforming bubble instead of keeping the full liquid column fine.

Mesh recordAbout 8,000–10,000 AMR leaves · 32,768 uniform fine cells

02 / Dynamic cylinder wake — complete case record Open simulation

Animated AMR refinement levels following a vortex street behind a cylinder at Reynolds number 100

CYLINDER / RE = 100 / UNSTEADY

Adaptive wake tracking

A circular cylinder starts a periodic wake. A static region resolves the near body; dynamic tagging then responds as vortices travel downstream.

DOMAIN64 D × 40 D with slip side walls, uniform inflow, and pressure outlet.
BASE GRID1 D base spacing; static refinement to D/16 near the cylinder.
DYNAMIC AMRVelocity-magnitude tagging, threshold 0.06; regrid every 20 steps to D/32.
RUN250 time units, 35,630 steps, and 1,350 regrids.
ACTIVE CELLS21,184–32,128 leaf cells; 2,621,440 cells for a uniform D/32 grid.

Rising bubble snapshots showing bubble shape, AMR refinement levels, and speed field over time

MULTIPHASE AMR / HYSING CASE 1

Refinement follows the interface.

The rising-bubble study brings the same AMR idea into a moving two-phase interface: concentrate the hierarchy around the bubble while retaining a direct uniform-grid comparison for velocity and centre of mass.

Rising bubble velocity, centre of mass, and AMR leaf-cell count compared with uniform grids

8k–10kAMR leaf cells during the evolution

32,768cells in the uniform fine reference

03 / Motion studies
Animated AMR

See the hierarchy follow the event.

Each animation is a compact verification record: the geometry evolves, the AMR mesh stays concentrated near the interface or deformation, and the expanded note states the comparison that makes the case useful.

Animated two-dimensional water-drop impact into a pool with adaptive mesh refinement

CASE 04 / DROPLET IMPACT

Impact, crater, jets

A water drop enters a pool at 1000:1 density ratio; refinement follows the free surface through impact and jet formation.

Open case record

Evidence
1,014 steps over 0.5 time units. AMR uses 7,370 mean leaf cells (9,472 peak) versus 16,384 uniform-equivalent cells; phase-volume drift is 2.0 × 10⁻¹⁴ and the final water centre of mass matches the conservative uniform run within 0.01.

Animated Rayleigh-Taylor instability at 1000 to 1 density ratio with adaptive mesh refinement

CASE 05 / RAYLEIGH–TAYLOR

Growth against theory

A perturbed heavy-over-light interface grows under gravity while the fine band remains tied to the instability.

Open case record

Evidence
1000:1 density ratio, evaluated against two-layer linear theory and a uniform 128² reference. At t = 0.2, amplitude growth is within 2.9% of theory; the AMR run averages 6,147 leaf cells versus 16,384 uniform cells.

Animated two-dimensional vortex-reversal transport test with adaptive mesh refinement

CASE 06 / 2D VORTEX REVERSAL

Stretch, reverse, recover

The LeVeque single-vortex test deforms a disc into a thin spiral, then reverses the flow to recover it.

Open case record

Evidence
At T = 4, the AMR run has a 1.03% relative L1 shape error—matching the uniform 128² reference—with zero recorded mass drift. Mean AMR occupancy is 7,968 leaves versus 16,384 uniform cells.

Animated lid-driven cavity flow and adaptive refinement levels at Reynolds number 100

CASE 07 / CAVITY SPIN-UP

Vortex development

The primary vortex forms while gradient-driven AMR holds the fine cells where the velocity field changes most quickly.

Open case record

Evidence
The animated hierarchy complements the centreline comparison above. The Re = 100 AMR run uses 5,824 active cells against 16,384 cells on the uniform 128² reference, with RMS errors of 4.7 × 10⁻⁴ in u and 2.7 × 10⁻⁴ in v.

Animated rising bubble with adaptive mesh refinement following the two-phase interface

CASE 08 / RISING BUBBLE

Interface tracking

The Hysing case 1 bubble rises and deforms while refinement moves with the two-phase interface.

Open case record

Evidence
Velocity and centre-of-mass histories are compared against uniform-grid runs. The AMR hierarchy stays near the interface at roughly 8,000–10,000 leaf cells, compared with 32,768 cells on the uniform fine reference.

02 / Validation record
AMR evidence

One benchmark, one question, one record.

Read each case in the same order: a comparison establishes the reference, an animation shows where the hierarchy moves, and a compact readout states the numerical evidence. The sequence starts with the lid-driven cavity and then moves to wakes, interfaces, and stress tests.

Case records
Open to inspect

Each record uses the same interaction. Open a case to load the full, uncropped simulation GIF beside the setup and comparison basis. This keeps the page readable while preserving the full animation when you want to inspect it.

01 /Inspect the AMR evolutionOpen animation

Full animated lid-driven cavity flow and adaptive refinement levels at Reynolds number 100

CAVITY / RE = 100 / GRADIENT AMR

Start with a reference flow.

The cavity is the first validation record because its centreline profiles give a direct numerical comparison before interpreting adaptive behaviour.

REFERENCEUniform 128² grid and Ghia et al. (1982) centreline data.
AMR SIZE5,824 active cells, versus 16,384 uniform 128² cells.
ERRORRMS u = 4.7 × 10⁻⁴; RMS v = 2.7 × 10⁻⁴ relative to the uniform 128² field.

5,824AMR active cells

16,384uniform 128² cells

4.7 × 10⁻⁴RMS u error vs. 128²

2.7 × 10⁻⁴RMS v error vs. 128²

02 /Cylinder wake — static and dynamic AMROpen animation

Full animated AMR refinement levels following a vortex street behind a cylinder at Reynolds number 100

CYLINDER / RE = 40 AND 100

Refinement follows the wake.

The steady Re = 40 case establishes body and near-wake resolution. The Re = 100 record then shows dynamic tagging following the moving vortex street.

STATIC CASERe = 40: 15,600 leaf cells, with D/16 finest spacing.
DYNAMIC CASERe = 100: velocity-magnitude tagging every 20 steps, up to D/32.
ACTIVE CELLS21,184–32,128 leaf cells; uniform D/32 equivalent: 2,621,440 cells.
RUN250 time units, 35,630 steps, and 1,350 regrids.

03 /Rising bubble — interface-tracking animationOpen animation

Full animated rising bubble with AMR refinement following the two-phase interface

HYSING CASE 1 / MOVING INTERFACE

Keep the interface resolved.

The GIF shows the hierarchy moving with the bubble rather than retaining fine resolution across the entire liquid column.

COMPARISONRise velocity and centre-of-mass histories against uniform-grid runs.
AMR SIZEAbout 8,000–10,000 active leaf cells during the evolution.
FINE REFERENCE32,768 cells on the uniform fine grid.

COMPARISON / HYSING CASE 1

Snapshots make the interface-following refinement visible; the chart compares velocity and centre of mass with uniform-grid runs.

8k–10kAMR leaf cells during the evolution

32,768cells in the uniform fine reference

CASES 04–06 / STRESS AND TRANSPORT TESTS

Additional evidence, same representation.

These cases use the same expandable full-animation record: a drop impact for robustness, Rayleigh–Taylor growth against theory, and vortex reversal for interface transport.

04 /Droplet impact — crater and jetsOpen animation

Full animated two-dimensional water-drop impact into a pool with adaptive mesh refinement

DROP INTO POOL / 1000:1

Robustness through impact.

A falling water drop impacts a pool, forming a crater and jets. The record monitors conservative transport as the free surface changes rapidly.

AMR SIZE7,370 mean leaf cells; 9,472 peak, versus 16,384 uniform-equivalent cells.
CONSERVATIONPhase-volume drift: 2.0 × 10⁻¹⁴.
CHECKFinal water centre of mass agrees with the conservative uniform run within 0.01.

05 /Rayleigh–Taylor instability — growth against theoryOpen animation

Full animated Rayleigh-Taylor instability at 1000 to 1 density ratio with adaptive mesh refinement

RAYLEIGH–TAYLOR / 1000:1

Growth measured against theory.

A perturbed heavy-over-light interface develops under gravity while the AMR band follows the instability.

COMPARISONTwo-layer linear theory and a uniform 128² run.
RESULTAt t = 0.2, amplitude growth is within 2.9% of theory.
AMR SIZE6,147 mean leaf cells versus 16,384 uniform cells.

06 /2D vortex reversal — stretch, reverse, recoverOpen animation

Full animated two-dimensional vortex-reversal transport test with adaptive mesh refinement

LEVEQUE VORTEX / T = 4

Test transport reversibility.

A disc stretches into a thin spiral and the velocity field reverses, making recovery of the initial shape a clear transport check.

COMPARISONMatches the uniform 128² reference at the final state.
RESULT1.03% relative L1 shape error and zero recorded mass drift.
AMR SIZE7,968 mean leaf cells versus 16,384 uniform cells.

Project status

Under active development.

OctFlux CFD is an independent technical project. Public updates will be added as reproducible benchmark material becomes available.

Adaptive flow,resolved whereit matters.

Make resolution a decision, not a default.

Structured blocks

Interfaces matter

Measure the basics

Small cases, useful evidence.

Lid-driven cavity

Flow past a cylinder

Transport & shock cases

One benchmark, one question, one record.

Start with a reference flow.

Refinement follows the wake.

Keep the interface resolved.

Additional evidence, same representation.

Robustness through impact.

Growth measured against theory.

Test transport reversibility.

Under active development.

Adaptive flow,
resolved where
it matters.