NS–0003 · CFD Technical Report

REPORT SUMMARY

Engineering question and conclusion

Can a computationally practical, verified 2D axisymmetric Navier–Stokes model quantify flow around a generic intravascular device and supply consistent training data for design optimization?

The NS–0003 baseline models a smooth enlarged body on a continuous catheter shaft inside a 4 mm vessel at 100 mL/min. The coupled solver converged on the 161 × 41 production grid. Pressure drop was 846.262 Pa, peak velocity 0.314003 m/s, and device maximum wall shear 6.525 Pa. A three-grid study supports the medium mesh for the declared parametric dataset, while wall shear retains an explicit numerical-quality qualification.

A separately run candidate, OPT1–001, passed its solver gate and reduced the computed pressure drop to 752.932 Pa. These are numerical engineering results for a generic model. They are not experimental, patient-specific, or clinical validation.

57baseline outer iterations

0.599%medium-to-fine pressure change

3.374%device P95 WSS sensitivity

01 / PHYSICAL MODEL

Geometry and operating point

The 100 mm domain is a concentric annulus between a rigid vessel wall and a continuous solid shaft. A local enlarged device body is joined to the shaft by smooth C² transitions. The solver uses a meridional (z, r) domain revolved about the axis; this is axisymmetric cylindrical CFD, not planar Cartesian flow. The model has no free-ended centerline tip.

Solver-generated NS-0003 baseline device geometry

Fig. 1 · Device geometry. Solver-generated body-fitted boundary; the enlarged body occupies the center of a continuous shaft. Source ↗

Frozen baseline geometry and fluid inputs
Vessel inner diameter	4.0 mm
Continuous shaft OD	2.0 mm
Device body OD / length	2.4 mm / 15 mm
Upstream / downstream transition	3 mm / 3 mm, C² smooth
Minimum radial clearance	0.8 mm
Axial domain / device center	100 mm / 50 mm

Operating point and modeling assumptions
Volumetric flow rate	100 mL/min (1.667 × 10⁻⁶ m³/s)
Density ρ	1060 kg/m³
Dynamic viscosity μ	0.0035 Pa·s
Flow / material model	Steady, incompressible, Newtonian, laminar
Walls / symmetry	Rigid, no slip; axisymmetric, no swirl
Production grid	161 axial × 41 radial nodes; β = 1.8

Solver-generated 161 by 41 body-fitted NS-0003 mesh

Fig. 2 · Production mesh. The structured grid conforms to the shaft, enlarged body, transitions, and vessel wall. Source ↗

Optimized candidate OPT1–001Body OD 2.100 mm; body length 11.169 mm; transitions 4.471 mm. The vessel, shaft, flow rate, fluid properties, and 161 × 41 production grid match the baseline. Select the candidate in the solution gallery to see its geometry and mesh.

02 / GOVERNING PHYSICS

Equations, boundaries, and method

The solved velocity is u = (u_z, u_r) with u_θ = 0 and no circumferential gradients. The steady incompressible cylindrical equations are:

(1) Continuity

∂u_z/∂z + (1/r) ∂(r u_r)/∂r = 0

(2) Axial momentum

ρ [u_z ∂u_z/∂z + u_r ∂u_z/∂r] = −∂p/∂z + μ [∂²u_z/∂z² + ∂²u_z/∂r² + (1/r) ∂u_z/∂r]

(3) Radial momentum

ρ [u_z ∂u_r/∂z + u_r ∂u_r/∂r] = −∂p/∂r + μ [∂²u_r/∂z² + ∂²u_r/∂r² + (1/r) ∂u_r/∂r − u_r/r²]

Volume flow and Newtonian wall shear are extracted as Q = 2π∫ u_zr dr over a cross section and |τ_w| = μ |∂u_t/∂n|_wall. The radial momentum equation includes the cylindrical vector-Laplacian term −μu_r/r².

Boundary conditions

Inlet: prescribed 100 mL/min mass flow through the annulus.
Outlet: pressure reference and outflow treatment in the coupled solver.
Device and vessel: stationary no slip and no penetration.
Azimuth: rotational symmetry; no swirl.

Numerical implementation

Body-fitted, cell-centered, conservative axisymmetric finite-volume geometry with revolved face areas and cell volumes.
Implicit axial/radial momentum predictor; first-order upwind convective fluxes and geometry-consistent wall diffusion.
Pressure correction, conservative face-flux correction, and velocity/pressure under-relaxation (0.7 / 0.2).
Iteration stops when continuity ≤ 10⁻⁹ kg/s and outer flux change ≤ 2 × 10⁻⁵; both conditions are required.

(4) Body-fitted mapping

r(z, η) = R_i(z) + [R_o − R_i(z)] S(η)

η = 0 on the solid; η = 1 at the vessel wall. Smooth C² device transitions use 6ξ⁵ − 15ξ⁴ + 10ξ³.

The repository's general numerical-method note includes historical NS–0002 development status. The method summary here follows the NS–0003 solver implementation and frozen model record at the evidence commit. Inspect NS–0003 solver ↗

03 / SOLVER OUTPUT

Computed solution fields

Switch cases to inspect their actual saved figures. Numeric comparison stays visible below. The color range is set separately in each source figure, so compare the reported values rather than color alone.

Baseline NS-0003 static pressure contour — **Fig. 3 · Static pressure [Pa].** Baseline pressure drop 846.262 Pa. Source ↗

Baseline NS-0003 velocity magnitude contour — **Fig. 4 · Velocity magnitude [m/s].** Baseline peak 0.314003 m/s. Source ↗

Baseline NS-0003 wall-shear distribution — **Fig. 5 · Wall shear stress [Pa].** Baseline device max 6.525 Pa; WSS remains mesh-qualified. Source ↗

Baseline NS-0003 solver convergence history — **Fig. 6 · Solver convergence.** Baseline: 57 outer iterations, recorded solver gate passed. Source ↗

Solver-derived engineering responses at 100 mL/min on 161 × 41 grids
Output	Baseline	OPT1–001	Change vs baseline
Static pressure drop	846.262 Pa	752.932 Pa	−11.03%
Peak velocity magnitude	0.314003 m/s	0.277215 m/s	−11.72%
Device max WSS	6.525 Pa	4.547 Pa	−30.31% · qualified
Device P95 WSS	5.909 Pa	4.473 Pa	−24.30% · qualified
Vessel max WSS	5.289 Pa	3.709 Pa	−29.86% · qualified
Solver iterations	57	56	Both converged

Percentage change = (OPT1–001 − baseline) / baseline × 100, using the stored solver results. Static pressure is gauge-dependent; pressure drop is the reported comparison quantity.

04 / NUMERICAL CREDIBILITY

Verification and mesh decision

The baseline solve passed both recorded stopping gates. Three systematically refined NS–0003 grids converged and conserved mass. The 161 × 41 mesh was frozen for dataset production because bulk pressure and velocity responses changed little against 201 × 51; wall-shear sensitivity is larger and remains qualified.

NS–0003 three-grid baseline study
Grid	Nodes	Iterations	Δp (Pa)	Peak \|u\| (m/s)	Device P95 WSS (Pa)
Coarse	121 × 31	42	841.838	0.313769	6.006
Production	161 × 41	57	846.262	0.314003	5.909
Fine reference	201 × 51	71	851.358	0.314234	5.716

MEDIUM → FINE0.599%Pressure drop

MEDIUM → FINE0.074%Peak velocity

MEDIUM → FINE3.374%Device P95 WSS

Case-specific solver gates
Gate	Acceptance	Baseline	OPT1–001
Continuity	≤ 1 × 10⁻⁹ kg/s	7.36 × 10⁻¹⁹ kg/s · pass	9.38 × 10⁻²⁰ kg/s · pass
Outer flux change	≤ 2 × 10⁻⁵	1.956 × 10⁻⁵ · pass	1.908 × 10⁻⁵ · pass
Inlet/outlet mass imbalance	Recorded with solver gate	2.17 × 10⁻¹⁹ kg/s	2.17 × 10⁻¹⁹ kg/s

The three-grid study is for the frozen baseline engine. OPT1–001 passed its own solver gate on the production grid, but a separate fine-grid study for that candidate is not recorded here. Three-grid data ↗ · Decision D-013 ↗

05 / ENGINEERING MEANING

Interpretation, scope, and limitations

The enlarged baseline body reduces the open annular area locally and accelerates flow around the device. The recorded OPT1–001 geometry has a smaller body OD and produces lower computed pressure drop, peak velocity, and wall-shear maxima at the same flow rate. This is a within-model design comparison, independently rerun with the frozen CFD solver after candidate selection.

Numerical qualification

Device P95 WSS changes 3.374% from medium to fine; wall-gradient outputs should carry that uncertainty flag. The OPT1–001 candidate has no independent three-grid study in this package.

Model boundaries

Steady, rigid-wall, incompressible Newtonian, laminar, concentric, 2D axisymmetric geometry. No pulsatility, eccentricity, 3D flow, FSI, or patient-specific anatomy is modeled.

Geometry topology

The solid is a continuous shaft with a local enlarged body. It is not a free-ended catheter tip. Separate free-ended-tip experiments remain unconverged in the latest development log.

Validation boundary

No experimental or clinical validation is reported. CFD verification establishes numerical behavior for the declared model, not medical safety, efficacy, or general-device performance.

SOURCE & REPRODUCTION

Traceable result package

Evidence was read from private repository commit 695403bf71dcac1f884dcb1fd3ba786836fbecc7 ↗ on 23 September 2026. The figures and values on this page are a static snapshot, not live results. GitHub evidence links require collaborator access.

Frozen NS–0003 model and acceptance notes ↗Baseline fields, figures, and verification JSON ↗OPT1–001 fields, figures, and verification JSON ↗Baseline execution script ↗NS–0003 coupled solver ↗Parameterized device geometry ↗

NS–0003 / CFD Physics Engine v1 · Engineering report · Snapshot 23 Sep 2026

Flow around anintravascular device.