🟦 2D Lid-Driven Cavity Flow (Ghia Benchmark)

Calculate square lid-driven cavity Reynolds number, primary vortex center coordinates (xv, yv), secondary corner eddies, and wall boundary layer thickness (Ghia benchmark).

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

2D Lid-Driven Cavity Flow (Ghia Benchmark)

Cfd

📊 Solver Telemetry ● ACTIVE

👁️ Views 16

⚡ Solves 13

💾 Downloads 358 📦 Fortran Code 4.4 KB

📅 Released Jun 2026

⏱️ Latency < 1 ms

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🟦 2D Lid-Driven Square Cavity & Multi-Eddy Streamlines

Real-time visual simulation of top moving lid, primary central vortex & corner recirculating eddies

📝 Configuration & Presets

🔬 Benchmark Re = 100 ⭐ Classic Ghia Re = 1,000 🌪️ Multi-Eddy Re = 5,000 💧 Viscous Microcavity

📐 Cavity Geometry & Lid Velocity

Cavity Side Length L [mm]:

Top Lid Velocity U_lid [m/s]:

💧 Fluid Physical Properties

Kinematic Viscosity ν [cSt]: Water: 1.0 cSt, Air: 15.0 cSt

Fluid Density ρ [kg/m³]:

Ghia Benchmark Formulations:
• Cavity Reynolds: Re = (U_lid · L) / ν
• Primary Vortex Core: (x_v/L, y_v/L) migrating toward (0.50, 0.50) as Re → ∞
• Wall Boundary Layer: δ_wall ≈ L / √Re [mm]
• Lid Shear Drag: F_drag ≈ ρ ν U_lid (L / δ_wall) [N/m]

📊 Cavity Flow Results

📊 Output Summary
💾 Fortran Source

Cavity Reynolds Number (Re)

Re = 1,000

Regime: Top-Left Tertiary Eddy Formation

Core: (0.531, 0.565)

Primary Vortex Center (x_v, y_v) (53.1 mm, 56.5 mm) Normalized: (0.531 L, 0.565 L)

Minimum Streamfunction (ψ_min) -0.1200 Ghia benchmark correlation

Bottom-Right Corner Eddy Size 37.0 mm Bottom-Left: 27.0 mm

Wall Boundary Layer (δ_wall) 3.16 mm Top Lid Drag: 0.0003 N/m

📈 Primary Vortex Vertical Center y_v/L vs Reynolds Number

📉 Wall Boundary Layer Thickness δ (mm) vs Reynolds

=================================================================
 THERMOFLUIDCALC — 2D LID-DRIVEN CAVITY BENCHMARK REPORT
=================================================================
Case Title                 : Classic Ghia Reference Benchmark (Re = 1,000)
Cavity Dimensions          : 100.00 mm x 100.00 mm
Top Lid Velocity           : 0.0100 m/s
Fluid Properties           : nu = 1.00 cSt, rho = 998.0 kg/m3
-----------------------------------------------------------------
REYNOLDS NUMBER (Re)       : 1,000.0
Flow Regime                : Top-Left Tertiary Eddy Formation
Primary Vortex Core Center : (x = 0.5310 L, y = 0.5650 L) -> (53.10 mm, 56.50 mm)
Minimum Streamfunction psi : -0.1200 (dimensionless)
Secondary Corner Eddies    : BR = 37.00 mm (0.370 L), BL = 27.00 mm (0.270 L)
Wall Boundary Layer Thick  : 3.162 mm
=================================================================

📘 Calculation Methodology & Ghia Benchmark Standards

Ghia et al. Reference Benchmark

The 2D incompressible Navier-Stokes square cavity driven by a tangential moving top wall is the universal gold standard for CFD solver validation:

                    Re = (Ulid · L) / ν
                

Vortex Core Migration Dynamics

At low $Re = 100$, the primary vortex is centered high at $(0.62, 0.73)$. As inertial convection dominates at $Re \ge 1000$, the vortex core shifts downward toward the geometric center $(0.51, 0.53)$.

Key Engineering Assumptions

2D planar incompressible laminar Navier-Stokes equations.
No-slip boundary conditions on left, right, bottom, and moving top lid.
Regularized corner singularities.

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