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Scale-Resolving Simulation at Scale
Verifying the Viscous Operator with Compressible Couette Flow
- Manufacturing
- Automotive
- Energy
What This Simulation Does
The 2d-couette-flow example solves compressible Couette flow between two walls: the upper wall translates at constant speed while both walls are held isothermal. The steady velocity and temperature profiles have a closed-form solution, so the case provides a clean, exact verification of the viscous (Navier–Stokes) operator and its coupled heat-conduction term.
- Compressible Navier–Stokes with viscous stress and heat conduction; LDG viscous treatment
- Analytic solution — a linear velocity profile and a quadratic temperature profile set by the Prandtl number and wall speed
- Moving isothermal walls — driven no-slip isothermal boundary conditions that exercise both momentum and thermal wall physics
Key Parameters
- Grid: mixed triangle/quadrilateral channel mesh, polynomial order 2
- Fluid: ideal gas γ = 1.4, μ = 0.417, Pr = 0.72, cp = 1005
- Walls: wall speed Uw = 70, wall temperature Tw = 300, isothermal no-slip
- Scheme: Rusanov flux, LDG viscous (β = 0.5, τ = 0.1), explicit RK4; Δt = 4 × 10-5, tend = 4
The core transferable physics: A shear-driven flow develops coupled velocity and temperature profiles, with viscous heating balanced by wall heat conduction. Getting this right is the prerequisite for every wall-bounded thermal-fluid prediction — from lubricated bearings to cooling channels — because it verifies the solver reproduces shear stress and wall heat flux exactly.
What Makes This Capability Unique
Closed-form verification
Linear velocity and quadratic temperature profiles are known exactly, so viscous-operator and wall-heat-flux accuracy is measured, not assumed.
Coupled momentum + heat
Verifies viscous dissipation and Fourier heat conduction together — the physics behind viscous heating in bearings, seals, and cooling passages.
Mixed-element robustness
Runs on a mixed triangle/quadrilateral mesh, confirming the LDG viscous scheme is accurate on the unstructured grids used in real geometry.
Fast parametric sweeps
Change wall speed, temperature, viscosity, or Prandtl number and re-run in the browser to map viscous-heating regimes in minutes.
Domain Applications
Select a domain to see how this simulation applies, with industry-specific scenarios and ROI.
The Problem
Precision machining, polymer extrusion, and coating processes are dominated by shear-driven viscous heating in thin films. When a lubricant film, molten polymer, or coating layer is sheared between moving surfaces, viscous dissipation raises local temperature — changing viscosity, film thickness, and ultimately part quality.
- Journal and thrust bearings fail when viscous heating exceeds the lubricant's thermal limit; predicting the temperature rise requires an accurately verified viscous+thermal solver.
- Polymer extrusion quality depends on shear heating in the die; over-prediction wastes energy, under-prediction degrades the product.
Unplanned bearing and tooling failures cost discrete manufacturing an estimated $4–6B/year globally.
Applications
| Application | How this simulation maps |
|---|---|
| Lubricated bearing film | Moving-wall shear + isothermal walls map directly to a bearing gap; verified viscous heating predicts film temperature rise |
| Polymer die shear heating | Wall speed and viscosity sweeps predict melt temperature in the die and the resulting product uniformity |
| Coating / calendering nip | Shear-driven film with heat transfer to rolls; validates the coupled momentum–thermal prediction |
| Seal face thermal balance | Verifies wall heat flux used to size seal cooling and avoid thermal cracking |
Quantifiable Business Value
Scenario: A bearing manufacturer uses a verified viscous-thermal solver to set the operating envelope of a high-speed spindle bearing, replacing conservative de-rating with a right-sized thermal limit.
Right-sizing thermal limits from verified simulation typically recovers 8–15% of throughput otherwise lost to conservative de-rating.
Recommended Next Steps
Verify against the analytic profile
Run the case and compare the computed velocity and temperature fields against the closed-form solution to confirm viscous-operator accuracy.
Sweep your operating conditions
Vary wall speed, temperature, viscosity, and Prandtl number to map viscous-heating regimes for your bearing, seal, or channel.
Scale to real geometry
Carry the verified viscous settings into a 2D/3D simulation of your actual clearance or cooling passage.
Ready to Run This Simulation?
Run this example on SRS's cloud platform. No installation, no infrastructure management — just results.
For questions or to schedule a technical briefing, contact the SRS simulation team.
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