--- title: Physical validation summary: A canonical viscous flow — the steady wake of a circular cylinder at Reynolds number 40 — is compared with the literature as a plausibility check on the physics, boundary conditions and force evaluation. section: verification order: 12 level: 2 study: cylinder_re40 keywords: [validation, cylinder, drag, laminar] --- **Verification status: Laminar cylinder at Re = 40** (study `cylinder_re40`): **PASSED**, 7 of 7 checks passed, 417.2 s. Steady separated flow past a circular cylinder at Reynolds number 40 (based on diameter) and Mach 0.2 on a 24 x 10 curved O-mesh extending 40 diameters. The drag coefficient is compared with the incompressible literature value of about 1.5 (e.g. 1.52 in Dennis & Chang 1970, 1.50 in Fornberg 1980); small differences are expected from compressibility and the finite domain. This is a plausibility check against physics, complementing the exact verification studies. The numerical energy flux through the adiabatic wall is zero by construction (its viscous part is masked out) and is therefore not checked; instead the conductive flux that the converged solution carries at the wall when the mask is lifted, which is zero for the exact solution, is required to decrease with the polynomial degree. | Check | Value | Expected | Result | |---|---|---|---| | p = 2: converged | yes | true | pass | | p = 2: symmetric wake, \|cl\| | 3.3453e-14 | < 1e-6 | pass | | p = 3: converged | yes | true | pass | | p = 3: symmetric wake, \|cl\| | 1.7153e-14 | < 1e-6 | pass | | drag coefficient (highest order) | 1.53727 | 1.45 … 1.65 | pass | | drag change between the two highest orders (rel.) | 0.00149973 | < 0.02 | pass | | wall heat conduction of the solution with the adiabatic mask lifted: p = 3 relative to p = 2 | 0.405582 | < 1 (vanishes for the exact solution: must decrease under p-refinement) | pass | Provenance: gyre 0.4.0; revision `39979fcf90` (commit `39979fcf902ad6116eb550b881b4278d4599c8e2`); 2026-11-12T11:25:40-0500; device cpu; quick suite. **Revision check: Same code as this build.** Produced by 39979fcf902ad6116eb550b881b4278d4599c8e2. Every commit between it and the commit this site was built from (ceb1f4b0bed41de53e586df10858079f5a2bcdd8) changes only documentation text, evidence records or bookkeeping: the code is the same. Full record: [cylinder_re40.json](../data/verification/cylinder_re40.json). **Table: Drag by polynomial degree** (Laminar cylinder at Re = 40) | p | DOF | converged | cd | cl | wall heat conduction with the mask lifted (∫\|q_n\| dS) | |---|---|---|---|---|---| | 2 | 8640 | yes | 1.53957 | -3.3453e-14 | 0.0653139 | | 3 | 15360 | yes | 1.53727 | -1.7153e-14 | 0.0264902 | | reference | — | — | 1.52 | 0 | 0 | Provenance: gyre 0.4.0; revision `39979fcf90` (commit `39979fcf902ad6116eb550b881b4278d4599c8e2`); 2026-11-12T11:25:40-0500; device cpu; quick suite. **Revision check: Same code as this build.** Produced by 39979fcf902ad6116eb550b881b4278d4599c8e2. Every commit between it and the commit this site was built from (ceb1f4b0bed41de53e586df10858079f5a2bcdd8) changes only documentation text, evidence records or bookkeeping: the code is the same. Full record: [cylinder_re40.json](../data/verification/cylinder_re40.json). **[L2 Practice] What is compared** At $Re_D = 40$ the flow past a cylinder is steady with a closed recirculation bubble. Its drag coefficient is about 1.5 in the incompressible limit (for example 1.52 in the computations of Dennis and Chang, 1970, and 1.50 in Fornberg, 1980). Gyre computes the flow at Mach 0.2 on a 24 × 10 curved O-mesh extending 40 diameters; small differences from the incompressible values are expected from compressibility and the finite domain, so the check accepts 1.45–1.65. **[L3 Mechanics] What else the study asserts** * the lift coefficient is zero to solver tolerance (the steady wake is symmetric); * the conduction that the converged solution carries at the adiabatic wall decreases from the second-highest to the highest polynomial degree. The numerical energy flux through the wall is zero by construction (the energy row of the viscous boundary flux is masked) for any state, so it is not checked; the quantity checked is the conductive flux with the mask lifted, which vanishes for the exact solution. Its value per degree is in the table; * the drag changes by less than 2 % between the two highest polynomial degrees. This is a plausibility check, not a validation campaign: one flow, one quantity. Its role is to catch gross errors in the physical model that exact verification cannot see — a wrong sign in the stress tensor satisfies every conservation test.