# Source-to-equation ledger

This ledger separates inviscid geometry, finite-Re closure, and viscous stability.

- Crowdy (2006), *Analytical solutions for uniform potential flow past multiple cylinders*: exact multiply connected circular-domain uniform-flow construction. Reuse: independent reference for impermeability, circulation periods and far field; it does not impose no slip or predict separation.
- Crowdy & Marshall (2007), *Green's functions for Laplace's equation in multiply connected domains*: Schottky–Klein Green-function machinery. Reuse: exact/reference formulation for circular multiply connected domains.
- Kharlamov & Filip (2012), generalized method of images for several moving parallel cylinders. Reuse: iterative image cross-check and convergence logic.
- Chan, Jameson & Smits (2011), *Vortex suppression and drag reduction in the wake of counter-rotating cylinders*: viscous doublet-like/reverse-doublet topologies and virtual-body mechanism. Reuse: mechanism observables, not a sign oracle for this code.
- Mittal (2001), *Control of flow past bluff bodies using rotating control cylinders*: steady-wake suppression near tip-speed ratio five in a different geometry. Reuse: prior for search scale only, never a fixed optimum.
- Watson (1996), *Slow viscous flow past two rotating cylinders*: matched/Oseen rotating-cylinder precedent. Reuse: conceptual finite-Re interface; regime and geometry differ.
- Deng et al. (2018), fluidic-pinball bifurcations; Sierra et al. (2020), rotating-cylinder bifurcations. Reuse: require continuation/perturbation and do not assume unique symmetric steady state.
- Marquet, Sipp & Jacquin (2008): global sensitivity of cylinder flow. Reuse: independent viscous base-flow/eigenvalue workflow after empirical stability.

## Equations and claim limits

The outer field is `u = U_inf e_x + sum_j grad[Q_j log|z-z_j|/(2pi)] + sum_k Gamma_k e_theta/(2pi r)` with source strengths chosen to satisfy cylinder no penetration and zero net source per body. In a strip, scalar sources use equal-sign reflections and vortices opposite-sign reflections at free-slip walls. Truncation, source radius, collocation order, precision, boundary residual, wall residual and an independent exact/image formulation must be reported.

`Gamma_k` is prescribed in the inviscid problem. Mapping wall rotation to an effective circulation is a finite-Re empirical interface requiring contour plateaus and held-out outer profiles; it is not `Gamma=2pi R^2 omega` by assumption. Potential flow cannot predict viscous separation, drag, base pressure, or global stability.
