Appendix B — Notation and symbols

Symbol Meaning
\(\Omega\) Fluid domain
\(\partial\Omega\) Domain boundary
\(\mathbf u\) Velocity vector
\(p\) Pressure
\(\rho\) Fluid density
\(\mu\) Dynamic viscosity
\(\nu=\mu/\rho\) Kinematic viscosity
\(\mathbf f\) Body force per unit volume in the stated momentum equation
\(\mathbf v, q\) Velocity and pressure test functions
\(V, Q\) Continuous velocity and pressure spaces
\(V_h, Q_h\) Discrete finite-element spaces
\(h\) Characteristic mesh length
\(\Delta t\) Time increment
\(\mathrm{Re}\) Reynolds number

Convention note: Pressure, forcing, residual signs, and divergence operators may have alternate but consistent conventions in other references. State the convention before comparing block matrices.