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Solver setup, convergence, grid independence

Short answer

Setup: choose pressure-based solver, turbulence model, materials, boundary conditions, second-order discretisation, and SIMPLE coupling with under-relaxation. Convergence is judged by residuals dropping 3-4 orders, steady monitors (drag, pressure drop), and mass balance error <1%. Grid independence: solve on three systematically refined meshes; when a key output changes <1-2%, the coarser mesh is sufficient.

Describe the main steps in setting up a CFD solver for a steady incompressible flow. Explain how convergence is judged and how a grid independence study is carried out.

Solver setup

  1. Select the solver type: pressure-based (incompressible and low Mach) or density-based (high-speed compressible); steady or transient.
  2. Choose the physics: laminar or turbulence model (e.g. k-ε\varepsilon, k-ω\omega SST), energy equation on/off, gravity, other models.
  3. Materials: density, viscosity, specific heat, conductivity.
  4. Boundary conditions: velocity inlet (with turbulence intensity and length scale), pressure outlet, no-slip wall, symmetry, periodic.
  5. Discretisation schemes: first-order upwind to start, then second-order upwind or QUICK for accuracy; gradients by least squares or Green-Gauss; pressure scheme (PRESTO or second order).
  6. Pressure-velocity coupling: SIMPLE, SIMPLEC or PISO (transient); set under-relaxation factors (e.g. 0.3 for pressure and 0.7 for momentum).
  7. Initialise the field (from inlet values or hybrid initialisation) and run.

Convergence criteria

  • Residuals (imbalance of each discretised equation) normalised; typically fall by three to four orders of magnitude (10−310^{-3} continuity/momentum, 10−610^{-6} energy).
  • Monitors of quantities of interest (drag, pressure drop, outlet temperature) become steady.
  • Global balances: mass flow in equals mass flow out (error below 0.1 to 1%); energy balance closes. Low residuals alone are not proof, so the monitored values must be checked.

Grid independence study

  1. Create at least three meshes (coarse, medium, fine) with a uniform refinement ratio r≥1.3r\ge1.3.
  2. Solve each with identical settings and compare a key output (e.g. pressure drop or CDC_D).
  3. When the change between the last two meshes is small (say below 1 to 2%), the solution is considered grid independent; use the coarser of these two.
  4. Optionally apply Richardson extrapolation and the Grid Convergence Index (GCI) to estimate the discretisation error.

Finally, validate the results against experimental or analytical data.

✓ Answer checked by Claude Opus 5.5 (high effort)

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