---
title: "Solver setup, convergence, grid independence"
subject: "Applied Computational Fluid Dynamics"
chapter: 4
key: "semester_7/applied_computational_fluid_dynamics:solver-setup-convergence-grid-independence"
source: https://www.bctengineer.com/q/semester_7/applied_computational_fluid_dynamics/solver-setup-convergence-grid-independence
site: BCT Engineering
---

# Solver setup, convergence, grid independence

Applied Computational Fluid Dynamics · Chapter 4: Mesh Generation and Solver Setup

- Asked in: year not given, 5 marks
- Video: [Grid Independence Study | Mesh Sensitivity Analysis in CFD | Mesh Convergence| Ansys Fluent Tutorial](https://www.youtube.com/watch?v=3xJHutLBskM) — MECH Tech Simulations
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/applied_computational_fluid_dynamics/solver-setup-convergence-grid-independence
- Whole chapter: https://www.bctengineer.com/md/semester_7/applied_computational_fluid_dynamics/chapter-4

## Question

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.

## 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.

## Answer

#### 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-$\varepsilon$, k-$\omega$ 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 ($10^{-3}$ continuity/momentum, $10^{-6}$ 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 $r\ge1.3$.
2. Solve each with identical settings and compare a key output (e.g. pressure drop or $C_D$).
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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For steady incompressible flow, which solver and coupling are typically chosen?
   A. Density-based solver with PISO
   B. Pressure-based solver with SIMPLE or SIMPLEC and under-relaxation
   C. Density-based solver with no under-relaxation
   D. Pressure-based solver with no coupling algorithm
   Answer: B. Pressure-based solvers suit incompressible/low Mach flow; SIMPLE-type coupling with under-relaxation is used for steady cases. (Key point: Solver choice)

2. Why are residuals alone not enough to declare convergence?
   A. Residuals are never meaningful
   B. Low residuals do not guarantee that monitored quantities are steady or that global mass and energy balances close
   C. Residuals only apply to transient problems
   D. Convergence requires residuals to reach exactly zero
   Answer: B. One should also check that monitors (drag, pressure drop) are steady and that mass flow in equals out within about 0.1 to 1%. (Key point: Judging convergence)

3. How is a grid independence study carried out?
   A. Run one fine mesh and trust it
   B. Use at least three meshes with a uniform refinement ratio and compare a key output; accept when the change is small (1 to 2%)
   C. Change the turbulence model between meshes
   D. Refine until residuals reach 10^-12
   Answer: B. Coarse, medium and fine meshes with identical settings are compared; when the last two agree within about 1 to 2%, the solution is grid independent. (Key point: Grid independence procedure)

## Related in Applied Computational Fluid Dynamics

- [Steps of a CFD analysis](https://www.bctengineer.com/question.md?key=semester_7%2Fapplied_computational_fluid_dynamics%3Acfd-solution-procedure) — Applied Computational Fluid Dynamics, chapter 1
- [Streamline and acceleration of a flow field](https://www.bctengineer.com/question.md?key=semester_7%2Fapplied_computational_fluid_dynamics%3Astreamline-acceleration-numerical) — Applied Computational Fluid Dynamics, chapter 1
- [Plane Poiseuille flow from Navier-Stokes](https://www.bctengineer.com/question.md?key=semester_7%2Fapplied_computational_fluid_dynamics%3Aplane-poiseuille-flow-numerical) — Applied Computational Fluid Dynamics, chapter 2

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