This chapter focuses on numerical performance, accuracy, and reliability in CFD simulations. It introduces the main sources of error in CFD, explains how numerical and modeling decisions affect engineering results, and outlines best practices for achieving trustworthy simulations under realistic time and resource constraints. The chapter also places CFD within an industrial validation framework and briefly connects the fundamentals module to advanced CFD topics

CFD as an Engineering Compromise

CFD simulations are performed under fixed constraints:

Limited computational resources
Limited project timelines
Incomplete knowledge of real operating conditions

As a result, CFD outcomes are always approximations of reality. Engineering practice accepts this limitation and focuses on controlling and understanding errors, rather than eliminating them entirely.

The goal is to obtain engineering-relevant quantities with sufficient accuracy to support decisions.

Quantities of Interest and Engineering Accuracy

Not all flow variables matter equally.

In practice:

Extensive quantities (forces, moments, mass flow rates, heat transfer rates) often dominate design decisions
Intensive quantities (local pressure, velocity, temperature) become critical when failure mechanisms depend on extrema, such as cavitation or material limits

Local numerical errors may be acceptable if integrated quantities converge reliably. This perspective strongly influences meshing, modeling, and convergence strategies

Sources of Error in CFD

CFD error arises from several distinct contributions, each with different origins and mitigation strategies.

Modeling Error

Modeling error reflects simplifications introduced to represent reality:

Turbulence models
Combustion, radiation, or multiphase closures
Simplified material properties
Idealized boundary conditions

Modeling error typically dominates industrial simulations and cannot be eliminated through mesh refinement alone. Understanding model assumptions is therefore essential.

Discretization Error

Discretization error arises from representing continuous equations on a finite mesh.

Key characteristics:

Decreases with mesh refinement
Depends on discretization order
Influenced by mesh quality and flow gradients

Mesh refinement studies aim to reach a regime where further refinement produces negligible changes in the quantities of interest.

Iterative Error

Iterative error reflects the difference between:

The exact solution of the discretized equations
The current iterative solution

Residual reduction alone is insufficient. Monitoring convergence of engineering quantities is essential to confirm iterative adequacy.

Round-Off and Numerical Precision

Round-off errors stem from finite numerical precision.

They become relevant in cases involving:

Extremely high aspect ratio meshes
Very large scale separations
Large variable ranges

Double-precision arithmetic usually mitigates these effects in modern CFD workflows

Convergence from an Engineering Perspective

Convergence should be assessed through multiple lenses:

Residual reduction trends
Stabilization of quantities of interest
Conservation of mass, momentum, and energy

Monotonic residual convergence is desirable but not always achievable in complex flows. Engineering convergence focuses on solution stability and physical consistency, not numerical perfection.

Mesh Strategy and Grid Independence

Good mesh quality does not guarantee low discretization error.

Key principles:

Gradients must be resolved where physics demands it
Refinement should target regions controlling quantities of interest
Global mesh density alone is insufficient

Grid independence studies compare solutions on progressively refined meshes until changes in key outputs become negligible.

Best Practices for Industrial CFD

Successful CFD workflows emphasize robustness and traceability:

Start with conservative numerical settings
Increase accuracy gradually
Validate intermediate results
Document assumptions clearly

CFD credibility depends as much on process discipline as on solver capability.

Customization and Solver Extension (Conceptual)

CFD solvers provide general-purpose capabilities, but advanced applications may require customization.

Customization enables:

Problem-specific boundary conditions
Custom source terms
Specialized material behavior
Tailored post-processing

While powerful, customization increases responsibility and validation requirements. It should be used only when standard models cannot represent the required physics adequately

Verification and Validation

Verification and validation address two complementary questions:

Verification

Ensures that the numerical implementation solves the chosen equations correctly.

Validation

Assesses whether the chosen equations and models represent physical reality accurately.

Validation relies on:

Analytical benchmarks
Experimental data
Well-documented reference cases

Agreement with experiments increases confidence but does not eliminate uncertainty.

CFD in Industrial Context

CFD is widely used across industries because it:

Reduces reliance on physical prototypes
Enables early design exploration
Supports “what-if” analyses
Integrates naturally into digital engineering workflows

Its effectiveness depends on informed usage and realistic expectations.

Connection to Advanced CFD Modules

This chapter bridges foundational CFD to advanced topics:

Turbulence modeling
Multiphase flows
Heat transfer
Combustion
Turbomachinery
Fluid–structure interaction
Optimization

Each advanced module builds directly on the numerical and methodological principles established here

Engineering Intuition

CFD accuracy is purpose-driven, not absolute
Modeling choices dominate error budgets
Mesh refinement supports, but does not replace, physical insight
Convergence must be interpreted through engineering outputs
Validation strengthens confidence, not certainty

A reliable CFD engineer understands both what the solver computes and why the result can be trusted.

Study Priorities

If short on time, focus on:

Error categories and their origins
Quantities of interest vs local accuracy
Discretization and mesh independence
Engineering interpretation of convergence
Verification vs validation
Role of CFD in industrial decision-making

Key Takeaways

CFD results are approximations shaped by modeling, discretization, and iteration.
Engineering relevance guides acceptable accuracy.
Mesh and solver settings must support quantities of interest.
Validation strengthens credibility but does not eliminate uncertainty.
CFD performance depends on methodology as much as software.

Introduction to CFD Chapter 7: Numerical performance and reliability