This chapter introduces the conceptual foundations of Computational Fluid Dynamics (CFD), combining historical context, physical modeling assumptions, and the high-level workflow used in industrial CFD practice. Emphasis is placed on understanding CFD as an abstraction of physical flow problems into mathematical and numerical representations, rather than on software-specific aspects. Geometry preparation, data flow between simulation stages, and key preprocessing concepts such as shared topology are framed from a modeling and numerical-consistency perspective.

Why CFD Exists

CFD emerged from the need to analyze fluid flows that:

Are governed by highly nonlinear equations
Involve multiple spatial and temporal scales
Cannot be solved analytically except in trivial cases

The governing equations (Navier–Stokes) are universal, but:

Their solutions depend almost entirely on geometry and boundary conditions
Small modeling or setup choices can fundamentally alter results

CFD provides:

Full-field flow information (velocity, pressure, temperature, species)
Access to quantities difficult or impossible to measure experimentally
A way to explore design variations before physical prototyping

CFD as an Engineering Approximation

CFD is not an exact solution of fluid motion.

Every CFD simulation involves:

Modeling assumptions (continuum hypothesis, turbulence closure, etc.)
Numerical approximations (discretization, linearization)
Practical compromises (mesh resolution, solver settings)

A CFD result should therefore always be interpreted as:

A model-based prediction consistent with assumptions, not a ground truth.

Understanding what was assumed is as important as reading the result.

Continuum Hypothesis and Eulerian Description

CFD relies on the continuum assumption:

Fluids are treated as continuous media
Properties like velocity and pressure are defined at every point in space

This assumption breaks down only at very small scales (e.g. rarefied gases), which are outside the scope of standard CFD.

The Eulerian framework is used:

Flow variables are described at fixed locations in space
Control volumes are defined over the domain
Fluxes across control-volume boundaries govern conservation

This description is the foundation of finite-volume CFD solvers such as Fluent

Order-of-Magnitude Thinking in CFD

Before solving anything numerically, engineers implicitly perform order-of-magnitude analysis:

Which terms in the equations dominate?
Which effects are negligible?
Which physical mechanisms control the flow?

This reasoning explains why:

Inviscid models work for external aerodynamics
Turbulence modeling is essential in most internal flows
Compressibility can often be ignored, but sometimes cannot

Good CFD setup begins before meshing, with physical scaling insight.

What CFD Actually Solves

Modern CFD solvers:

Discretize conservation laws over a finite set of control volumes
Convert partial differential equations into algebraic equations
Solve these equations iteratively to obtain a field solution

Key point:

CFD does not solve “the flow”, but a discretized approximation of the governing equations on a specific mesh.

Therefore:

Mesh quality and topology are part of the mathematical model
Geometry preparation is a numerical step, not just a CAD step

High-Level CFD Workflow

Regardless of software, CFD follows the same logical chain:

Physical problem definition
Geometry abstraction
Mesh generation
Model selection (physics, turbulence, multiphase, etc.)
Boundary and initial conditions
Numerical solution
Post-processing and validation

ANSYS Workbench formalizes this chain, but the structure reflects physics-first thinking, not UI design.

Geometry Preparation as a Modeling Step

Geometry used for CFD is not CAD geometry.

Its purpose is to:

Define flow boundaries
Preserve relevant length scales
Enable high-quality meshing

Good CFD geometry:

Removes unnecessary details (fillets, bolts, logos)
Preserves flow-relevant features (edges, gaps, curvature)
Is watertight and topologically consistent

Poor geometry leads to poor meshes, regardless of solver quality

Shared Topology: Why It Matters

Shared topology ensures that:

Adjacent bodies share faces, edges, and vertices
The mesh is conformal across interfaces

Physically, this means:

Fluxes are exchanged consistently across material or fluid interfaces
No artificial numerical gaps or overlaps exist

Numerically, shared topology:

Eliminates interpolation errors at interfaces
Improves conservation
Is essential for multiphase, conjugate heat transfer, and FSI problems

In CFD terms:

Shared topology is a numerical continuity condition, not a CAD convenience

Multi-Body Geometry and CFD Domains

Many CFD problems involve:

Fluids interacting with solids
Internal volumes embedded in larger domains
Multiple regions with different physics

Treating these as a multi-body system with shared topology allows:

Correct interface treatment
Unified meshing strategies
Consistent data transfer between regions

This becomes critical later for:

Conjugate heat transfer
Multiphase flows
Fluid–structure interaction

Data Flow Between Simulation Stages

A key CFD principle emphasized in this chapter is data dependency:

Downstream stages depend on upstream definitions
Changing geometry invalidates mesh
Changing mesh invalidates solution

Workbench visualizes this dependency, but conceptually:

CFD is a causal pipeline, not a collection of independent steps.

Understanding this avoids many common beginner errors.

CFD as Part of the Engineering Design Loop

CFD is most powerful when used:

Early in design
Iteratively
In combination with engineering judgment

It complements experiments by:

Reducing test iterations
Guiding design changes
Explaining why a design behaves as observed

CFD should not replace experiments blindly, but it can drastically reduce development cost when used correctly.

Engineering Intuition

CFD accuracy is limited more by modeling choices than solver sophistication
Geometry preparation is part of the numerical model
Shared topology ensures physical and numerical continuity
Mesh quality is as important as turbulence modeling
CFD results must always be interpreted through assumptions

A useful mindset:

Treat every CFD simulation as a hypothesis about the flow, not a fact.

Study Priorities

If short on time, focus on:

CFD as an approximation of Navier–Stokes
Continuum and Eulerian assumptions
Role of order-of-magnitude reasoning
Conceptual CFD workflow
Purpose of shared topology
Geometry as a numerical abstraction

Key Takeaways

CFD solves discretized conservation laws, not “the real flow”.
Physical assumptions precede numerical choices.
Geometry preparation is a modeling step.
Shared topology enables conservative, conformal meshes.
Workflow structure reflects physics dependencies.
Good CFD begins with thinking, not clicking.

Introduction to CFD Chapter 1: Background and workflow