Advection Term

The advection term in the Euler equations represents the effect of flow position change over time. Also known as the "convective rate of change," it is a crucial aspect of the Navier-Stokes equations, impacting pressure, viscosity, and external forces.

Boundary Conditions

Boundary conditions define the limits of a simulation, such as walls or free surfaces, crucial for accurate CFD modeling.

Computational Buckets

Buckets reduce computational costs in particle simulations by dividing the domain into subdomains, facilitating efficient neighboring particle searches.


Compilers translate programming code into executable files. Popular compilers in CFD include Visual Studio, gcc, Intel Compiler, and Xcode.

Conjugate Gradient Method

An iterative solver for simultaneous equations, essential for handling large, sparse matrices in CFD simulations.

Conservation of Mass

Expressed by the equation of continuity, this fundamental principle ensures mass conservation in fluid simulations.

Courant Number

A dimensionless number, crucial in explicit methods, defined as 𝑐=𝑢Δ𝑡/Δ𝑥c=uΔt/Δx, where 𝑢u is the maximum fluid velocity.

CSF Model

The Continuum Surface Force (CSF) model, introduced by Brackbill et al. (1992), models surface tension in computational fluid dynamics.

Dummy Wall Particles

Used behind wall particles, dummy wall particles assist in calculating fluid or wall particle densities but are excluded from pressure calculations.

Differential Operators

Operators like nabla (∇) and Laplacians (∇²) are fundamental in expressing fluid behavior mathematically.

Diffusion Equation and Number

The diffusion equation describes diffusive phenomena, while the dimensionless diffusion number 𝐷=𝜈Δ𝑡/(Δ𝑥)2D=νΔt/(Δx)2 is key for ensuring stability in simulations.

Dirichlet and Neumann Boundary Conditions

These conditions specify fixed values or derivatives at boundaries, essential for solving differential equations in CFD.


Dividing space or time into small segments, discretization is fundamental for translating continuous functions into computable forms.


A mathematical operator (∇∙) used to describe fluid flow properties.

Euler Description

A method for describing physical quantities using fixed spatial positions, contrasted with Lagrangian descriptions that follow the substance's movement.

External Forces

Forces originating outside the fluid system, like gravity, significantly influence fluid dynamics.

Fluid Properties

Key properties like fluid density and viscosity define the behavior and simulation of fluids in CFD.

Fractional Step Method

A time integration scheme that solves differential equations step-by-step, enhancing accuracy.

Free Surface Dynamics

The behavior of fluid boundaries, such as liquid-air interfaces, which are critical in many CFD applications.

Gaussian Elimination

A direct method for solving simultaneous equations, important for non-iterative approaches in CFD.

Governing Equations

Fundamental equations like the Navier-Stokes equations govern fluid behavior and are central to CFD simulations.

Gradient Models

These models calculate gradients (∇) on computers, essential for representing fluid flow changes.

Implicit and Explicit Methods

Numerical methods for solving fluid dynamics problems, where implicit methods handle unknown future values, and explicit methods use known values at each time step.

Initial Particle Spacing

Defines the regular intervals at which particles are initially placed in simulations, impacting resolution.

Kernel Functions in SPH

Essential in Smoothed Particle Hydrodynamics (SPH), kernel functions approximate interactions between particles.

Laplacian Models

Numerical models that discretize the Laplacian operator (∇²) for computational purposes.

Marching Cubes and Metaball Visualization

Techniques for visualizing fluid simulations, with marching cubes representing density contours and metaballs displaying free surfaces.

Mesh-Based and Particle Methods

Simulation methods where mesh-based methods use discretized space, and particle methods like MPS move calculation points called particles.

MPI and OpenMP

Libraries for parallel computing, critical for large-scale CFD simulations, with MPI for distributed memory and OpenMP for shared-memory systems.

Navier-Stokes Equations

Central to CFD, these equations describe fluid motion by relating forces and acceleration.


Processes for adjusting values to ensure consistency in calculations, crucial for stable simulations.

Poisson Equation

A partial differential equation used in pressure calculations, expressed as ∇²P = b.

Pressure and Viscosity Terms

Key components of the Navier-Stokes equations, these terms describe the effects of pressure and viscosity on fluid motion.

Semi-Implicit Methods

Combining explicit and implicit procedures, these methods balance computational efficiency and accuracy.

Sloshing Dynamics

The periodic movement of fluid surfaces, often studied in contexts like partially filled tanks during earthquakes.

Turbulent Flow

Characterized by irregular disturbances, turbulent flow involves complex interactions that enhance momentum and heat transfer.

V&V (Verification and Validation)

Processes ensuring simulation accuracy by comparing results with analytical solutions or experimental data.

Visualization Techniques

Methods for graphically representing CFD data, essential for analyzing and communicating simulation results.

Water Column Collapse

Often termed a dam break, this phenomenon involves a stationary water column collapsing under gravity, a critical test case in fluid dynamics.