This page is currently under development. Content may be incomplete or contain inaccuracies. If you notice any errors or have suggestions, please contact us.
Simulation & Modeling Glossary
This glossary provides definitions for common terms used in computational simulation, numerical modeling, and related data management.
Numerical Methods
Finite Element Method (FEM / FEA)
A numerical technique that divides a domain into small elements and solves governing equations (e.g., elasticity, heat transfer) approximately on each element, then assembles a global solution.
Finite Volume Method (FVM)
A numerical method that divides the domain into control volumes and ensures conservation of quantities (mass, momentum, energy) across each volume. The basis of most CFD solvers.
Finite Difference Method (FDM)
A numerical method that approximates derivatives using differences between values at discrete grid points. Simple but limited to structured grids.
Navier-Stokes Equations
The fundamental partial differential equations describing the motion of viscous fluids. Solving these equations (in simplified or full form) is the core of CFD.
PDE (Partial Differential Equation)
A differential equation involving partial derivatives of an unknown function with respect to multiple independent variables. Most physics-based simulations solve PDEs.
Mesh and Discretization
Mesh (Grid)
A discretization of the computational domain into small cells (finite volumes) or elements (finite elements) on which equations are solved.
Structured Mesh
A mesh with regular connectivity (each interior cell has the same number of neighbors), typically using hexahedral or quadrilateral cells. Efficient but limited to simple geometries.
Unstructured Mesh
A mesh with irregular connectivity, typically using tetrahedral or polyhedral cells. Flexible for complex geometries but less computationally efficient.
Mesh Convergence (Grid Independence)
The process of demonstrating that simulation results do not change significantly when the mesh is refined. Essential for credible results.
Adaptive Mesh Refinement (AMR)
A technique that dynamically refines (or coarsens) the mesh during simulation in regions where higher (or lower) resolution is needed.
Boundary Layer Mesh
A region of refined, thin cells near walls to resolve the steep gradients in velocity and temperature that occur in boundary layers.
y+ (y-plus)
A dimensionless wall distance used to determine whether the near-wall mesh resolution is appropriate for the chosen turbulence model.
CFD-Specific Terms
Turbulence
Chaotic, irregular fluid motion characterized by eddies, vortices, and rapid fluctuations. Most engineering flows are turbulent.
RANS (Reynolds-Averaged Navier-Stokes)
A turbulence modeling approach that solves time-averaged equations with turbulence models (e.g., k-ε, k-ω SST) to close the system.
LES (Large Eddy Simulation)
A turbulence approach that directly resolves large-scale eddies and models only the smallest scales. More accurate than RANS but 10-100x more expensive.
DNS (Direct Numerical Simulation)
Solving the Navier-Stokes equations without any turbulence modeling, resolving all scales of motion. Extremely expensive; limited to low Reynolds numbers and research.
CFL Number (Courant-Friedrichs-Lewy)
A dimensionless number relating time step size, cell size, and flow velocity. Must be below a threshold (typically 1) for stability in explicit time-stepping schemes.
Residual
A measure of how well the discrete equations are satisfied at a given iteration. Decreasing residuals indicate convergence toward a solution.
Under-Relaxation
A technique that limits the change in a variable between iterations to improve solver stability, at the cost of slower convergence.
FEA-Specific Terms
Degrees of Freedom (DOF)
The number of independent values that can vary in the system. In structural FEA, each node typically has 3 translational and 3 rotational DOF.
Von Mises Stress
A scalar stress measure derived from the stress tensor that predicts yielding in ductile materials under complex loading.
Eigenvalue / Natural Frequency
In modal analysis, the eigenvalues of the structural system correspond to the squares of the natural frequencies at which the structure vibrates.
Mode Shape
The characteristic deformation pattern of a structure at a natural frequency.
Contact
The interaction between surfaces of different bodies that come into contact during deformation. Adds significant nonlinearity to the analysis.
Stress Singularity
A point where stress theoretically approaches infinity (e.g., sharp re-entrant corner). An artifact of the mathematical model, not physical reality.
General Simulation Terms
Steady-State
A solution that does not change with time. The system has reached equilibrium.
Transient (Unsteady)
A time-dependent simulation where the solution evolves over time.
Boundary Condition
A constraint applied at the boundary of the computational domain (e.g., fixed wall, inlet velocity, prescribed temperature).
Initial Condition
The state of the system at the start of a transient simulation.
Convergence
The process by which an iterative solver approaches the solution. A simulation has converged when residuals are sufficiently small and monitored quantities have stabilized.
Validation
Comparing simulation results against experimental measurements to assess accuracy.
Verification
Confirming that the numerical implementation correctly solves the mathematical model (code correctness), typically against analytical or benchmark solutions.
Checkpoint / Restart File
A saved state of the simulation at a specific time, allowing the simulation to be resumed if interrupted.
Post-Processing
The extraction, visualization, and analysis of results after a simulation has completed.
HPC (High-Performance Computing)
The use of parallel computing resources (clusters, supercomputers) to run large-scale simulations.
MPI (Message Passing Interface)
A standard for parallel computing that allows processes running on different nodes to communicate. Used by most simulation solvers for parallel execution.
Need clarification on a term? Contact us at rdhub@mdsi.tum.de or explore our Use Cases for practical examples.