Verification Database

Primary Verification type

Database reference

Topic / Application

Physics

Short description

Analytical Solutions

ANA-1

Sod’s Shock Tube

Laminar Premixed Flame

DNS

LES

Compressible reactive flows. Combustion

Detonations

Supersonic

Extensive case verification of a highly accurate solver with applications in compressible flows with combustion

Analytical Solution

ANA-2

Hydrogen LES

Detonation

Authors use LES to simulate hydrogen-air detonation. The solution is verified against a simplified /analytical model (ZND)

Analytical Solution

ANA-3

Discretisation scale

Length Scale

Laminar Premixed Hydrogen-Air Flames

The Paper identifies the spatial discretization required to capture all detailed continuum physics in the reaction zone for one-dimensional steady laminar premixed hydrogen-air flames

Analytical Solution

ANA-4

Analytical Solutions

Manufactured Solutions

Numerical Solutions

Validation

Compartment Fires

Taylor Green Vortices

Beltrami Flows

Laminar Flow around circular obstacle

This paper contains a comprehensive set of references for analytical solutions to flowfields of relevance to fires and internal flows. MMS and Numerical solutions are also used on more complex flows

Analytical Solution

ANA-5

Analytical Solutions (1-D semi exact)

Manufactured Solutions

Compressible flows

Sedov blast wave Problem

Riemann Problem

Taylor Green Vortices

Verification results for a three-dimensional unstructured finite element method have been presented. Accuracy and convergence measurements were given for both shock-dominated and smooth flows

Analytical Solution

ANA-6

AIAA verification test cases

Expansion fan

oblique shock

incompressible boundary layer flow

Coquette Thermal Flow

Detonation wave

Burgers Equation

Paper presents a collection of fluid mechanics problems with exact solutions

Analytical Solution

ANA-7

Jet releases

Laminar Flow

Jet Flows

Analytical Solution for Laminar Two-Dimensional Jet

Analytical Solution

ANA-8

Combustion

1-D

Combustion

Flame Front Propagation

This provides an analytical solution to solving the 1-D flame propagation speed in 1-D

Analytical Solution

ANA-9

Analytical solution

Combustion

Heat of reaction

Flame temperature

This solves the energy equation for a hydrogen-air mixture to calculate the flame temperature

Analytical Solution

ANA-10

Analytical Solution

Navier-Stokes Equations

This test case exercises the terms in the Navier-Stokes equations

Code Verification

CV-1

Code Verification

Mass balance

Continuity Equation

A simple procedure for determining mass balance errors in H2 release simulations

Code Verification

CV-2

Code Verification

Energy balance

Energy Equation

Verifying that the basic FDS algorithm is energy conserving

Code Verification

CV-3

Code verification

Numerical Diffusion

Flux terms.

This test case demonstrates the qualitative behaviour of the Superbee flux limiter scheme for transport of a square wave

Code Verification

CV-4

Code verification

Structured Grids

Unstructured Grids

Numerical Diffusion

Flux terms.

This set of verification tests explore numerical diffusion in OpenFoam operators on various grids (structured and unstructured)

Manufactured Solutions

MAN-1

Manufactured Solution

Numerical Solutions

Error Norms

Grid Convergence Study

Steady

Laminar

Incompressible

The Method of Manufactured Solutions is applied to the quantitative verification of a code. A highly accurate numerical solution is also used for verification

Manufactured Solutions

MAN-2

Manufactured Solution

Order of convergence

Discontinuities

Shocks

Turbulent flow

This review study explains the state of the art for verification, focussing on MMS techniques. Recent advances in MMS applied to flows with discontinuities are explained

Manufactured Solutions

MAN-3

Code Verification

Manufactured Solutions

Procedures

Incompressible Navier Stokes

Burgers Equation

This document is a comprehensive description of the MMS applied to CFD problems. The focus of the paper is on highlighting coding mistakes

Manufactured Solutions

MAN-4

Manufactured Solutions

Navier Stokes

Euler Equations

A PhD paper which comprehensively describes the verification process on a NS 3-D code, as well as its boundary conditions

Methodology

MET-1

Methodology

Analytical Solution

1-D wave equation

Boundary layer flows

RANS

A very useful tutorial paper explaining the verification process applied to CFD codes, including analytical solutions, calculation of error norms

Methodology

MET-2

Methodology

Numerical Error Sources

Aerodynamics

Best practice

Supersonic / Compressible flows

Paper compares the numerical errors from a RANS and a simpler multi-block inviscid “zonal” model of compressible flows

Methodology

MET-3

Methodology

Analytical Solution

1-D wave equation

Boundary layer flows

RANS

A comprehensive approach to verification and validation methodology and procedures for CFD simulations from an already developed CFD code applied without requiring availability of the source code for specified objectives, geometry, conditions, and available benchmark information

Methodology

MET-4

Methodology

Analytical

Manufactured

Numerical benchmark

Taylor-Green

Natural Convection

Heated cavity

a computational code, named ISIS, dedicated to the simulation of buoyant
re in a mechanically ventilated compartment, undergoes an range of verification and validation procedures, applied to buoyant flows with heat exchange (e.g. fire simulation)

Methodology

MET-5

Methodology

Nuclear

RANS

Couette flow

Flat Plate Boundary layers

An extensive paper on the methods recommended for generating V&V benchmarks.

Methodology

MET-6

Methodology

FDS

Fire models

Methods for undertaking V&V on fire models are show, including reference for benchmarks.

Methodology

MET-7

Code verification

Solution verification

Manufactured Solution

General

This paper provides a comprehensive review of the processes that comprise verification of CFD codes

Methodology

MET-8

Verification Methodology

Benchmarks

General

This document comprehensively describes the process of verification of a computational code, and the requirements of high quality benchmarks

Methodology

MET-9

Verification Methodology

General

Comprehensive overview of the process of verification and validation

Methodology

MET-10

Manufactured Solutions

Error Taxonomies

General

Clarification of terminology for V&V processes applied to CFD.

Methodology

MET-11

Nuclear Safety

General

Process for verifying (and validating) 5 fire models

Methodology

MET-12

Methodology

General

Comprehensive paper on methodology behind V&V

Methodology

MET-13

Methodology

General

Comprehensive document on verification of a CFD code (FDS) with verification test cases

Numerical Solution

NUM-1

Aerodynamics

Aeroelastics

Dynamic Gust response

Verification of FUN3D CFD Code for aerofoil dynamic gust response, primarily using numerical solutions but also an analytical solution

Numerical Solution

NUM-2

Hydrogen release,

Nuclear reactor safety

Momentum, Diffusion release and mixing

Stratification

Fr ≈ 1

Verification of numerical modelling approach to LOWMA-3 experiment at MISTRA facility via two CFD codes

Numerical Solution

NUM-3

Verification and Validation

Deflagration

Detonation

Hydrogen Flames

A highly relevant paper in terms of physics related to hydrogen safety, this paper states it undertakes verification but only validation cases are provided

Numerical Simulation

NUM-4

Nuclear Reactor Safety

Hydrogen Release

Jet Release

Stratification

Numerical verification is undertaken for eight codes (versions of CFX, Fluent, and codes APROS and MELCOR in a blind test applied to Hydrogen release and stratification of relevance to Nuclear Reactor Safety

Numerical Simulation

NUM-5

Numerical solution verification

Ship Hydrodynamics

Drag  estimation

Verification via comparison of 13 numerical  solutions of ship hydrodynamic

Numerical Simulation

NUM-6

Nuclear Safety

Fires

Combustion

This article sets out comparisons of numerical studies of fires with applications to Nuclear Safety

Numerical Simulation

NUM-7

Boundary layer flows, shear.

Turbulence model implementation

Turbulence modelling

NASA verification of turbulence models including Spalart-Allmaras, Shear Stress Transport, and others. Flat Plate

Numerical Simulation

NUM-8

Planar Shear Flow

Turbulence model implementation

Turbulence modelling

NASA verification of turbulence models including Spalart-Allmaras, Shear Stress Transport, and others

Shear Flow

Numerical Simulation

NUM-9

2-D bump

Turbulence model implementation

Flow around obstacles

Tube bundles

Turbulence modelling

Flow Separation

Pressure gradient

NASA verification of turbulence models including Spalart-Allmaras, Shear Stress Transport, and others

2-D bump

Numerical Simulation

NUM-10

Nuclear Safety

Combustion

Flame front

Comparison of 6 CFD codes simulating turbulent combustion

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-1

Nuclear

Detonation

DDT

Paper addresses some numerical requirements regarding the valid numerical modelling of DDT

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-2

H2-Air combustion

Grid sensitivity

Resolved calculations

Length scales, premixed flames, detailed kinetics

Paper considers the grid resolution necessary to resolve combustion in a mixture of calorically imperfect ideal gases described by detailed kinetics and multicomponent transport

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-3

Nuclear Safety

Verification and Validation

Wave propagation

Compressible Flows

Thermal-hydraulic

Uncertainty quantification applied to simulations in Nuclear Safety Engineering

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-4

Nuclear Safety

Verification and Validation

N/A

Presents an identification and ranking of the main physical phenomena in a nuclear safety simulation, to inform appropriate use of codes

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-5

Nuclear Safety

Hydrogen Release

Helium

Release

Jets

Stratification

Froude number

Primarily a validation study on the MiniPanda experimental facility but with useful grid refinement investigation

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-6

Hydrogen release in tunnels

Deflagration

Paper undertakes a sensitivity analysis of solution outputs to grid size, turbulence models, and turbulence flame speed

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-7

Nuclear safety

Hydrogen release

Stratification

Spray cooling

Thermal-hydraulics

Primarily concerned with validation of complex multiphase flows with heat transfer, but with some sensitivity analysis of CFD simulation

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-8

Hydrogen flame propagation

Combustion

Turbulence

Flame structure

Primarily a validation exercise but where the authors incorrectly conclude verification has occurred. Included for reference

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-9

Hydrogen flame propagation

Combustion model

Turbulence-chemistry interaction

Shear Layer

MILD

Primarily a validation exercise but where boundary condition sensitivity(on the CFD model)  is identified as being important

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-10

Nuclear Safety

Uncertainty Quantification

Shear flows

Mixing

Paper explores impact of uncertain inputs on the results of a CFD study

Sensitivity Studies (Grid and Parameter sensitivity)

SEN-11

Nuclear safety

Grid dependency

User parameters

Experimental Uncertainty

Primarily a validation exercise but where some numerical implementations such as grid sensitivity and user inputs are studied