This page contains a summary of the verification database entries gathered in the Susana Project.

The database entries here are grouped according to the Primary verification process they refer to. These are:

Analytical Solutions: where the accuracy of numerical outputs from a code can be assessed against an analytical solution to the same equations.

Code verification: checking for consistency of outputs following simple operations such as translating or rotating the domain, mirroring the domain, mass continuity tests.

Manufactured Solutions: where source terms are added to the governing equations such that the solution to the modified equations is amenable to an analytical solution.

Methodology: A reference which explains verification processes or terminology.

Numerical Solutions: where the accuracy of numerical outputs from a code can be assessed against the outputs from other codes which have been well tested and are of known high quality.

Sensitivity Studies (Grid and Parameter Sensitivity): where the impact of numerical parameters (such as grid size) and case parameters (such as fluid properties, boundary conditions) are assess.

In addition, to aid the identification of useful references, the table below give keywords for

The main topic / application area for the reference

The physical phenomena tested in that reference

 

 

 

 

Clicking on the Database Reference will open a page with that reference case

 

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 implementation such as grid sensitivity and user inputs are studied.