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  ANA1 
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  ANA2  Hydrogen LES 
Detonation 
Authors use LES to simulate hydrogenair detonation. The solution is verified against a simplified /analytical model (ZND). 
Analytical Solution  ANA3 
Discretisation scale Length Scale 
Laminar Premixed HydrogenAir Flames 
The Paper identifies the spatial discretization required to capture all detailed continuum physics in the reaction zone for onedimensional steady laminar premixed hydrogenair flames. 
Analytical Solution  ANA4 
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  ANA5 
Analytical Solutions (1D semi exact) Manufactured Solutions 
Compressible flows Sedov blast wave Problem Riemann Problem Taylor Green Vortices 
Verification results for a threedimensional unstructured finite element method have been presented. Accuracy and convergence measurements were given for both shockdominated and smooth flows. 
Analytical Solution  ANA6  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  ANA7  Jet releases 
Laminar Flow Jet Flows 
Analytical Solution for Laminar TwoDimensional Jet 
Analytical Solution  ANA8 
Combustion 1D 
Combustion Flame Front Propagation 
This provides an analytical solution to solving the 1D flame propagation speed in 1D. 
Analytical Solution  ANA9 
Analytical solution Combustion 
Heat of reaction Flame temperature 
This solves the energy equation for a hydrogenair mixture to calculate the flame temperature. 
Analytical Solution  ANA10  Analytical Solution  NavierStokes Equations  This test case exercises the terms in the NavierStokes equations 


Code Verification  CV1 
Code Verification Mass balance 
Continuity Equation  A simple procedure for determining mass balance errors in H2 release simulations 
Code Verification  CV2 
Code Verification Energy balance 
Energy Equation  Verifying that the basic FDS algorithm is energy conserving 
Code Verification  CV3  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  CV4 
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  MAN1 
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  MAN2 
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  MAN3 
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  MAN4  Manufactured Solutions 
Navier Stokes Euler Equations 
A phD paper which comprehensively describes the verification process on a NS 3D code, as well as its boundary conditions 


Methodology  MET1 
Methodology Analytical Solution 
1D 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  MET2 
Methodology Numerical Error Sources Aerodynamics Best practice 
Supersonic / Compressible flows  Paper compares the numerical errors from a RANS and a simpler multiblock inviscid “zonal” model of compressible flows.. 
Methodology  MET3 
Methodology Analytical Solution 
1D 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  MET4 
Methodology Analytical Manufactured Numerical benchmark 
TaylorGreen 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  MET5  Methodology 
Nuclear RANS Couette flow Flat Plate Boundary layers 
An extensive paper on the methods recommended for generating V&V benchmarks. 
Methodology  MET6 
Methodology FDS 
Fire models 
Methods for undertaking V&V on fire models are show, including reference for benchmarks. 
Methodology  MET7 
Code verification Solution verification Manufactured Solution 
General  This paper provides a comprehensive review of the processes that comprise verification of CFD codes. 
Methodology  MET8 
Verification Methodology Benchmarks 
General  This document comprehensively describes the process of verification of a computational code, and the requirements of high quality benchmarks 
Methodology  MET9 
Verification Methodology 
General  Comprehensive overview of the process of verification and validation 
Methodology  MET10 
Manufactured Solutions Error Taxonomies 
General  Clarification of terminology for V&V processes applied to CFD. 
Methodology  MET11  Nuclear Safety  General  Process for verifying (and validating) 5 fire models 
Methodology  MET12  Methodology  General  Comprehensive paper on methodology behind V&V 
Methodology  MET13  Methodology  General  Comprehensive document on verification of a CFD code (FDS) with verification test cases. 


Numerical Solution  NUM1 
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  NUM2 
Hydrogen release, Nuclear reactor safety 
Momentum, Diffusion release and mixing Stratification Fr ≈ 1 
Verification of numerical modelling approach to LOWMA3 experiment at MISTRA facility via two CFD codes 
Numerical Solution  NUM3  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  NUM4 
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  NUM5 
Numerical solution verification Ship Hydrodynamics 
Drag estimation  Verification via comparison of 13 numerical solutions of ship hydrodynamic 
Numerical Simulation  NUM6  Nuclear Safety 
Fires Combustion 
This article sets out comparisons of numerical studies of fires with applications to Nuclear Safety. 
Numerical Simulation  NUM7 
Boundary layer flows, shear. Turbulence model implementation 
Turbulence modelling  NASA verification of turbulence models including SpalartAllmaras, Shear Stress Transport, and others. Flat Plate 
Numerical Simulation  NUM8 
Planar Shear Flow Turbulence model implementation 
Turbulence modelling 
NASA verification of turbulence models including SpalartAllmaras, Shear Stress Transport, and others. Shear Flow 
Numerical Simulation  NUM9 
2D bump Turbulence model implementation Flow around obstacles Tube bundles 
Turbulence modelling Flow Separation Pressure gradient 
NASA verification of turbulence models including SpalartAllmaras, Shear Stress Transport, and others 2D bump. 
Numerical Simulation  NUM10  Nuclear Safety 
Combustion Flame front 
Comparison of 6 CFD codes simulating turbulent combustion 


Sensitivity Studies (Grid and Parameter sensitivity)  SEN1 
Nuclear 
Detonation DDT 
Paper addresses some numerical requirements regarding the valid numerical modelling of DDT 
Sensitivity Studies (Grid and Parameter sensitivity)  SEN2 
H2Air 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)  SEN3 
Nuclear Safety Verification and Validation 
Wave propagation Compressible Flows Thermalhydraulic 
Uncertainty quantification applied to simulations in Nuclear Safety Engineering 
Sensitivity Studies (Grid and Parameter sensitivity)  SEN4 
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)  SEN5 
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)  SEN6  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)  SEN7  Nuclear safety 
Hydrogen release Stratification Spray cooling Thermalhydraulics 
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)  SEN8  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)  SEN9  Hydrogen flame propagation 
Combustion model Turbulencechemistry 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)  SEN10 
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)  SEN11  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. 