Verification Resources

Below is a list of verification quality solutions graciously proved by Prof. Chris Roy and Dr. William Oberkampf suitable for compressible flow solvers. In addition, Farshad Navah of McGill University has povided a set of manufactured solutions suitable for verification of the RANS SA turbulence model [Navah et al, 2017].

These are suggested verification test that participants can use to verify their solver implementations. These cases are NOT part of the workshop, but provided as a supplemental resource to participants.


Exact Solutions (no source terms, all are inviscid)


* Ringleb's flow [Satav et al., 2005]
* Supersonic vortex flow [Ollivier-Gooch et al., 2009]
* Oblique shock [Anderson, 1990]
* Expansion fan [Anderson, 1990]
* Shock with rapid Expansion fan [Doebling, 2016]

Exact Solutions (with source terms)

* Manufactured solutions [Roy et al, 2004] [Navah et al, 2017]
* Karman-Trefftz inviscid airfoil: requires source term for energy equation only [Tyson, 2015]
* Steady and unsteady inviscid vortex flow [Yan and Ollivier-Gooch, 2017]

Benchmark Numerical Solutions

* Inviscid NACA 0012 (M=0.5, 0.8 and AOA=0, 1.25 deg.) [Vassberg and Jameson, 2010]
* NACA 0012 airfoil w/ Spalart-Allmaras turbulence model [Langley turbmodels web site]
* JCEAP hypersonic laminar flow over blunted cone [Roy et al, 2003,]


J. D. Anderson, Modern Compressible Flow with Historical Perspective, 2nd Ed., McGraw-Hill, New York, 1990. 

NASA Langley Turbulence Modeling Resource web site, 2D NACA 0012 Airfoil Validation Case: (last accessed 12/8/2016)

C. Ollivier-Gooch, A. Nejat, and K. Michalak, “Obtaining and verifying higher-order unstructured finite volume solutions to the euler equations,” AIAA Journal, vol. 47, no. 9, pp. 2105–2120, 2009

C. J. Roy, M. A. McWherter-Payne, and W. L. Oberkampf, “Verification and Validation for Laminar Hypersonic Flowfields Part 1: Verification,” AIAA Journal, Vol. 41, No. 10, 2003, pp. 1934-1943

C. J. Roy, C. C. Nelson, T. M. Smith, and C. C. Ober, “Verification of Euler / Navier-Stokes Codes using the Method of Manufactured Solutions,” International Journal for Numerical Methods in Fluids, Vol. 44, No. 6, 2004, pp. 599-620

F. Navah and S. Nadarajah, "Motivations and methods of verification for high-order RANS solvers and solutions", AIAA Paper 2017-3290

Satav, V., Hixon, R., Nallasamy, M., Sawyer, S., “Validation of a Computational Aeroacoustics Code for Nonlinear Flow about Complex Geometries Using Ringleb's Flow,” Presented at the 11th AIAA/CEAS Aeroacoustics Conference, 23-25 May 2005, Monterey, California

W. C. Tyson, "Application of r-Adaptation Techniques for Discretization Error Improvement in CFD," Masters Thesis, Virginia Tech, December 2015.

J. C. Vassberg and A. Jameson, “In pursuit of grid convergence for two-dimensional Euler solutions,” Journal of Aircraft, vol. 47, no. 4, pp. 1152–1166, 2010

G. K. Yan , C. Ollivier-Gooch, "Towards Higher Order Discretization Error Estimation by Error Transport using Unstructured Finite-Volume Methods for Unsteady Problems," accepted w/ minor revision, Computers and Fluids, 2017. 

Doebling, S. W. (2016), "The Escape of High Explosive Products: An Exact-Solution Problem for Verification of Hydrodynamics Codes," Journal of Verification, Validation and Uncertainty Quantification. Vol. 1, p. 041001-1,041001-13.

how5 [at]