Dr.
Burg, along with his first graduate student Vasanth Murali, studied the issues
involved in code verification as applied to unstructured flow solvers. Code
verification is the rigorous process of determining the order of accuracy of
the implementation of a discretization method. Vasanth Murali and Dr. Burg
studied these issues in regards to the SimCenter's 2D version of their
unstructured flow solver. In the process, Dr. Burg developed a means for code
verification that relies solely on the residual and not the converged solution,
allowing the process of code verification to be performed without the
computational cost and associated difficulties of obtaining a converged
solution.
In the method of manufactured solutions,
the governing equations are altered by adding an algebraic source term which
drives the solution to a pre-determined manufactured solution. In this methodology, the order of
accuracy of the implementation is obtained by analyzing the difference between
the converged solution and the manufactured solution. But to obtain the converged solution on
a sequence of more and more refined grids can be computationally expensive,
especially for the most refined grid in 3D, and the solution must be strongly
converged in order for these errors to be meaningful.
The residual formulation of the method
of manufactured solutions avoids the computational cost and the other
difficulties associated with obtaining a strongly converged solution by only
considering the magnitude of the residual at the first iteration. By using the exact solution as the
initial conditions, the residual that is generated contains the order of
accuracy information, just as a Taylor’s
series expansion of the finite difference expression contains the order of
accuracy term. Thus, the order of
accuracy can be analyzed immediately and simply.
Burg, C. O. E., and Murali, V. K., “The
Residual Formulation of the Method of Manufactured Solutions for
Computationally Efficient Code Verification”, submitted to the
International Journal of Computational Fluid Dynamics, July, 2004.
Burg, C. O. E., and Murali, V. K.,
“Efficient Code Verification Using the Residual Formulation of the Method
of Manufactured Solutions”, AIAA Paper 2004-2628, 34th AIAA
Fluid Dynamics Conference, Portland, Oregon, June, 2004. PDF
Murali, V., Burg, C. O. E.,
"Verification of 2D Navier-Stokes Codes by the Method of Manufactured
Solutions," AIAA Paper 2002-3109, 32nd AIAA Fluid Dynamics Conference, St. Louis, June, 2002.