Aniruddha Choudhary, Christopher J. Roy, Jean-François Dietiker, Mehrdad Shahnam, Rahul Garg, Jordan Musser, Code verification for multiphase flows using the method of manufactured solutions, International Journal of Multiphase Flow, Volume 80, April 2016, Pages 150-163, ISSN 0301-9322, http://dx.doi.org/10.1016/j.ijmultiphaseflow.2015.12.006.
Abstract: Code verification is the process of ensuring, to the extent possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a scientific computing simulation. Order of accuracy testing using the Method of Manufactured Solutions (MMS) is a rigorous technique that is employed here for code verification of the main components of an open-source, multiphase flow code – MFIX. Code verification is performed here on 2D and 3D, uniform and stretched meshes for incompressible, steady and unsteady, single-phase and two-phase flows using the two-fluid model of MFIX. Currently, the algebraic gas-solid exchange terms are neglected as these can be verified via techniques such as unit-testing. The no-slip wall, free-slip wall, and pressure outflow boundary conditions are verified. Temporal orders of accuracy for first-order and second-order time-marching schemes during unsteady simulations are also assessed. The presence of a modified SIMPLE-based algorithm in the code requires the velocity field to be divergence free in case of the single-phase incompressible model. Similarly, the volume fraction weighted velocity field must be divergence-free for the two-phase incompressible model. A newly-developed curl-based manufactured solution is used to generate manufactured solutions that satisfy the divergence-free constraint during the verification of the single-phase and two-phase incompressible governing equations. Manufactured solutions with constraints due to boundary conditions as well as due to divergence-free flow are derived in order to verify the boundary conditions.
Keywords: Multiphase flows; Code verification; Method of manufactured solutions; Order of accuracy; Two-fluid model