Code verification for multiphase flows using the method of manufactured solutions

• We apply the method of manufactured solutions to verify two-phase flow equations.
• We introduce curl-based manufactured solutions for verifying incompressible flows.
• We present verification of common boundary conditions and two time-stepping schemes.

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.