A General Methodology for Symbolically Generating Manufactured Solutions Satisfying Prescribed Conditions: Application to Two-phase Flows Equations

The Method of Manufactured Solution (MMS) is a powerful technique for code verification. It provides a systematic procedure for generating analytical solutions to be discretized by a numerical solver. Usually, an arbitrary continuous solution is selected before being inserted into the governing equations. Although sufficient in many situations, this procedure may be inappropriate if the problem at hand imposes some constraints on the shape of the manufactured solutions. In such cases, some unknown parameters should be included in the continuous solution and computed to satisfy the imposed constraints. This limitation of the standard MMS has already been recognized in previous work. However, the way to handle it is most of the time case-dependent and based on ad-hoc strategies. In this work, we develop a generic framework based on the Sympy library to produce manufactured solutions complying with arbitrary complex Dirichlet and Neumann-type conditions. It is made available through an open-source Python software. As a challenging illustrative application, analytical solutions obeying the interface jumps conditions of a two-phase compressible Navier–Stokes system are built.