Code verification for unsteady 3-D fluid–solid interaction problems

Abstract

This paper describes a procedure to synthesize Manufactured Solutions for Code Verification of an important class of Fluid–Structure Interaction (FSI) problems whose behaviors can be modeled as rigid body vibrations in incompressible fluids. We refer this class of FSI problems as Fluid–Solid Interaction problems, which can be found in many practical engineering applications. The methodology can be utilized to develop Manufactured Solutions for both 2-D and 3-D cases. We demonstrate the procedure with our numerical code. We present details of the formulation and methodology. We also provide the reasonings behind our proposed approach. Results from grid and time step refinement studies confirm the verification of our solver and demonstrate the versatility of the simple synthesis procedure. In addition, the results also demonstrate that the modified decoupled approach to verify flow problems with high-order time-stepping schemes can be employed equally well to verify code for multi-physics problems (here, those of the Fluid–Solid Interaction) when the numerical discretization is based on the Method of Lines.