An Extension of Explicit Coupling for Fluid–Structure Interaction Problems

• Main Author: Martina Bukač
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Mathematics
• Subjects: fluid–structure interaction; loosely coupled method; sub-optimal accuracy; partitioned method; moving-domain problems
• Online Access: https://www.mdpi.com/2227-7390/9/15/1747

We present an extension of a non-iterative, partitioned method previously designed and used to model the interaction between an incompressible, viscous fluid and a thick elastic structure. The original method is based on the Robin boundary conditions and it features easy implementation and unconditional stability. However, it is sub-optimally accurate in time, yielding only <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mo>Δ</mo><msup><mi>t</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><mo>)</mo></mrow></semantics></math></inline-formula> rate of convergence. In this work, we propose an extension of the method designed to improve the sub-optimal accuracy. We analyze the stability properties of the proposed method, showing that the method is stable under certain conditions. The accuracy and stability of the method are computationally investigated, showing a significant improvement in the accuracy when compared to the original scheme, and excellent stability properties. Furthermore, since the method depends on a combination parameter used in the Robin boundary conditions, whose values are problem specific, we suggest and investigate formulas according to which this parameter can be determined.