Higher-order time integration through smooth mesh deformation for 3D fluid–structure interaction simulations

• Published in: Journal of computational physics Vol. 224; no. 1; pp. 414 - 430
• Main Authors: van Zuijlen, A.H., de Boer, A., Bijl, H.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 20.05.2007; Elsevier
• Subjects: Computational techniques; Exact sciences and technology; Fluid–structure interaction; Higher-order time integration; Mathematical methods in physics; Mesh deformation; Partitioned coupling; Physics; Higher-order time integration; Fluid–structure interaction; Partitioned coupling; Mesh deformation; Second order; Deformation; Fluid dynamics; Third order; Fluid-structure interaction; Optimization; Spline; Calculation methods; Interpolation; Algorithms; Calculation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2007.03.024

In this paper, we present a higher-order accurate in time, partitioned integration scheme (IMEX) for fluid–structure interaction. The scheme is based on a combination of an implicit, L-stable, multi-stage Runge–Kutta scheme and an explicit Runge–Kutta scheme. Fluid and structure dynamics are integrated using the implicit scheme and only the pressure loads acting on the structure are integrated explicitly. For an academic problem we show that mesh optimization functions, which are often necessary in standard mesh deformation algorithms, can have a detrimental effect on the temporal order and accuracy. We use a radial basis function (RBF) interpolation with a thin plate spline to create a smooth displacement field for the whole fluid domain, which does not affect the order of the IMEX time integration scheme. For reasonable accuracies, the IMEX schemes outperform a second-order staggered scheme by a factor of 2–3. As an example for a three-dimensional, real-world problem, a simulation of a transonic wing flutter case, the AGARD 445.6 wing, is performed. For this test case, a clear third-order time accuracy is observed for IMEX3.