Large-Scale Parallel Fluid Analysis Based on Domain Decomposition Using B-spline S-Version of Finite Element Method

  • Magome, Nozomi (Graduate School of Systems and Information Engineering, University of Tsukuba)
  • Morita, Naoki (Faculty of Engineering, Information and Systems, University of Tsukuba)
  • Mitsume, Naoto (Faculty of Engineering, Information and Systems, University of Tsukuba)

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Our main focus is to analyze a flapping-wing motion of a free-flying insect as a fluid–structure interaction (FSI) phenomenon. The flapping motion is associated with a large deformation, movement, and contact of boundaries. They generate distorted mesh for fluid domain and make the calculation unstable in the tracking method. Furthermore, to analyze a free-flight insect, it is necessary to set a large analysis domain while maintaining high spatial resolution near the insects. For low computational cost, we need to achieve high-resolution only in a local domain. To overcome these challenges, we use structured meshes based on interface capturing method, and for high spatial resolution in an arbitrary local domain, we apply s-version of FEM (SFEM), which has been studied mainly in the field of structural mechanics. However, in conventional SFEM, it is well known that using Lagrange polynomials as the basis functions leads to discontinuous integrand which reduces the accuracy. To solve this problem, many studies have been conducted to improve the integral accuracy by subdividing integral domains, but all of them are computationally expensive. In this study, we propose B-SFEM that adopts B-spline function as basis functions of the structured meshes in SFEM in order to make the integrand continuous and improve the integral accuracy while reducing computational cost. Numerical benchmark tests using manufactured solutions are presented to validate the numerical accuracy. In addition, along with the development of computers and the necessity of highly accurate analysis, the number of DOFs is increasing. Owing to the constraints of computational time and memory capacity, distributed memory parallel computing based on domain decomposition method is important. We apply a parallelization method based on overlapping domain decomposition to the proposed method and perform a strong scaling test to evaluate its performance.