Mesh moving techniques in fluid-structure interaction: robustness, accumulated distortion and computational efficiency
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ORIGINAL PAPER
Mesh moving techniques in fluid-structure interaction: robustness, accumulated distortion and computational efficiency Alexander Shamanskiy1
· Bernd Simeon1
Received: 19 June 2020 / Accepted: 16 November 2020 © The Author(s) 2020
Abstract An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh moving technique (MMT) used to adapt the computational mesh in the moving fluid domain. An ideal MMT is computationally inexpensive, can handle large mesh motions without inverting mesh elements and can sustain an FSI simulation for extensive periods of time without irreversibly distorting the mesh. Here we compare several commonly used MMTs which are based on the solution of elliptic partial differential equations, including harmonic extension, bi-harmonic extension and techniques based on the equations of linear elasticity. Moreover, we propose a novel MMT which utilizes ideas from continuation methods to efficiently solve the equations of nonlinear elasticity and proves to be robust even when the mesh undergoes extreme motions. In addition to that, we study how each MMT behaves when combined with the mesh-Jacobian-based stiffening. Finally, we evaluate the performance of different MMTs on a popular two-dimensional FSI benchmark reproduced by using an isogeometric partitioned solver with strong coupling. Keywords Isogeometric analysis · Arbitrary Lagrangian–Eulerian methods · Mesh-Jacobian-based stiffening · Nonlinear elasticity · Continuation methods
1 Introduction Fluid-structure interaction (FSI) constitutes a class of problems involving two-way dependence between structural objects and a fluid. As such, FSI is a vast topic with applications spanning a spectrum from aerospace and civil engineering [1] to biomechanical and cardiovascular simulations [9]. In FSI problems, the fluid exerts a force on the structure which deforms in response. As the structure moves, it changes the shape of the domain occupied by the fluid together with the fluid motion and, as a result, the force that the fluid exerts on the structure. This two-way coupling between the fluid and structure behavior as well as the necessity to accommodate the fluid domain motion in both the continuous and discrete formulations of the problem is what makes FSI so notoriously complex.
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Alexander Shamanskiy [email protected] TU Kaiserslautern, Department of Mathematics, Felix-Klein-Zentrum, Paul-Ehrlich-Str. 31, 67663 Kaiserslautern, Germany
Since FSI problems rarely admit analytical solutions, computational methods are widely adopted in FSI research. Here, one can distinguish between the static-mesh and moving-mesh methods. While the former attempt to resolve the motion of the fluid domain implicitly, for example by means of a stationary background Cartesian mesh [21], the latter deal with the motion of the fluid domain by tracking its boundary and adapting the computational mesh correspondingly. In this work, we study and compare various mesh moving techniques (MMTs) which
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