Good mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers. Mesh moving based on linear elasticity and mesh-Jacobian-based stiffening (MJBS) has been in use with the ST and ALE methods since 1992. In the MJBS, the objective is to stiffen the smaller elements, which are typically placed near solid surfaces, more than the larger ones, and this is accomplished by altering the way we account for the Jacobian of the transformation from the element domain to the physical domain. In computing the mesh motion between time levels $$t_n$$ t n and $$t_{n+1}$$ t n + 1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at $$t_n$$ t n . While this option works well for most problems, because the method is path-dependent, it involves cycle-to-cycle accumulated mesh distortion. The back-cycle-based mesh moving (BCBMM) method, introduced recently with two versions, can remedy that. In the BCBMM, there is no cycle-to-cycle accumulated distortion. In this article, for the first time, we present mesh moving test computations with the BCBMM. We also introduce a version we call “half-cycle-based mesh moving” (HCBMM) method, and that is for computations where the boundary or interface motion in the second half of the cycle consists of just reversing the steps in the first half and we want the mesh to behave the same way. We present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching. The computations show that all versions of the BCBMM perform well, with no cycle-to-cycle accumulated distortion, and with the HCBMM, as the wing in the second half of the cycle just reverses its motion steps in the first half, the mesh behaves the same way.
A numerical investigation is performed here using a NURBS-based finite element formulation applied to classical Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems. Model capabilities related to refinement techniques are analyzed using a finite element formulation with NURBS (non uniform rational B-splines) basis functions, where B-splines and low-order Lagrangian elements can be considered as particular cases. An explicit two-step Taylor-Galerkin model is utilized for discretization of the fundamental flow equations and turbulence is considered using Large Eddy Simulation (LES) and the Smagorinsky's sub-grid scale model. FSI is considered using an ALE kinematic formulation and a conservative partitioned coupling scheme with rigid body approach for large rotations is adopted. CFD and FSI applications are analyzed to evaluate the accuracy associated with the different refinement procedures utilized. Results show that high order basis functions with appropriate refinement and non-uniform parameterization lead to better predictions, compared with low-order Lagrangian models.
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