TY - JOUR

T1 - A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion

AU - Tonon, Patrícia

AU - Sanches, Rodolfo André Kuche

AU - Takizawa, Kenji

AU - Tezduyar, Tayfun E.

N1 - Funding Information:
This work was supported (third author) in part by JST-CREST; Grant-in-Aid for Scientific Research (A) 18H04100 from Japan Society for the Promotion of Science; and Rice–Waseda research agreement. The work was also supported (fourth author) in part by ARO Grant W911NF-17-1-0046 and Top Global University Project of Waseda University. The first author was supported by Coordenac̨ão de Aperfeic̨oamento de Pessoal de Nível Superior-Brasil (CAPES) - Finance Code 001.

PY - 2021/2

Y1 - 2021/2

N2 - 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 tn and tn+1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at tn. 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.

AB - 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 tn and tn+1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at tn. 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.

KW - Back-cycle-based mesh moving

KW - Cycle-to-cycle accumulated distortion

KW - Half-cycle-based mesh moving

KW - Linear-elasticity equations

KW - Mesh moving method

KW - Mesh-Jacobian-based stiffening

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U2 - 10.1007/s00466-020-01941-y

DO - 10.1007/s00466-020-01941-y

M3 - Article

AN - SCOPUS:85099183418

VL - 67

SP - 413

EP - 434

JO - Computational Mechanics

JF - Computational Mechanics

SN - 0178-7675

IS - 2

ER -