A comprehensive assessment of accuracy of adaptive integration of cut cells for laminar fluid-structure interaction problems

Kadapa, Chennakesava; Wang, Xinyu; Mei, Ying

doi:10.1016/j.camwa.2022.07.006

Cited by 5 publications

(1 citation statement)

References 47 publications

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“…1c), leading to important simulation aspects, such as the 1. Integration of discontinuous element matrices (FCM: [5,[14][15][16][17], XFEM: [18][19][20][21], CutFEM: [22]), 2. Stabilization schemes for ill-conditioned problems (FCM: [23][24][25], XFEM: [13,26,27], CutFEM: [28,29]),…”

Section: Immersed Boundary Problemsmentioning

confidence: 99%

Code verification of immersed boundary techniques using the method of manufactured solutions

Petö,

Gorji,

Duvigneau

et al. 2023

Comput Mech

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Code verification plays a crucial role for all finite element applications, especially for non-standard ones, such as immersed boundary approaches, which are typically based on novel algorithms and often error-prone in-house implementations. Instead of relying on rarely available analytical solutions or overkill FEM simulations, in this article, the capabilities of themethod of manufactured solutions(MoMS) are explored, enabling an easy and straightforward derivation of closed-form reference solutions. The focus is kept on immersed problems, in particular, on the finite cell method (FCM), and manufactured solutions are derived for 2D and 3D problems involving voids and single/multiple inclusions. We propose several approaches for the construction of the manufactured solutions, where zero traction conditions for void regions and continuous normal stresses along material interfaces are directly fulfilled. Thus, no weak boundary conditions are required for reproducing the manufactured solution via FCM. This not only enables code verification for FCM implementations that lack the option of applying weak boundary conditions, but also keeps the simulation complexity low, when testing other relevant features, e.g., different integration schemes or the implementation of enrichment functions. The flexibility and wide application range of the MoMS in the context of immersed boundary simulations is demonstrated using static, quasi-static, and transient problems in the context of linear elasticity. Finally, the analytical derivations of the manufactured solutions used in this paper are provided as supplementary material.

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Section: Immersed Boundary Problemsmentioning

confidence: 99%

Code verification of immersed boundary techniques using the method of manufactured solutions

Petö,

Gorji,

Duvigneau

et al. 2023

Comput Mech

View full text Add to dashboard Cite

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Jacobi polynomials and the numerical solution of ray tracing through the crystalline lens

Abd El-Hady,

El-shenawy

2024

Opt Quant Electron

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The human eye is a fascinating optical system, with the crystalline lens playing a significant role in focusing light onto the retina of the eye. The ray tracing through the crystalline lens problem is a challenging problem in optics. In this paper, the case of a non-homogeneous optical medium is investigated, and the ray equation is numerically solved to get the ray paths. The governing equation is an ODE with a fractional derivative given in the Caputo sense. A novel numerical scheme is based on the Jacobi polynomial collocation technique to tackle this problem. A fast and accurate Broyden’s Quasi-Newton algorithm is applied to solve the nonlinear system of equations obtained from the collocation process. Numerical results are stated in detail to show the efficiency of our technique and are compared with other analytical and numerical methods using tables and illustrated figures, which will be useful to corroborate the clinical and physical data. Ray tracing through the crystalline lens is not only fascinating from a scientific perspective but also has practical implications across various domains, and the proposed scheme is considered a promising and practically reliable method to address such types of applications.

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Implementation and Validation of an Original OpenFOAM Code for Fluid–Structure Interaction Problems in Compressible Flow

Benhamou,

Belghoula

2024

Arab J Sci Eng

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A comprehensive assessment of accuracy of adaptive integration of cut cells for laminar fluid-structure interaction problems

Cited by 5 publications

References 47 publications

Code verification of immersed boundary techniques using the method of manufactured solutions

Code verification of immersed boundary techniques using the method of manufactured solutions

Jacobi polynomials and the numerical solution of ray tracing through the crystalline lens

Implementation and Validation of an Original OpenFOAM Code for Fluid–Structure Interaction Problems in Compressible Flow

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