A monolithic arbitrary Lagrangian–Eulerian‐based finite element strategy for fluid–structure interaction problems involving a compressible fluid

Dutta, Suman; Jog, C. S.

doi:10.1002/nme.6783

Cited by 6 publications

(1 citation statement)

References 95 publications

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“…Pan et al 29 proposed a high-order gas dynamics scheme based on ALE that updates the flux within a finite volume frame, captures the discontinuities by moving the grid, and improves the accuracy and robustness through the newly developed WENO scheme. Furthermore, Dutta et al 30 proposed a new overall finite element strategy to solve the fluid-structure interaction problem by considering compressible fluids and a super elastic structure; this helps analyze the field of compressible fluids using the velocity-based ALE and interpolated variables. Furthermore, researchers have coupled the Euler grid with the Lagrange particle because of the automatic tracking and low dissipation of the Lagrange particle; for example, the particle-in-cell (PIC) method 31,32 is used for arranging the Lagrange particles in the Euler grid to track the movement of the material.…”

Section: Introductionmentioning

confidence: 99%

A novel coupled Euler–Lagrange method for high resolution shock and discontinuities capturing

Jin,

Ning,

2023

Numerical Methods in Fluids

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The accurate capturing of shock waves by numerical methods has long been a focus of attention in engineering owing to singularity problems in discontinuities. In this article, a novel coupled Euler–Lagrange method (CELM) is proposed to capture shock waves and discontinuities with high resolution and high order of mapping accuracy. CELM arranges the Lagrange particles on an Euler grid to track the discontinuous points automatically, and the data pertaining to the grids and particles interact via a weighted mutual mapping method that not only achieves fourth‐order accuracy in a smooth area of the solution but also maintains a steep discontinuous transition in the discontinuous area. In the virtual particle method, virtual particles are derived from the existing real particles; thus, the inflow and outflow of the particles and interpolation accuracy of the boundary are more easily realized. An accuracy test and energy convergence test demonstrated the fourth‐order convergence accuracy and low energy dissipation of the CELM; the method exhibited lower error and better conservation ability than high‐precision schemes such as WENO3 and WENO5. The Sod shock tube problem and Woodward–Colella problem showed higher discontinuity resolution of the CELM and ability to accurately track discontinuity points. Examples of Riemann problems were employed to prove that the CELM exhibits lower dissipation and higher shock resolution than WENO3 and WENO5. The CELM also showed an accurate structure based on particle distribution. Shockwave diffraction tests were conducted to prove that the CELM results showed good agreement with the experimental data and exhibited an accurate expansion wave. The CELM can also accurately simulate the collision of an expansion wave and vortex.

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Section: Introductionmentioning

confidence: 99%

A novel coupled Euler–Lagrange method for high resolution shock and discontinuities capturing

Jin,

Ning,

2023

Numerical Methods in Fluids

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Monolithic finite element modeling of compressible fluid‐structure‐electrostatics interactions in MEMS devices

Dutta,

Jog

2024

Numerical Methods in Fluids

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This work presents a monolithic finite element strategy for the accurate solution of strongly‐coupled fluid‐structure‐electrostatics interaction problems involving a compressible fluid. The complete set of equations for a compressible fluid is employed within the framework of the arbitrary Lagrangian–Eulerian (ALE) fluid formulation on the reference configuration. The proposed numerical approach incorporates geometric nonlinearities of both the structural and fluid domains, and can thus be used for investigating dynamic pull‐in phenomena and squeeze film damping in high aspect‐ratio micro‐electro‐mechanical systems (MEMS) structures immersed in a compressible fluid. Through various illustrative examples, we demonstrate the significant influence of fluid compressibility on the dynamics of MEMS devices subjected to constrained geometry and/or high‐frequency electrostatic actuation. Moreover, we compare the proposed formulation with the nonlinear compressible Reynolds equation and highlight that, particularly at low pressures and high fluid viscosity, the Reynolds equation fails to provide a reliable approximation to the complete set of equations utilized in our proposed formulation.

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A monolithic finite element strategy for conjugate heat transfer

Santhosh

Jog²

2022

Sādhanā

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A monolithic arbitrary Lagrangian–Eulerian‐based finite element strategy for fluid–structure interaction problems involving a compressible fluid

Cited by 6 publications

References 95 publications

A novel coupled Euler–Lagrange method for high resolution shock and discontinuities capturing

A novel coupled Euler–Lagrange method for high resolution shock and discontinuities capturing

Monolithic finite element modeling of compressible fluid‐structure‐electrostatics interactions in MEMS devices

A monolithic finite element strategy for conjugate heat transfer

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