Full Eulerian deformable solid‐fluid interaction scheme based on building‐cube method for large‐scale parallel computing

Nishiguchi, Koji M.; Bale, Rahul; Okazawa, Shigenobu; Tsubokura, Makoto

doi:10.1002/nme.5954

Cited by 23 publications

(44 citation statements)

References 48 publications

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“…Shock and elastic obstacles interactions were simulated in Mouronval, Tie, Hadjadj and Moebs (2019). Full Eulerian deformable solid-fluid interaction was simulated for large-scale parallel computing in Nishiguchi, Bale, Okazawa and Tsubokura (2019). Wave impact pressure and kinematics due to breaking wave impingement on a monopile were studied in Chella, Bihs and Myrhaug (2019a).…”

Section: Applicationsmentioning

confidence: 99%

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Shu¹

2020

Acta Numerica

103

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Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.

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Section: Applicationsmentioning

confidence: 99%

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Shu¹

2020

Acta Numerica

103

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“…More than 200 papers were retrieved by database searches for 2015-2020 using the terms artificial compressibility, pseudo compressibility, and dual time stepping. These studies include analysis of the relationships between AC and fractional step methods [86,87], studies of turbulent flow [88][89][90], development of discontinuous Galerkin methods [91][92][93], parallel solution of large-scale problems [94][95][96], multi-fluid simulations [97], further advances to entropically-damped AC methods [98][99][100], implementation high-order numerical schemes [101][102][103], use of characteristic methods [104][105][106], application for non-hydrostatic effects [107,108], magneto-hydrodynamic simulations [109][110][111], solution with lattice Boltzmann methods [112], and solution by smoothed particle hydrodynamics [113,114]. Note the above are examples and should not be considered an exhaustive list of recent work.…”

Section: Recent Development Of the Artificial Compressibility Methodsmentioning

confidence: 99%

An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow

Hodges

2020

Water

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Piping systems (e.g., storm sewers) that transition between free-surface flow and surcharged flow are challenging to model in one-dimensional (1D) networks as the continuity equation changes from hyperbolic to elliptic as the water surface reaches the pipe ceiling. Previous network models are known to have poor mass conservation or unpredictable convergence behavior at such transitions. To address this problem, a new algorithm is developed for simulating unsteady 1D flow in closed conduits with both free-surface and surcharged flow. The shallow-water (hydrostatic) approximation is used as the governing equations. The artificial compressibility (AC) method is implemented as a dual-time-stepping discretization for a finite-volume solver with timescale interpolation used for face reconstruction. A new formulation for the AC celerity parameter is proposed such that the AC celerity matches the equivalent gravity wave speed for the local hydraulic head—which has some similarities to the classic Preissmann Slot used to approximate pressurized flow in conduits. The new approach allows the AC celerity to be set locally by the flow (i.e., non-uniform in space) and removes it as a free parameter of the AC solution method. The derivation of the AC method provides for only a minor change in the form of the solution equations when a computational element switches from free-surface to surcharged. The new solver is tested for both unsteady free-surface (supercritical, subcritical) and surcharged flow transitions in a circular pipe and is implemented in an open-source Python code available under the name “PipeAC.” The results are compared to laboratory experiments that include rapid flow changes due to opening/closing of gates. Results show that the new algorithm is satisfactory for 1D representation of unsteady transition behavior with two caveats: (i) sufficient grid resolution must be applied, and (ii) the shallow-water equation approximations (hydrostatic, single-fluid) limit the accuracy of the solution with regards to the celerity of the turbulent unsteady bore that propagates upstream. This research might benefit any piping network model that must smoothly handle unsteady transitions from free surface to surcharged flow.

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“…Full Eulerian methods [1,2,3] using a fixed mesh to compute motions of fluids and solids have been developed to solve fluid-structure interaction (FSI) problems. These methods are suitable for high-performance computing and computing large deformation of solids.…”

Section: Introductionmentioning

confidence: 99%

Eulerian Formulation Using Lagrangian Marker Particles with Reference Map Technique for Fluid-structure Interaction Problem

Shimada¹,

Nishiguchi²,

Peco³

et al. 2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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Full Eulerian methods constitute a family of numerical techniques used to simulate fluid-structure interaction problems. In a full Eulerian method, the velocity gradient tensor is used to compute deformation of solid. However, it is difficult to compute solid stress accurately near the interface, where the velocity between fluid and solid changes drastically. In this work, we propose an Eulerian formulation for fluid-structure interaction problems using Lagrangian marker particles with the Reference Map Technique to compute the deformation of solid accurately near material interfaces without using the gradient of the velocity. We illustrate and validate the proposed method through the presentation of various benchmark problems.

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Full Eulerian deformable solid‐fluid interaction scheme based on building‐cube method for large‐scale parallel computing

Cited by 23 publications

References 48 publications

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow

Eulerian Formulation Using Lagrangian Marker Particles with Reference Map Technique for Fluid-structure Interaction Problem

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