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Discrete embedded boundary method with smooth dependence on the evolution of a fluid-structure interface

INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 2021年第19期122卷 5353-5383页

作者： Ho, Jonathan Farhat, Charbel Stanford Univ Dept Aeronaut & Astronaut Durand BldgRoom 224-12496 Lomita Mall Stanford CA 94305 USA Stanford Univ Dept Mech Engn Stanford CA 94305 USA Stanford Univ Inst Computat & Math Engn Stanford CA 94305 USA

embedded boundary methods (EBMs) are robust solution methods for highly nonlinear fluid-structure interaction (FSI) problems. They suffer, however, some disadvantages because they perform their computations on embedding, nonbody-fitted fluid meshes. In particular, they tend to generate discrete events that introduce discontinuities in the semi-discretization process and lead to numerical solutions that are insufficiently smooth for differentiation with respect to the evolution of a discrete, fluid/structure interface Gamma hF/S. This hinders their application to the gradient-based solution of fluid-structure optimization problems. Discrete events also promote spurious oscillations in the post-processing of time-dependent results computed at Gamma hF/S.z This paper addresses these issues in the context of Finite Volume method with Exact two-material Riemann problems (FIVER), a comprehensive framework for developing EBMs for highly nonlinear, compressible, FSI problems. It revisits the concept of the status of a node of an embedding fluid mesh and introduces that of a smoothness indicator nodal function, to eliminate discrete events and achieve smoothness in the semi-discretization process. It also introduces a moving least squares approach in the loads evaluation algorithm, to suppress spurious oscillations from integral quantities computed on Gamma hF/S. Equipped with these enhancements, FIVER is shown to deliver, for three different FSI applications, smooth results that are differentiable with respect to evolutions of Gamma hF/S.

关键词： discrete events embedded boundary method FIVER fluid-structure interaction immersed boundary method moving least squares radial basis functions

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AN embedded boundary method FOR ELLIPTIC AND PARABOLIC PROBLEMS WITH INTERFACES AND APPLICATION TO MULTI-MATERIAL SYSTEMS WITH PHASE TRANSITIONS

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Acta Mathematica Scientia 2010年第2期30卷 499-521页

作者： Shuqiang Wang Roman Samulyak Tongfei Guo Department of Applied Mathematics and Statistics Stony Brook University Stony Brook NY 11794 USA Computational Science Center Brookhaven National Laboratory Upton NY 11973 USA

The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems.

关键词： embedded boundary method elliptic interface problem front tracking Ste-fan problem

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Universal AMG Accelerated embedded boundary method Without Small Cell Stiffness

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JOURNAL OF SCIENTIFIC COMPUTING 2023年第2期97卷 1-29页

作者： Peng, Zhichao Appelo, Daniel Liu, Shuang Hong Kong Univ Sci & Technol Dept Math Kowloon Clear Water Bay Hong Kong Peoples R China Virginia Tech Dept Math 225 Stanger St Blacksburg VA 24061 USA Univ North Texas Dept Math Denton TX 76201 USA

We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat and Poisson equation with Dirichlet boundary conditions. When the system needs to be inverted we can use the conjugate gradient method, accelerated by algebraic multigrid techniques. A series of numerical tests for the wave, heat and Poisson equation and applications to shape optimization problems verify the accuracy, stability, and efficiency of our method. Our fast computational techniques can be extended to moving boundary problems (e.g. Stefan problem), to the Navier-Stokes equations, and to the Grad-Shafranov equations for which problems are posed on domains with complex geometry and fast simulations are of great interest.

关键词： Algebraic multigrid embedded boundary method Line-by-line interpolation Radial basis function interpolation

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An embedded boundary method for soluble surfactants with interface tracking for two-phase flows

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JOURNAL OF COMPUTATIONAL PHYSICS 2014年 256卷 768-790页

作者： Khatri, Shilpa Tornberg, Anna-Karin NYU Courant Inst Math Sci New York NY 10003 USA Royal Inst Technol KTH Dept Math Linne Flow Ctr Stockholm Sweden

Surfactants, surface reacting agents, lower the surface tension of the interface between fluids in multiphase flow. This capability of surfactants makes them ideal for many applications, including wetting, foaming, and dispersing. Due to their molecular composition, surfactants are adsorbed from the bulk fluid to the interface between the fluids, leading to different concentrations on the interface and in the fluid. In a previous paper [21], we introduced a new second order method using uniform grids to simulate insoluble surfactants in multiphase flow. This method used Strang splitting allowing for a fully second order treatment in time. Here, we use the same numerical methods to explicitly represent the singular interface, treat the interfacial surfactant concentration, and couple with the Navier-Stokes equations. Now, we introduce a second order method for the surfactants in the bulk that continues to allow the use of regular grids for the full problem. Difficulties arise since the boundary condition for the bulk concentration, which handles the flux of surfactant between the interface and bulk fluid, is applied at the interface which cuts arbitrarily through the regular grid. We extend the embedded boundary method, introduced in [22], to handle this challenge. Through our results, we present the effect of the solubility of the surfactants. We show results of drop dynamics due to resulting Marangoni stresses and of drop deformations in shear flow in the presence of soluble surfactants. There is a large nondimensional parameter space over which we try to understand the drop dynamics. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Soluble surfactants embedded boundary method Interface tracking Two-phase flows Strang splitting Marangoni forces

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A conservative coupling algorithm between a compressible flow and a rigid body using an embedded boundary method

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JOURNAL OF COMPUTATIONAL PHYSICS 2012年第7期231卷 2977-2994页

作者： Monasse, L. Daru, V. Mariotti, C. Piperno, S. Tenaud, C. Univ Paris Est CERMICS F-77455 Marne La Vallee France CEA DIF F-91297 Arpajon France CNRS LIMSI F-91403 Orsay France Arts & Metiers Paris Tech DynFluid Lab F-75013 Paris France

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an embedded boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a finite volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [V. Daru, C. Tenaud, J. Comput. Phys. (2004)]. The embedded boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The efficiency of the method is demonstrated on challenging one- and two-dimensional benchmarks. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Compressible flows Shock capturing scheme Discrete Element method Fluid-structure interaction embedded boundary method

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Adaptive Mesh Refinement and embedded boundary method for Streamer Discharge Simulations 21

Adaptive Mesh Refinement and Embedded Boundary Method for St...

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IEEE 21st Biennial Conference on Electromagnetic Field Computation (IEEE CEFC)

作者： Lin, Bo Zhuang, Chijie Shi, Qingyuan Natl Univ Singapore Dept Math Singapore 119076 Singapore Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

ISBN: (纸本)9798350348958;9798350348965

We simulate streamer discharges in both two and three dimensions parallelly using an adaptive Cartesian mesh refinement and the embedded boundary method. A minimal fluid model is considered with a typical pin-plate domain. The embedded boundary method is taken to handle the curve boundary, and the adaptive mesh is introduced to reduce the number of degrees of freedom. Numerical experiments demonstrate the second-order convergence of the embedded boundary method and validate the efficiency of the adaptive mesh refinement. The effects of two different anode shapes are compared in three-dimensional streamer discharges.

关键词： Adaptive mesh refinement embedded boundary method parallel simulation streamer discharge

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High-order dimensionally-split Cartesian embedded boundary method for non-dissipative schemes

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JOURNAL OF COMPUTATIONAL PHYSICS 2022年 464卷

作者： Sharan, Nek Brady, Peter T. Livescu, Daniel Auburn Univ Dept Aerosp Engn Auburn AL 36849 USA Los Alamos Natl Lab CCS 2 Los Alamos NM 87545 USA

Centered finite-difference schemes are commonly used for high-fidelity turbulent flow simulations in canonical configurations because of their non-dissipative property and computational efficiency. However, their use in flow simulations over complex geometries is limited by the requirements of a structured grid and a stable boundary treatment in the absence of artificial (numerical) dissipation. Cartesian embedded boundary (EB) approaches provide an efficient structured-grid framework to apply difference schemes over complex domains. However, they are often restricted to low orders of accuracy because of numerical instabilities at the embedded boundaries and the issues of smallcell problem that are difficult to address with high-order accuracy. The present work discusses a systematic approach to obtain high-order EB methods with non-dissipative centered schemes in the interior. This approach, based on satisfying the primary and secondary conservation conditions, is employed to derive EB schemes that are up to sixthorder accurate in the interior and fourth-order accurate globally for hyperbolic, parabolic as well as incompletely parabolic problems. The proposed finite-difference discretization is, by construction, dimensionally split and addresses the small-cell problem without any cell/geometry transformations, thus, highly simplifying implementation in a flow solver. Various linear and non-linear numerical tests are performed to evaluate the stability and the accuracy of the proposed EB schemes.

关键词： embedded boundary method Conservative schemes High order Finite-difference schemes

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Frequency-domain acoustic full waveform inversion with an embedded boundary method for irregular topography

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EXPLORATION GEOPHYSICS 2023年第3期54卷 241-252页

作者： Park, Yunhui Hwang, Jongha Korea Inst Ocean Sci & Technol Marine Act Fault Res Grp 385 Haeyang Ro Busan 49111 South Korea

In the implementation of full waveform inversion (FWI) to identify subsurface velocity distributions with land seismic data, which are often acquired in regions with irregular topography, wave equation-based modelling requires caution. In particular, when using the finite difference method (FDM), unwanted scattered waves are generated because irregular surfaces crossing a rectangular grid are discretized via a staircase approximation;hence, if the problems caused by this staircase approximation are disregarded, FDM-based FWI may fail due to the presence of undesirable wavefields. To resolve this problem, this study develops a 2D frequency-domain acoustic FWI technique using a 9-point FDM-based modelling scheme that includes an embedded boundary method (EBM). This study suggests a workflow for the whole EBM-based FWI process from the calculation of coefficients for the EBM-based 9-point FDM modelling to applying it to FWI for proper velocity updates. In numerical examples, using velocity models with a tilted surface and an arbitrarily fluctuating surface, we synthesize seismic data and verify the accuracy of EBM-based 9-point FDM modelling and its superiority over the conventional FDM by comparing it with wavefields derived from the spectral element method. Then, we show that our EBM-based FWI is able to estimate subsurface velocity distributions even though the model has irregular topography, which spoils the result of the conventional FWI.

关键词： embedded boundary method full waveform inversion irregular topography complex surface Lagrangian interpolation

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Aerodynamic optimization with large shape and topology changes using a differentiable embedded boundary method

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JOURNAL OF COMPUTATIONAL PHYSICS 2023年 488卷

作者： Ho, Jonathan Farhat, Charbel Stanford Univ Dept Aeronaut & Astronaut Durand Bldg Room 224-12 Stanford CA 94305 USA Stanford Univ Dept Aeronaut & Astronaut Dept Mech Engn Durand Bldg Room 257 Stanford CA 94305 USA Stanford Univ Inst Computat & Math Engn Durand BldgRoom 257 Stanford CA 94305 USA

embedded (or immersed) boundary methods (EBMs) for CFD and fluid-structure interaction (FSI) are attractive for aerodynamic optimization problems characterized by large shape deformations and surface topology changes. At each iteration, they eliminate the need for explicitly remeshing a computational fluid domain and avoid the pitfalls of transferring information from one CFD mesh to another. However, they are vulnerable to discrete events that compromise the smoothness of the aerodynamic objective and/or constraint functions they may compute. For this reason, the realization of EBMs for gradient-based aerodynamic shape optimization requires first their endowment with sufficient smoothness guarantees. Drawing on a recently developed EBM for the solution of compressible viscous fluid and FSI problems with such guarantees, this paper demonstrates the potential of shape-differentiable EBMs for discovering optimal aerodynamic designs featuring significant shape deformations and surface topology changes. Specifically, it highlights their advantages in terms of reliability with respect to large shape adjustments and surface topology changes, efficiency, simplicity, and reduced need for user intervention. To this end, the paper showcases the application of an advanced EBM with smoothness guarantees to wing shape, wing section, and nacelle-pylon placement optimization problems formulated for a NASA Common Research Model (CRM). & COPY;2023 Elsevier Inc. All rights reserved.

关键词： Computational fluid dynamics Aerodynamic shape optimization embedded boundary method Immersed boundary method Discrete events Spurious force oscillations

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A strongly coupled, embedded-boundary method for fluid-structure interactions of elastically mounted rigid bodies

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JOURNAL OF FLUIDS AND STRUCTURES 2008年第2期24卷 167-182页

作者： Yang, J. Preidikman, S. Balaras, E. Univ Maryland Dept Mech Engn College Pk MD 20816 USA

In the present paper, an embedded-boundary formulation that is applicable to fluid-structure interaction problems is presented. The Navier-Stokes equations for incompressible flow are solved on a Cartesian grid which is not aligned with the boundaries of a body that undergoes large-angle/large-displacement rigid,body motions through the fixed grid. A strong-coupling scheme is adopted, where the fluid and the structure are treated as elements of a single dynamical system, and all of the governing equations are integrated simultaneously and interactively in the time domain. A demonstration of the accuracy and efficiency of the method is given for a variety of fluid-structure interaction problems. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： fluid-structure interactions strong coupling incompressible flows embedded boundary method sharp interface finite difference method

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