Applications of Boundary Element Methods to Fluid Mechanics

Liggett, James A.; Liu, P. L.-F.

doi:10.1007/978-1-4899-2877-1_5

Cited by 5 publications

(4 citation statements)

References 27 publications

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“…Generally, all the NWT2D simulations show an excellent agreement with laboratory experiments, as they use the fullynonlinear governing water wave equations for an idealized fluid (Liggett and Liu 1984;Yeung 1982). In fact, the wave features in them are almost identical.…”

Section: Results Of Bem-based Nwt2d Simulationsmentioning

confidence: 53%

Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

Chabchoub

Waseda

Kibler

et al. 2017

J. Ocean Eng. Mar. Energy

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A possible mechanism that is responsible for the occurrence of rogue waves in the ocean is the Benjamin-Feir instability or modulation instability. The deterministic framework that describes this latter instability of Stokes waves in deep water is provided by the family of Akhmediev breather (AB) solutions of the nonlinear Schrödinger equation (NLS). It is indeed very convenient to use these exact pulsating envelopes particularly for laboratory experiments, since they allow to generate extreme waves at any location in space at any instant of time. As such, using this framework is more advantageous compared to the classical initialization of the unstable wave dynamics from a three wave system (main wave frequency and one pair of unstable sidebands). In this work, we report an experimental study on higher-order AB hydrodynamics that describe a higher-order stage of modulation instability, namely, starting from five wave systems (main wave frequency and two pairs of unstable sidebands). The corresponding laboratory experiments, that have been conducted in a large water wave facility, confirm the NLS wave dynamics forecast while boundary element method-

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Section: Results Of Bem-based Nwt2d Simulationsmentioning

confidence: 53%

Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

Chabchoub

Waseda

Kibler

et al. 2017

J. Ocean Eng. Mar. Energy

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“…Comments on the difficulty in obtaining the flow profile in spillway flow follow. Cheng et al [27] and Liggett [29] used the boundary element method to compute spillway flow. Their model considered a discrete version of Equation (11), which was forced to be satisfied by the free surface each time it was displaced using the Newton-Raphson method.…”

Section: Flow Over the Spillway Of A High Dammentioning

confidence: 99%

“…Comments on the difficulty in obtaining the flow profile in spillway flow follow. Cheng et al [27] and Liggett [29] used the boundary element method to compute spillway Figure 9 depicts remarkable aspects of the proposed computational method; Figure 9a,c,e show the critical depth profile, minimum total energy head profile, and the critical point for H/H D = 0.5, 1 and 1.33. Note that this is a generalization to 2D irrotational flows of open channel flow concepts used in gradually varied flow computations [32,40].…”

Section: Flow Over the Spillway Of A High Dammentioning

confidence: 99%

“…The elliptic problem can be solved by a variety of numerical methods [13]; obtaining an accurate solution is feasible with simple means. Solution methods in the literature include the finite difference method [12,[14][15][16][17][18], the finite element method [19][20][21][22][23][24][25][26], and the boundary element method [27][28][29]. The determination of the critical point, the energy head of irrotational flow, and the water surface profile for a given discharge is, however, not simple.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Determination of Irrotational Flow Profiles in Open-Channel Transitions

Castro-Orgaz,

Hager

2023

Water

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Transitional free surface flow profiles with a critical point occur with weak vorticity and viscosity effects and thus can be modeled with an irrotational flow approach. Important examples in hydraulic engineering include flow over low obstacles, transition structures in canals, and flow over high spillways. While solving Laplace’s equation is relatively simple, the determination of the unknown free surface and energy head of the flow is challenging. Both hydraulic quantities need to be iterated before solving the Laplace equation. Former models iterated the energy head on a trial-and-error basis, assuming that the linked free surface profile is smooth, i.e., free of waves. The iteration of the free surface for a given head is frequently accomplished using the Newton–Rapshon method, which is difficult for the challenging case of spillway flow, giving no solution in some cases. An alternative method of computing irrotational flow profiles in transitional flows involving a critical point is proposed in this work. The model contains three elements: mapping of Laplace’s equation to directly track the streamlines, determination of the critical point and unknown energy head using a critical flow condition for irrotational flows, and determination of the water surface position using an exact analytical solution. The proposed model is favorably compared with experimental data from different sources and CFD results, indicating a reasonable agreement.

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Applications of boundary integral equation methods for two‐dimensional non‐linear water wave problems

Liu

Hsu

Lean

1992

Numerical Methods in Fluids

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On the basis of the integral equation approach, numerical algorithms for solving non-linear water wave problem are presented. The free surface flow is assumed to be irrotational. Two different Green functions are used in the integral equations. The non-linear free-surface boundary conditions are treated by a timestepping Lagrangian technique. Several numerical examples are given, including permanent periodic waves, overturning progressive waves, breaking standing waves and sloshing problems.

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Applications of Boundary Element Methods to Fluid Mechanics

Cited by 5 publications

References 27 publications

Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

Analytical Determination of Irrotational Flow Profiles in Open-Channel Transitions

Applications of boundary integral equation methods for two‐dimensional non‐linear water wave problems

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