A potential flow method combining immersed boundaries and overlapping grids: Formulation, validation and verification

Hanssen, Finn-Christian W.; Greco, Marilena

doi:10.1016/j.oceaneng.2021.108841

Cited by 7 publications

(5 citation statements)

References 20 publications

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“…The application of the Monte Carlo method in similar research was reported by Xia et al [9]. Moreover, meshfree techniques are gaining attention in the simulation of groundwater flow, and the literature reported includes the meshfree collocation method [5,6], element-free Galerkin method [10], meshless local Petrov-Galerkin method [11], and immersed boundary method [12]. Other environmental flows which require the application of potential flow theory are groundwater-surface water interaction [13], granular flow [14], and interface flow [15].…”

Section: Introductionmentioning

confidence: 70%

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Semi-Analytical Method for Unsymmetrical Doublet Flow Using Sink- and Source-Dominant Formulation

et al. 2022

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Potential flow formed by doublet flow has been well applied in environmental applications and geothermal designs such as reservoir and fuel injectors. Most of the doublet flow is assumed based on the sink and source with equivalent strength and distance from the origin, forming the well-known Rankine oval structure when a far-field flow is superposed. A semi-analytical method is formulated to systematically investigate the unsymmetrical doublet flow with different strengths of sink and source. The general mathematical expression for unsymmetrical doublet flow is derived analytically before the streamline and the potential line can be visualised via a numerical approach. The results revealed that the doublet flows altered the Rankine oval structure to form aerofoil-like geometry. When the far-field flow interferes with the general Doublet configuration, unique flow structures such as convex, concave, and various wing shapes could be generated. The current study provides new insight on producing aerodynamic curves for the design of bio-inspired structures.

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Section: Introductionmentioning

confidence: 70%

“…With the trigonometric formulation as in Table 1, Equation ( 10) can be thus written as a function of tan (θ g ). Now, tan (θ g ), or tan (θ 1 ) and tan (θ 2 ) can further be expanded to form Equations ( 11) and (12), respectively.…”

Section: Mathematical Formulation Of Unsymmetrical Doublet Flowmentioning

confidence: 99%

Semi-Analytical Method for Unsymmetrical Doublet Flow Using Sink- and Source-Dominant Formulation

et al. 2022

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“…Such high values of the λ/D ratio, often encountered in practical engineering applications, are more easily taken into account with a second grid fitting the body than with a choice of higher order cell or with a local refinement of the grid. Note that the solution combining both a secondary grid and a solid immersed boundary has been tested by Hanssen (2019); Hanssen and Greco (2021) with promising results. On this subject Ma et al (2017, § 4.2.2) applied this combination to model the free surface and obtained a important reduction of the resulting error.…”

Section: A Double Mesh Strategy To Adapt the Resolution In The Vicinity Of A Bodymentioning

confidence: 99%

“…Note that using a single free surface with different set of markers is also possible (see e.g. Hanssen, 2019;Hanssen and Greco, 2021). The free surface evolving in the background grid is truncated such that no marker is defined inside the body (i.e.…”

Section: Free Surface Piercing Bodymentioning

confidence: 99%

Development and validation of a numerical wave tank based on the Harmonic Polynomial Cell and Immersed Boundary methods to model nonlinear wave-structure interaction

Robaux

Benoît

2021

Journal of Computational Physics

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A fully nonlinear potential Numerical Wave Tank (NWT) is developed in two dimensions, using a combination of the Harmonic Polynomial Cell (HPC) method for solving the Laplace problem on the wave potential and the Immersed Boundary Method (IBM) for capturing the free surface motion. This NWT can consider fixed, submerged or wall-sided surface piercing, bodies. To compute the flow around the body and associated pressure field, a novel multi overlapping grid method is implemented. Each grid having its own free surface, a two-way communication is ensured between the problem in the body vicinity and the larger scale wave propagation problem. Pressure field and nonlinear loads on the structure are computed by solving a boundary value problem on the time derivative of the potential. The stability and convergence properties of the solver are studied basing on extensive tests with standing waves of large to extreme wave steepness, up to H/λ = 0.2 (H is the crest-to-trough wave height and λ the wavelength). Ranges of optimal time and spatial discretizations are determined and high-order convergence properties are verified, first without using any filter. For cases with either high level of nonlinearity or long simulation duration, the use of mild Savitzky-Golay filters is shown to extend the range of applicability of the model. Then, the NWT is tested against two wave flume experiments, analyzing forces on bodies in various wave conditions. First, nonlinear components of the vertical force acting on a small horizontal circular cylinder with low submergence below the mean water level are shown to be accurately simulated up to the third order in wave steepness. The second case is a dedicated experiment with a floating barge of rectangular cross-section. This very challenging case (body with sharp corners in large waves) allows to examine the behavior of the model in situations at and beyond the limits of its formal application domain. Though effects associated with viscosity and flow separation manifest experimentally, the NWT proves able to capture the main features of the wave-structure interaction and associated loads.

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“…Over the years, various solvers have been developed and proposed to address this challenge. These solvers include boundary element methods (BEMs), e.g., Yang and Ertekin (1992), Teng and Eatock Taylor (1995), Kashiwagi et al (1998), Newman and Lee (2002); finite element methods (FEMs), e.g., Wu and Eatock Taylor (1994), Ma et al (2001a, b); finite difference methods (FDMs), e.g., Bingham and Zhang (2007), Engsig Karup et al (2009); harmonic polynomial cell (HPC) methods, e.g., Faltinsen (2012, 2014a, b), Hanssen and Greco (2021). For a smooth variation (i.e., when the weak derivatives are continuous), the solution space can be embedded by appropriate regular basis spaces as 𝐻 𝑘∈ + , for example, the polynomial basis.…”

Section: Introductionmentioning

confidence: 99%

Semi-analytic solutions to edge singularities of three-dimensional axisymmetric bodies

2023

Physics of Fluids

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Axisymmetric geometries, such as cylindrical elements, are widely used in offshore structures. However, the presence of sharp edges in these geometries introduces challenges in numerical simulations due to singularities. To address this issue, one possible solution is to represent the singularities using analytic eigenfunctions. This approach can provide insights into the essence of the problem and has successfully applied to two-dimensional (2D) corner problems. However, finding appropriate eigenfunctions for the three-dimensional (3D) edges remains an open challenge. This paper proposes a semi-analytic scheme for 3D axisymmetric problems utilizing a scaled boundary finite element method (SBFEM). A dimensional reduction is introduced to the 3D Laplace equation, and a 3D edge is handled on the generatrix plane while governed by a complicated equation. The algorithm for resolving the SBFEM fundamental space is improved, and the singularities are approximated using a fractional-order basis. The effectiveness of the proposed method is demonstrated through its application to solve the radiation problem of a heaving cylinder. The method accurately captures the singular velocity field at the edge tip, ensuring that the boundary condition on the body surface is strictly satisfied in the neighborhood of the singularity. Accuracy of the mean drift force is ensured by performing direct pressure integrations over the body surface using a near-field formulation, which becomes as accurate as the middle-field formulation.

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A potential flow method combining immersed boundaries and overlapping grids: Formulation, validation and verification

Cited by 7 publications

References 20 publications

Semi-Analytical Method for Unsymmetrical Doublet Flow Using Sink- and Source-Dominant Formulation

Semi-Analytical Method for Unsymmetrical Doublet Flow Using Sink- and Source-Dominant Formulation

Development and validation of a numerical wave tank based on the Harmonic Polynomial Cell and Immersed Boundary methods to model nonlinear wave-structure interaction

Semi-analytic solutions to edge singularities of three-dimensional axisymmetric bodies

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