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Wavy properties and analytical modeling of free-surface flows in the development of the multi-domain method

Journal of Hydrodynamics 2016年第6期28卷 971-976页

作者： Xiaobo CHEN Hui LIANG Deepwater Technology Research Centre Bureau Veritas

The wavy （oscillatory both in space and in time） properties of free-surface flows due to presence of floating bodies are analyzed within the framework of the potential-flow theory by assuming that the fluid is perfect and flow irrotational. A so-called new multi-domain method has been developed based on the fluid domain division by an analytical control surface surrounding bodies and the application of different methods adapted in the external and internal domains. In the analytical domain external to the control surface, the fundamental solution satisfying the linear boundary condition on the free surface associated with a point singularity （often called Green fimction and referred here as point solution） is applied to capture all wavy features of free-surface flows extending horizontally to infinity. Unlike classical studies in which the control surface is discretized, the unknown velocity potential and its normal derivatives are expressed by expansions of orthogonal elementary functions. The velocity potential associa- ted with each elementary distribution （elementary solutions） on the control surface can be obtained by performing multi-fold inte- grals in an analytical way. In the domain internal to the control surface containing the bodies, we could apply different methods like the Rankine source method based on the boundary integral equations for which the elementary solutions obtained in the external domain playing the role of Dirichlet-to-Neumarm operator close the problem.

关键词： analytical modeling multi-domain method point solution (PS) elementary solution (ES) body solution (BS)

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A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

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JOURNAL OF COMPUTATIONAL PHYSICS 2017年 347卷 506-532页

作者： Liang, Hui Chen, Xiaobo Bur Veritas DTRC Singapore 117674 Singapore Univ Western Australia Sch Civil Environm & Min Engn Perth WA Australia

A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [D-N(2)] and Neumann-to-Dirichlet [N-D(2)] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Green function multi-domain method Fourier-Laguerre series Dirichlet-to-Neumann Irregular frequencies Wave radiation/diffraction

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Wavy properties and analytical modeling of free-surface flows in the development of the multi-domain method

Wavy properties and analytical modeling of free-surface flow...

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第二届全球华人水动学学术会议

作者： Xiaobo Chen Hui Liang Deepwater Technology Research Centre

The wavy(oscillatory both in space and in time) properties of free-surface flows due to presence of floating bodies are analyzed within the framework of the potential-flow theory by assuming that the fluid is perfect and flow irrotational.A so-called new multi-domain method has been developed based on the fluid domain division by an analytical control surface surrounding bodies and the application of different methods adapted in the external and internal *** the analytical domain external to the control surface,the fundamental solution satisfying the linear boundary condition on the free surface associated with a point singularity(often called Green function and referred here as point solution) is applied to capture all wavy features of free-surface flows extending horizontally to *** classical studies in which the control surface is discretized,the unknown velocity potential and its normal derivatives are expressed by expansions of orthogonal elementary *** velocity potential associated with each elementary distribution(elementary solutions) on the control surface can be obtained by performing multi-fold integrals in an analytical *** the domain internal to the control surface containing the bodies,we could apply different methods like the Rankine source method based on the boundary element integral equations for which the elementary solutions obtained in the external domain playing the role of Dirichlet-toNeumann operator close the problem.

关键词： Analytical modeling multi-domain method point solution(PS) elementary solution(ES) body solution(BS)

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A spectral coupled boundary element method for the simulation of nonlinear surface gravity waves

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JOURNAL OF OCEAN ENGINEERING AND SCIENCE 2025年第1期10卷 123-135页

作者： Shi, Kaiyuan Zhu, Renchuan Xu, Dekang Shanghai Jiao Tong Univ Sch Naval Architecture Ocean & Civil Engn State Key Lab Ocean Engn Shanghai 200240 Peoples R China

The challenge of simulating the broad open sea with limited computational resources has long been of interest in ocean engineering research. In view of this issue, this paper proposes a fully nonlinear potential flow method named the spectral coupled boundary element method (SCBEM). By leveraging the approach of domain decomposition, SCBEM achieves significantly reduced computational cost and an order of magnitude increase in computational domain compared to the conventional boundary element method (BEM). The SCBEM encompasses the marine structure with only a tiny BEM domain and employs a high-order spectral layer to simulate the broad water outside the BEM domain. The performance of the SCBEM is evaluated through comparison with the wave damping approach and literature results for regular waves, modulated wave trains, focused waves, and diffraction of a vertical cylinder. The numerical results demonstrate the effectiveness and accuracy of the SCBEM in simulating a wide range of wavelengths and nonlinear wave interactions. (c) 2023 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/)

关键词： domain decomposition multi-domain method Fully nonlinear Wave-body interaction Potential flow theory

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A multi-domain BEM based on dual interpolation boundary face method for 3D elasticity problem

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2022年 143卷 568-578页

作者： Chai, Pengfei Zhang, Jianming Xiao, Rongxiong He, Rui Lin, WeiCheng Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China

The dual interpolation boundary face method with Hermite-type moving-least-squares approximation (DiBFMHMLS), presented recently, has certain advantages in simulating the discontinuous fields. Based on the DiBFMHMLS and the matrix condensation technique, we proposed a multi-domain method for 3D elasticity problems in this paper. This method ensures an accurate interpolation for the multi-domain models with short edges or small chamfers. In the multi-domain DiBFM-HMLS, the virtual points in each subdomain, not as collocation points in the boundary integral equation (BIE), are eliminated by the HMLS approximation separately. Then, only the interfacial source points are reserved by the matrix condensation technique. The node-to-node interfacial condition in previous research is unemployed;instead of the former, a node-to-element format is constructed based on the moving-least-squares approximation (MLS). This mapping scheme possesses the potential for free mesh in the interface. Several numerical examples are used to reflect these advantages mentioned above.

关键词： multi-domain method Short edge and small chamfers Dual interpolation boundary face method Hermite-type approximation

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A multi-domain Fourier pseudospectral time-domain method for the linearized Euler equations

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JOURNAL OF COMPUTATIONAL PHYSICS 2012年第14期231卷 4759-4774页

作者： Hornikx, Maarten De Roeck, Wim Desmet, Wim Eindhoven Univ Technol Bldg Phys & Serv NL-5600 MB Eindhoven Netherlands Katholieke Univ Leuven B-3001 Heverlee Belgium

The Fourier pseudospectral time-domain (F-PSTD) method is computationally one of the most cost-efficient methods for solving the linearized Euler equations for wave propagation through a medium with smoothly varying spatial inhomogeneities in the presence of rigid boundaries. As the method utilizes an equidistant discretization, local fine scale effects of geometry or medium inhomogeneities require a refinement of the whole grid which significantly reduces the computational efficiency. For this reason, a multi-domain F-PSTD methodology is presented with a coarse grid covering the complete domain and fine grids acting as a subgrid resolution of the coarse grid near local fine scale effects. Data transfer between coarse and fine grids takes place utilizing spectral interpolation with super-Gaussian window functions to impose spatial periodicity. Local time stepping is employed without intermediate interpolation. The errors introduced by the window functions and the multi-domain implementation are quantified and compared to errors related to the initial conditions and from the time iteration scheme. It is concluded that the multidomain methodology does not introduce significant errors compared to the single-domain method. Examples of scattering from small scale density scatters, sound reflecting from a slitted rigid object and sound propagation through a jet are accurately modelled by the proposed methodology. For problems that can be solved by F-PSTD, the presented methodology can lead to a significant gain in computational efficiency. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Fourier pseudospectral method Linearized Euler equations multi-domain method multi-rate method Grid refinement

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A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2008年第25-28期197卷 2131-2146页

作者： Colonius, Tim Taira, Kunihiko CALTECH Div Engn & Appl Sci Pasadena CA 91125 USA

We report on the continued development of a projection approach for implementing the immersed boundary method for incompressible flows in two and three dimensions. Boundary forces and pressure are regarded as Lagrange multipliers that enable the no-slip and divergence-free constraints to be implicitly determined to arbitrary precision with no associated time-step restrictions. In order to accelerate the method, we further implement a nullspace (discrete streamfunction) method that allows the divergence-free constraint to be automatically satisfied to machine roundoff. By employing a fast sine transform technique, the linear system to determine the forces can be solved efficiently with direct or iterative techniques. A multi-domain technique is developed in order to improve far-field boundary conditions that are compatible with the fast sine transform and account for the extensive potential flow induced by the body as well as vorticity that advects/difluses to large distance from the body. The multi-domain and fast techniques are validated by comparing to the exact solutions for the potential flow induced by stationary and propagating Oseen vortices and by an impulsively-started circular cylinder. Speed-ups of more than an order-of-magnitude are achieved with the new method. (C) 2007 Elsevier B.V. All rights reserved.

关键词： immersed boundary method fractional step method projection method nullspace method vorticity/streamfunction formulation far-field boundary conditions multi-domain method fast Poisson solver finite volume method incompressible viscous flow

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Analysis of the dissipation and dispersion properties of the multi-domain Chebyshev pseudospectral method

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JOURNAL OF COMPUTATIONAL PHYSICS 2013年 255卷 31-47页

作者： Dragna, D. Bogey, C. Hornikx, M. Blanc-Benon, P. Univ Lyon Ecole Cent Lyon UMR CNRS 5509 Lab Mecan Fluides & Acoust F-69134 Ecully France Eindhoven Univ Technol NL-5600 MB Eindhoven Netherlands

The accuracy of the multi-domain Chebyshev pseudospectral method is investigated for wave propagation problems by examining the properties of the method in the wavenumber space theoretically in terms of dispersion and dissipation errors. For a number of (N + 1) points in the subdomains used in the literature, with N typically between 8 to 32, significant errors can be obtained for waves discretized by more than pi points per wavelength. The dispersion and dissipation errors determined from the analysis in the wavenumber space are found to be in good agreement with those obtained in test cases. Accuracy limits based on arbitrary criteria are proposed, yielding minimum resolutions of 7.7, 5.2 and 4.0 points per wavelength for N = 8, 16 and 32 respectively. The numerical efficiency of the method is estimated, showing that it is preferable to choose N between 16 and 32 in practice. The stability of the method is also assessed using the standard fourth-order Runge-Kutta algorithm. Finally, 1-D and 2-D problems involving long-range wave propagation are solved to illustrate the dissipation and dispersion errors for short waves. The error anisotropy is studied in the 2-D case, in particular for a hybrid Fourier-Chebyshev configuration. (c) 2013 Elsevier Inc. All rights reserved.

关键词： Chebyshev pseudospectral method Wave propagation multi-domain method

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A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations

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JOURNAL OF COMPUTATIONAL PHYSICS 2013年 244卷 63-79页

作者： Moghadam, Mahdi Esmaily Vignon-Clementel, Irene E. Figliola, Richard Marsden, Alison L. USCD San Diego CA USA INRIA Paris Rocquencourt Le Chesnay France Clemson Univ Clemson SC USA

Implementation of boundary conditions in cardiovascular simulations poses numerical challenges due to the complex dynamic behavior of the circulatory system. The use of elaborate closed-loop lumped parameter network (LPN) models of the heart and the circulatory system as boundary conditions for computational fluid dynamics (CFD) simulations can provide valuable global dynamic information, particularly for patient specific simulations. In this paper, the necessary formulation for coupling an arbitrary LPN to a finite element Navier-Stokes solver is presented. A circuit analogy closed-loop LPN is solved numerically, and pressure and flow information is iteratively passed between the 0D and 3D domains at interface boundaries, resulting in a time-implicit scheme. For Neumann boundaries, an implicit method, regardless of the LPN, is presented to achieve the desired stability and convergence properties. Numerical procedures for passing flow and pressure information between the 0D and 3D domains are described, and implicit, semi-implicit, and explicit quasi-Newton formulations are compared. The issue of divergence in the presence of back-flow is addressed via a stabilized boundary formulation. The requirements for coupling Dirichlet boundary conditions are also discussed and this approach is compared in detail to that of the Neumann coupled boundaries. Having the option to select between Dirichlet and Neumann coupled boundary conditions increases the flexibility of current framework by allowing a wide range of components to be used at the 3D-0D interface. (c) 2012 Elsevier Inc. All rights reserved.

关键词： Lumped parameter network Neumann Dirichlet Boundary condition Backflow stabilization Patient-specific blood flow Navier-Stokes FEM solver multi-domain method multi-scale modeling

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Interface integral BEM for solving multi-medium heat conduction problems

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2009年第4期33卷 539-546页

作者： Gao, Xiao-Wei Wang, Jing Southeast Univ Sch Civil Engn Dept Engn Mech Nanjing 210096 Peoples R China

In this paper, a new and simple boundary element method, called interface integral boundary element method (IIBEM), is presented for solving heat conduction problems consisting of multiple media. In the method, the boundary integral equation is derived by a degeneration technique from domain integrals involved in varying heat conductivity problems into interface integrals in multi-medium problems. The main feature of the presented technique is that only a single boundary integral equation is used to solve heat conduction problems with different material properties, The effect of nonhomogeneity between adjacent materials is embodied in the interface integrals including the material property difference between the two adjacent materials. Comparing with conventional multi-domain boundary integral equation techniques, the presented method is more efficient in computational time, data preparing, and program coding. Numerical examples are given to verify the correctness of the presented technique. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Boundary integral equation multi-domain method Heat conduction Nonhomogeneous problem

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