Abstract
The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.
Highlights
In the field of interaction between fluid and structures, Finite Element Method (FEM) and Boundary Element Method (BEM) [1, 2] have been applied to predict the hydrodynamic force acting on the ocean structures
This paper shows the numerical analysis of the Indirect Boundary Element Method (IBEM)/ Desingularized Boundary Integral Equation Method (DBIEM) for solving smooth and nonsmooth boundary problems
The IBEM here has been used to solve the flow around the sphere whether the normal vector of the mesh has a mutation at the symmetry surface by using the symmetric condition in Green’s function
Summary
In the field of interaction between fluid and structures, Finite Element Method (FEM) and Boundary Element Method (BEM) [1, 2] have been applied to predict the hydrodynamic force acting on the ocean structures. Compared to the time-domain prediction based on the DBEM/IBEM, the frequency domain approaches [16] have been widely adopted to solve hydrodynamic problems Some commercial software, such as WAMIT [17] and HYDROSTAR [18], can evaluate in practical offshore engineering within the frequency domain. In order to improve the computation accuracy of IBEM for the solution of nonsmooth boundary problems, the Desingularized Boundary Integral Equation Method (DBIEM) is used/ will be employed to analyze the fluid flow problems, which has been used previously in solving wave-structure interaction problems such as in the work by Zhang et al [25, 26], Beck [27], Kim et al [28], Celebi [29], Kara et al [30], and Xu et al [31].
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