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A hybrid finite element-least-square point interpolation method for solving multifluid coupling acoustic problems

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Recently, a finite element-least-square point interpolation method (FE-LSPIM) was introduced into solving the two-dimensional (2D) homogeneous acoustic problems. This paper presents the FE-LSPIM for solving multifluid coupling acoustic problems by incorporating the coupling interface condition between the different fluid domains. In the present work, the coupling interface between the different fluids should satisfy the continuity conditions of pressure and normal particle velocity, the multifluid domain is discretized using quadrilateral element (for 2D problem) or hexahedron element (for 3D problem), and the shape functions of the quadrilateral element (or hexahedron element) are used for partition of unity (PU) and the least-square point interpolation method (LSPIM) for local approximation. This paper derives the formulas of the FE-LSPIM for solving multifluid coupling acoustic problems. Considering the superior performance of the FE-LSPIM for the homogeneous acoustic problem, the FE-LSPIM can also deal well with the multifluid coupling acoustic problems, and numerical examples on a multifluid coupling tube show that the FE-LSPIM achieves more accurate results and higher convergence rates as compared with the corresponding finite elements and element-free Galerkin method (EFGM). Hence, the FE-LSPIM can be well applied in solving multifluid coupling acoustic problems.
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Keywords: 26; 75.3

Document Type: Research Article

Affiliations: Southwest University

Publication date: 01 June 2017

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