Scattering of a plane sound wave by a liquid body of complex shape
https://doi.org/10.22405/2226-8383-2025-26-1-164-180
Abstract
The problem of scattering of a plane harmonic sound wave by an obstacle in the form of a liquid body with a non-canonical shape and a piecewise-smooth surface, approximated by a polygonal mesh, is considered. The process model is based on the equations of hydrodynamics for an ideal fluid. Two numerical-analytical approaches to solving the problem are compared: the finite element method (FEM) and the boundary element method (BEM). In the first approach,
the obstacle is enclosed within a sphere, and the domain inside, taking into account the surface of the obstacle, is divided into spatial (3D) finite elements. In this domain, the problem is solved using FEM, which provides the potential values on the sphere. These values are then used to determine the coefficients of the spherical expansion of the scattered wave potential. In the second approach, using the spatial Green’s function for the Helmholtz equation, the problem is
reduced to a system of integral equations over the surface of the obstacle. The Burton-Miller method is also applied to eliminate the non-uniqueness of the solution, and singular integrals are regularized using identities for the static Green’s function. In the BEM, it is sufficient to divide the surface into boundary (2D) elements. The main equations for applying the numerical methods and the results of solving the sound scattering problem for a liquid body in the form of two spheres of equal radius are presented. It is established that to achieve acceptable accuracy in calculating the scattered field, the BEM requires significantly fewer computational resources compared to the FEM.
About the Authors
Dmitry Viktorovich Gorbachev
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Daniil Ruslanovich Lepetkov
Tula State University; Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
postgraduate student
Sergey Alekseevich Skobel’tsyn
Tula State University; Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
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Review
For citations:
Gorbachev D.V., Lepetkov D.R., Skobel’tsyn S.A. Scattering of a plane sound wave by a liquid body of complex shape. Chebyshevskii Sbornik. 2025;26(1):164-180. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-1-164-180
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