Computation of viscous flow between two arbitrarily moving cylinders of arbitrary cross section
A. O. Kazakovaa, A. G. Petrovb
a Chuvash State University, Cheboksary, 428015 Russia
b Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 117526 Russia
An algorithm is constructed for numerical study of the plane viscous flow (in the Stokes approximation) between two arbitrarily moving cylinders of arbitrary cross section. The mathematical model of the problem is described by the biharmonic equation, which is reduced, with the help of the Goursat representation, to a system of equations for two harmonic functions. The system is solved numerically by applying the boundary element method without saturation. As a result, the desired biharmonic stream function and the velocity field are determined. Test examples are used to compare the results with well-known exact solutions for circular cylinders.
viscous flow, Stokes approximation, stream function, biharmonic equation, boundary element method.
|Russian Science Foundation
|This work was supported by the Russian Science Foundation, project no. 19-19-00373.
Computational Mathematics and Mathematical Physics, 2019, 59:6, 1030–1048
A. O. Kazakova, A. G. Petrov, “Computation of viscous flow between two arbitrarily moving cylinders of arbitrary cross section”, Zh. Vychisl. Mat. Mat. Fiz., 59:6 (2019), 1063–1082; Comput. Math. Math. Phys., 59:6 (2019), 1030–1048
Citation in format AMSBIB
\by A.~O.~Kazakova, A.~G.~Petrov
\paper Computation of viscous flow between two arbitrarily moving cylinders of arbitrary cross section
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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