Solution of Viscous Flow around a Circular Cylinder by a New Integral Representation Method (NIRM)
Keywords:New integral representation method (NIRM), Primary space-differential operator, Vorticity, Navier-Stokes equation
AbstractNew nonlinear integral representations (NIRM) are derived from a nonlinear differential-type boundary value problem using a fundamental solution of the primary space-differential operator of the differential equation. Integral representations are equivalent to differential equations. A set of integral representations is an integral-type boundary value problem. Unknown variables of a boundary value problem can be determined by solving a set of integral equations obtained from a set of integral representations. In the present paper, a set of integral representations using the fundamental solution of the primary space-differential operator is derived for viscous flows. The velocity, vorticity, and pressure of the Navier-Stokes equation can be determined by solving a set of integral equations obtained from a set of integral representations. A new numerical solution of the Navier-Stokes equation is proposed based on integral representations. The integral representation method was used to obtain the numerical results of low-Reynolds-number laminar flows around a circular cylinder. The narrower regions and coarser meshes are used in the numerical calculations using the integral representation method than in those using the ordinary FEM. The numerical results correctly reflect the experimental ones. Unlike FEM, as seen from that constant distribution of the unknown variables is possible, NIRM may not assume the continuity of the unknown variables between elements from the beginning. It would be safe to say this is a big advantage of NIRM.
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