粘性流中の付加質量に関する高速計算法と有効性

概要

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In many fluid-structure interaction problems, the virtual mass, namely, the added mass, is one of important concepts. In the present study, we consider a simple method to specify the added-mass coefficients of arbitrary two-dimensional bodies with non-simple cross sections, efficiently and conveniently. Specifically, we consider a two-dimensional incompressible and viscous fluid under the assumption of infinitesimal oscillation amplitude of the body, and properly modify the full Navier-Stokes equations into linear equations, that is, the Brinkman equations. The solving method is based on a discrete singularity method (referred to as DSM), in which we employ a fundamental solution of the Brinkman equations as a singularity. In order to show the method's effectivity and validity, we compute a square cylinder in infinite flow field. Concretely speaking, we solve the full Navier-Stokes equations by a finite difference method (FDM), and compare such solutions with the DSMs. As a result, we reveal the non-linear amplitude effect and specify the valid range of the DSM.