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This paper proposes an Arbitrary Lagrangian-Eulerian incompressible finitevolume scheme based on Consistent Flux Reconstruction method (ALE-CFR) ondeforming two-dimensional unstructured triangular grids. The scheme is furtherapplied to solve for a problem of two-dimensional incompressible viscous flowpast a rotationally oscillating circular cylinder when subjected to forcedtransverse oscillations at Re = 100. The paper first focuses on themathematical development and validation of the ALE-CFR scheme and then itsapplication on the problem. The rotational oscillation frequencies were takencorresponding to the four primary vortex shedding mode frequencies discoveredfrom the studies conducted by Tokumaru and Dimotakis. The transverseoscillation frequency was varied for a frequency ratio $f_{tv}$ with respect tonatural strouhal frequency for flow past a stationary circular cylinder from$0.9 \leq f_{tv} \leq 3.0$. The amplitude ratio for transverse oscillations wastaken as 0.2 with respect to the cylinder diameter. The distinct effects on thevortex shedding patterns and the contributions of such rotational andtransverse oscillations on lift and drag characteristics of the circularcylinder are studied using the newly developed scheme.

Numerical Analysis of Flow Past an Oscillating Circular Cylinder using Arbitrary Lagrangian Eulerian Consistent Flux Reconstruction Scheme