  This paper proposes an Arbitrary Lagrangian-Eulerian incompressible finite
volume scheme based on Consistent Flux Reconstruction method (ALE-CFR) on
deforming two-dimensional unstructured triangular grids. The scheme is further
applied to solve for a problem of two-dimensional incompressible viscous flow
past a rotationally oscillating circular cylinder when subjected to forced
transverse oscillations at Re = 100. The paper first focuses on the
mathematical development and validation of the ALE-CFR scheme and then its
application on the problem. The rotational oscillation frequencies were taken
corresponding to the four primary vortex shedding mode frequencies discovered
from the studies conducted by Tokumaru and Dimotakis. The transverse
oscillation frequency was varied for a frequency ratio $f_{tv}$ with respect to
natural strouhal frequency for flow past a stationary circular cylinder from
$0.9 \leq f_{tv} \leq 3.0$. The amplitude ratio for transverse oscillations was
taken as 0.2 with respect to the cylinder diameter. The distinct effects on the
vortex shedding patterns and the contributions of such rotational and
transverse oscillations on lift and drag characteristics of the circular
cylinder are studied using the newly developed scheme.
