Simulation of viscoelastic fluids: Couette-Taylor flow
We present a numerical scheme for viscoelastic flow based on a second-order central differencing method recently introduced in the context of incompressible Newtonian flow; the incompressibility constraint is treated with the projection method. We implement the new method on Couette-Taylor flow for a fluid governed by the Oldroyd-B constitutive equations. A transient flow is simulated in a domain that includes at least eight wavelengths during many hundreds of natural periods. For weak elasticity, a stationary instability leading to Taylor vortices is observed. For a regime of parameters where both inertia and elasticity are important, the instability is oscillatory. In both cases the early stage growth rates are compared to linear stability calculations, showing good agreement. \(\copyright\) Academic Press.
second-order central differencing method
scientific article; zbMATH DE number 1282740