Viscoelastic flow in an undulating tube using spectral methods

The flow of a viscoelastic fluid through an undulating tube is considered. The fluid is modelled using the UCM constitutive equation. The governing set of equations is solved using a time-splitting technique. This is based on separate treatments of the convection and generalised Stokes operators. The spatial discretisation is based on a spectral discretisation in which the radial basis functions satisfy the conditions along the axis of symmetry of the tube explicitly. Compatible approximation spaces are chosen for velocity, pressure and extra-stress. The convection problem is solved in a type-sensitive manner using a high-order Runge-Kutta method. The weak formulation of the generalised Stokes problem is discretised and solved using a nested conjugate gradient technique. The effect of elasticity on flow resistance is investigated and comparisons made with other results in the literature.