This work presents a three-dimensional finite-element algorithm, based on the phase-field model, for computing interfacial flows of Newtonian and complex fluids. A 3D adaptive meshing scheme produces fine grid covering the interface and coarse mesh in the bulk. It is key to accurate resolution of the interface at manageable computational costs. The coupled Navier-Stokes and Cahn-Hilliard equati...

In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large class of nonlinear continuity equations, whose dynamics are driven by internal energies, given external potentials and/or interaction energies. The solver is bas...

Wire-coating flow is simulated, involving polymer melt coatings and tube-tooling process design. A finite element method is employed, based on a semi-implicit time-stepping Taylor-Galerkin/pressure-correction scheme. The exponential Phan-Thien/Tanner model is used in its multi-mode form to represent a high-density polyethelyne (HDPE) polymer. Both shear-thinning and elongation-softening propert...

A finite element study of two and three-dimensional incompressible viscoelastic flows in a planar lid-driven cavity and concentric rotating cylinders is presented. The hardware platforms consist of both homogeneous and heterogeneous clusters of workstations. A semi-implicit time-stepping TaylorGalerkin scheme is employed using the message passing mechanism provided by the Parallel Virtual Machi...

To solve PDE problems with different time scales that are localized in space, multirate time integration is examined. This technique enables one to use large time steps for slowly time-varying spatial regions, and small steps for rapidly varying ones. Multirate time stepping is coupled with the local uniform grid refinement and provides a robust and efficient method for the target problem class...

Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in t...

This work is devoted to the design of interior penalty discontinuous Galerkin (dG) schemes that preserve maximum principles at the discrete level for the steady transport and convectiondiffusion problems and the respective transient problems with implicit time integration. Monotonic schemes that combine explicit time stepping with dG space discretization are very common, but the design of such ...

We consider a family of space discretisations for the approximation of nonlinear parabolic equations, such as the regularised mean curvature flow level set equation, using semi-implicit or fully implicit time schemes. The approximate solution provided by such a scheme is shown to converge thanks to compactness and monotony arguments. Numerical examples show the accuracy of the method.