Efficient Unified Stokes using a Polynomial Reduced Fluid Model

Abstract

Unsteady Stokes solvers, coupling stress and pressure forces, are a key component of accurate free surface simulators for highly viscous fluids. Because of the simultaneous application of stress and pressure terms, this creates a much larger system than the standard decoupled approach. We propose a reduced fluid model wherein interior regions are represented with incompressible polynomial vector fields. Sets of standard grid cells are consolidated into super-cells, each of which are modelled using only 26 degrees of freedom. This reduced model retains desirable behaviour of the full Stokes system with smaller computational cost.