Characteristic-Based Split (CBS) Finite Element Method for Incompressible Viscous Flow with Moving Boundaries

Abstract

This paper gives an insight into the existing ALE (arbitrary Lagrangian Eulerian)-CBS (characteristic-based split) method and proposes an alternative CBS scheme for incompressible viscous flow with moving boundaries. First, the existing CBS scheme in ALE framework is reformulated from the Navier-Stokes (NS) equations in Eulerian description, and its advantages and drawbacks are discussed. Then, the classical semi-implicit CBS scheme is combined with the segment spring analogy method, and a new CBS solution procedure in Eulerian framework is developed for moving mesh. By the proposed CBS scheme, the influence of the mesh velocity in the existing ALE-CBS method is circumvented, and the extension of the existing CBS schemes and programs for fixed boundary problems to moving boundary problems seems to be more convenient. Finally, two moving boundary problems, namely the broken dam problem and the flow around an oscillating circular cylinder are presented. Numerical results from the proposed CBS scheme agree very well with available results in literature and show a slightly higher accuracy than those from the existing ALE-CBS method. Combined with other classical CBS schemes involving compressibility, turbulence, viscoelasticity, etc. and suitable moving mesh techniques, the proposed CBS solution procedure could be applied widely to the moving boundary problems in engineering.