Free-Surface And Two-Fluid Flow Simulations On Unstructured Grids

Abstract

Free-surface and two-fluid flow simulations are computationally demanding tasks.
The freedom allowed when using unstructured grids can be exploited to develop efficient methods
for this type of problems. For instance, level-set methods and front tracking methods can be
combined onto an unstructured grid method that combines advantages of both methods. In this
work, methods to solve incompressible two-dimensional two-fluid flows on unstructured grids
are discussed. The Navier-Stokes equations are discretized by suitable finite element methods.
The numerical method for the solution is based on the projection method to uncouple the
system of non-linear equations. Strategies employed for the representation of the interface between
fluids are discussed. For instance, the interface can be represented by the zero level set
of a function plus additional marker points of the computational mesh. In the standard Eulerian
level-set method, this function is advected through the domain by solving a pure advection
equation. To reduce mass conservation errors that can arise from this step, a Lagrangian technique,
which moves the nodes of the finite element mesh, and consequently, the information
stored in each node, can be employed. Due to the large distortion of the mesh that can occur,
remeshing procedures are required in order to control de quality of the mesh. Results from some
simulations are shown to compare the mass conservation and accuracy of the various discussed
methodologies.