Numerical Analysis of Fluid Flow in 2D Domains Containing Moving Objects

This study presented a two-dimensional (2D) numerical analysis of fluid flow in domains containing moving objects. The method falls into the general category of Arbitrary-Lagrangian-Eulerian (ALE) methods, which is based on a fixed mesh that is locally fitted at the moving objects and recovers its original shape once the moving objects go past the elements. The 2D domain occupied by the fluid at any time in the simulation is used as the reference domain and is discretized using a mesh of bilinear isoparametric finite elements, referred to as the basic mesh that remains fixed throughout the calculation. The moving objects are described using sets of marker points or nodes that define the moving bodies and can slide over the basic mesh at their velocity. At each time in the calculation the elements intersected by a moving object are subdivided to fit the boundary with a piecewise linear curve so that the nodes always remain on the element sides.  Once the moving object has gone through the stationary element, the element is restored to its original form. Therefore, the mesh adaptation is performed only in those elements intersected by an object and is local both in space and time. As a result, the method does not require interpolation and there are a fixed number of possible modifications to the intersected elements, only three in the 2D case, when quadrilateral elements are used.

As the global mesh is independent of object movement, therefore it eliminates the possibility of mesh entanglement. The mesh never becomes unsuitable due to its continuous deformation, thus eliminating the need for repeated re-meshing and interpolation. The present work concentrates on the development of the method to discretize and modify the mesh throughout the calculation. It has been applied to the case of only laminar incompressible flow at low Reynolds number. It should be noted that the same methodology can be applied directly to high Reynolds number compressible and turbulent flows and will be study in future. A validation is presented via a problem with an exact analytical solution to the case of 2D flow between two parallel plates separating with a prescribed velocity. Furthermore, the examples solved for a slanted interface, a horizontal interface, two thick interfaces, and three interfaces show that the method is fully robust and very efficient. One of its most significant advantages over other existing methods from the point of view of eliminating the need to periodically regenerate the computational meshes and the interpolation attached to mesh re-generation.