SUMMARY

In meshfree methods the governing partial differential equations are discretized in a given computational domain using only a set of points. A mesh, or rather, a collection of elements that partitions the domain into non-overlapping volumes (areas), is not present. Instead, elements are replaced by point clouds from which discrete operators can be constructed. The primary advantage of meshfree methods is that problem sets with moving interfaces and problem sets with adaptive refinement can be more readily handled as expensive re-meshing is no longer required. Despite this advantage, in the context of incompressible flow, meshfree methods are still plagued by a number of issues including grid degradation accompanying large fluid deformations, large stencil requirements, lack of consistency and conservation, restrictive time steps due to explicit weakly compressible fluid models used, and inability to resolve small spatial scales due to grid uniformity. To address these limitations, we propose to develop a consistent, semi-implicit meshfree solver that can be used with moving adaptive meshfree grids. The utility of the approach will be demonstrated by using moving adaptive grids to simulate viscous incompressible flow phenomena around complex moving interfaces.