A stabilized and coupled meshfree/meshbased method for the incompressible Navier–Stokes equations—Part II: Coupling

In Part I of this work, meshfree Galerkin methods have been used for the approximation of the incompressible Navier–Stokes equations in Eulerian or arbitrary Lagrangian–Eulerian formulation. The problem of stabilization of meshfree methods is addressed there. Analogously, in the meshbased context, the finite element method is frequently used in similar stabilized formulations for the simulation of flow problems. In order to combine the advantages of both methods, different coupling techniques are examined in this part of the work. Standard coupling approaches are modified in order to fulfill the requirements for a reliable stabilization found in Part I of this work. The resulting stabilized and coupled meshfree/meshbased flow solver employs the comparatively costly meshfree Galerkin method only where it is needed—i.e. in areas of the domain, where a mesh is difficult to maintain—and the efficient meshbased finite element method in the rest of the domain. This enables the solution of complex flow problems, as thus involving large deformations of the physical domain and/or moving and rotating obstacles.