A parallel dynamic-mesh Lagrangian method for Navier-Stokes flows with deformable boundaries

The major difficulties in simulating flows with deformable domains, is to efficiently and accurately resolve numerous dynamic interfaces and associated intense relative flow motion. Central difficulty is to develop and dynamically update and modify associated geometric structures. Existing methods are based on spatial flow formulation and require mechanisms for tracking the numerous boundaries. This poses major difficulties to efficient large-scale simulations on parallel computers, which are necessary for real-life simulations. Despite the fact that many of existing methods have been introduced more than a decade ago, many important problems, including the target problem of microstructural blood flow modeling, are not simulated at realistic scales.; In this work, a novel method for simulating flows with dynamic interfaces is developed and analyzed. It is based on two fundamental concepts: Lagrangian flow formulation and dynamic-mesh finite element method. Adopting the Lagrangian formulation is a key to efficiently resolving the dynamic interfaces. Discretization is done at the material level. Dynamic boundaries are naturally embedded in the formulation and flow with the fluid material. Hence, the method and the implementation remain the same regardless of the presence or complexity of the interfaces. The finite element method (FEM) is used as the underlying approximation scheme because of its ability to efficiently approximate complex geometry. However, unlike traditional FEMs for CFD problems, finite element meshes are completely and frequently regenerated, and are not constrained to resemble prior ones, bringing the concept of dynamic finite element meshes to life. In addition, parallel implementation of the dynamic-mesh Lagrangian CFD method has been derived for 2D application enabling efficient simulations of large-scale mechanical systems.; The developed method has been applied to simulate a variety of time-dependent viscous incompressible flows. Examples include free surface flows, flows around stationary and moving obstacles and multiphase flows with large systems of immersed deformable bodies. The research presented in this thesis, removes the obstacles that limited Lagrangian mesh-based methods to simulations of simplest flows. It gives a strong boost to this class of methods as a leading edge in simulating flows with dynamic interfaces with a wide range of possible applications including the target problem of multiscale blood flow modeling.