We present a general formulation for the analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral form, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.

The particle finite element method. An overview

▪ AbstractThis paper is a short and nonexhaustive survey of some recent developments in optimal shape design (OSD) for fluids. OSD is an interesting field both mathematically and for industrial applications. Existence, sensitivity, and compatibility of discretizations are important theoretical issues. Efficient algorithmic implementations with low complexity are also critical. In this paper we discuss topological optimization, algorithmic differentiation, gradient smoothers, Computer Aided Design (CAD)-free platforms and shock differentiation; all these are applied to a multicriterion optimization for a supersonic business jet.

Shape optimization in fluid mechanics

https://digital.library.unt.edu/ark:/67531/metadc933587/m2/1/high_res_d/978353.pdf

A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids

We review the treatment of trimmed geometries in the context of design, data exchange, and computational simulation. Such models are omnipresent in current engineering modeling and play a key role for the integration of design and analysis. The problems induced by trimming are often underestimated due to the conceptional simplicity of the procedure. In this work, several challenges and pitfalls are described.

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A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects

Formation of a properly branched vascular system during embryogenesis is crucial for embryo survival. Here we review the regulation of the morphogenesis of the arterial and venous system during embryogenesis. We show that in addition to deterministic patterning mechanisms and plasticity of endothelial cells, arterial-venous differentiation and branching morphogenesis involves a prominent role for blood flow. Based on in vivo observations of developing arteries, we identified a novel morphological event crucial for the morphogenesis of the arterial tree, disconnection of small side branches. This disconnection of side branches occurs exactly at the point of bifurcation. The rate of disconnection of side branches depends on flow velocity and branching angle. The balance between disconnection and maintenance of arterial side branches determines the number of side branches connected to a large artery. Based on these observations, we postulate that the number of pre-existing collaterals connected to a large artery is a function of the disconnection process and can be regulated by hemodynamics. We furthermore show that embryonic arteries already adapt their lumen diameter to the amount of flow carried. Taken together, we suggest that hemodynamics plays a pivotal role in shaping the arterial system. We suggest that flow-evoked remodeling processes determine the number of preexisting collaterals during critical periods of embryo-fetal development. Insight into these basic principles of arterial growth and branching during embryogenesis may aid to understanding the observed variability in the capacity to establish a collateral circulation in patients with ischemic diseases and finding new strategies for therapeutic arteriogenesis.

Control of arterial branching morphogenesis in embryogenesis: go with the flow.

The process of creating a finite element mesh is often termed as mesh generation. Mesh generation has always been a time-consuming and error-prone process. This is true in the practical science and engineering computations, where meshes have to be generated for three-dimensional geometries of various levels of complexity. The attempt to create a fully automatic mesh generator, which is a particular mesh generation algorithm that is capable of generating valid finite element meshes over arbitrary domains and needs only the information of the specified geometric boundary of the domain and the required distribution of the element size, started in the early 1970s. Since then, many methodologies have been proposed and different algorithms have been devised in the development of automatic mesh generators. This chapter focuses on the automatic mesh generation methods based on the advancing front method and the Delaunay triangulation method. These are the basis of many existing mesh generation programs and the basis of current research. This chapter discusses the algorithmic procedures of the advancing front method in two dimensions and the Delaunay triangulation method in three dimensions. It also discusses curve and surface mesh generations.

R.L. Taylor

Papers

Automatic Mesh Generation