Hydrodynamic interactions in polar liquid crystals on evolving surfaces

We consider the derivation and numerical solution of the flow of passive and active polar liquid crystals, whose molecular orientation is subjected to a tangential anchoring on an evolving curved surface. The underlying passive model is a simplified surface Ericksen-Leslie model, which is derived as a thin-film limit of the corresponding three-dimensional equations with appropriate boundary conditions. A finite element discretization is considered and the effect of hydrodynamics on the interplay of topology, geometric properties and defect dynamics is studied for this model on various stationary and evolving surfaces. Additionally, we consider an active model. We propose a surface formulation for an active polar viscous gel and exemplarily demonstrate the effect of the underlying curvature on the location of topological defects on a torus

Mathematical Aspects of Computational Fluid Dynamics

[no abstract available

Aluminium extrusion analysis by the finite volume method

Present work proposes a novel numerical scheme to calculate stress and velocity fields of metal flow in axisymmetric extrusion process in steady state. Extrusion of aluminium is one main metal forming process largely applied in manufacturing bars and products with complex cross section shape. The upper-bound, slab, slip-line methods and more recently the numerical methods such as the Finite Element Method have been commonly applied in aluminium extrusion analysis. However, recently in the academy, the Finite Volume Method has been developed for metal flow analysis: literature suggests that extrusion of metals can be modelled by the flow formulation. Hence, metal flow can be mathematically modelled such us an incompressible non linear viscous fluid, owing to volume constancy and varying viscosity in metal forming. The governing equations were discretized by the Finite Volume Method, using the Explicit MacCormack Method in structured and collocated mesh. The MacCormack Method is commonly used to simulate compressible fluid flow by the finite volume method. However, metal plastic flow and incompressible fluid flow do not present state equations for the evolution of pressure, and therefore, a velocity-pressure coupling method is necessary to obtain a consistent velocity and pressure fields. The SIMPLE Method was applied to attain pressure-velocity coupling. This new numerical scheme was applied to forward hot extrusion process of an aluminium alloy. The metal extrusion velocity fields achieved fast convergence and a good agreement with experimental results. The MacCormack Method applied to metal extrusion produced consistent results without the need of artificial viscosity as employed by the compressible flow simulation approaches. Therefore, present numerical results also suggest that MacCormack method together with SIMPLE method can be applied in the solution of metal forming processes in addition to the traditional application for compressible fluid flow

High-order incompressible computational fluid dynamics on modern hardware architectures

In this thesis, a high-order incompressible Navier-Stokes solver is developed in the Python-based PyFR framework. The solver is based on the artificial compressibility formulation with a Flux Reconstruction (FR) discretisation in space and explicit dual time stepping in time. In order to reduce time to solution, explicit convergence acceleration techniques are developed and implemented. These techniques include polynomial multigrid, a novel locally adaptive pseudo-time stepping approach and novel stability-optimised Runge-Kutta schemes. Choices regarding the numerical methods and implementation are motivated as follows. Firstly, high-order FR is selected as the spatial discretisation due to its low dissipation and ability to work with unstructured meshes of complex geometries. Be- ing discontinuous, it also allows the majority of computation to be performed locally. Secondly, convergence acceleration techniques are restricted to explicit methods in order to retain the spatial locality provided by FR, which allows efficient harnessing of the massively parallel compute capability of modern hardware. Thirdly, the solver is implemented in the PyFR framework with cross-platform support such that it can run on modern heterogeneous systems via an MPI + X model, with X being CUDA, OpenCL or OpenMP. As such, it is well-placed to remain relevant in an era of rapidly evolving hardware architectures. The new software constitutes the first high-order accurate cross-platform imple- mentation of an incompressible Navier-Stokes solver via artificial compressibility. The solver and the convergence acceleration techniques are validated for a range of turbu- lent test cases. Furthermore, performance of the convergence acceleration techniques is assessed with a 2D cylinder test case, showing speed-up factors of over 20 relative to global RK4 pseudo-time stepping when all of the technologies are combined. Fi- nally, a simulation of the DARPA SUBOFF submarine model is undertaken using the solver and all convergence acceleration techniques. Excellent agreement with previ- ous studies is obtained, demonstrating that the technology can be used to conduct high-fidelity implicit Large Eddy Simulation of industrially relevant problems at scale using hundreds of GPUs.Open Acces

Parallel three-dimensional simulations of quasi-static elastoplastic solids

Hypo-elastoplasticity is a flexible framework for modeling the mechanics of many hard materials under small elastic deformation and large plastic deformation. Under typical loading rates, most laboratory tests of these materials happen in the quasi-static limit, but there are few existing numerical methods tailor-made for this physical regime. In this work, we extend to three dimensions a recent projection method for simulating quasi-static hypo-elastoplastic materials. The method is based on a mathematical correspondence to the incompressible Navier-Stokes equations, where the projection method of Chorin (1968) is an established numerical technique. We develop and utilize a three-dimensional parallel geometric multigrid solver employed to solve a linear system for the quasi-static projection. Our method is tested through simulation of three-dimensional shear band nucleation and growth, a precursor to failure in many materials. As an example system, we employ a physical model of a bulk metallic glass based on the shear transformation zone theory, but the method can be applied to any elastoplasticity model. We consider several examples of three-dimensional shear banding, and examine shear band formation in physically realistic materials with heterogeneous initial conditions under both simple shear deformation and boundary conditions inspired by friction welding.Comment: Final version. Accepted for publication in Computer Physics Communication