A One-Field Monolithic Fictitious Domain Method for Fluid-Structure Interactions

In this article, we present a one- eld monolithic fictitious domain (FD) method for simulation of general fluid-structure interactions (FSI). "One-fi eld" means only one velocity field is solved in the whole domain, based upon the use of an appropriate L2 projection. "Monolithic" means the fluid and solid equations are solved synchronously (rather than sequentially). We argue that the proposed method has the same generality and robustness as FD methods with distributed Lagrange multiplier (DLM) but is signi ficantly more computationally e fficient (because of one-fi eld) whilst being very straightforward to implement. The method is described in detail, followed by the presentation of multiple computational examples in order to validate it across a wide range of fluid and solid parameters and interactions

Phase-Field Modelling of Intermetallic Solidification

Many important intermetallic compounds display a faceted morphology during solidification close to equilibrium but adopt a more continuous, dendritic like morphology with increasing departure from equilibrium. We present a phase-field model of solidification that is able to both reproduce the Wulff shape at low driving force and to simulate a continuous transition from faceted to dendritic growth as the driving force is increased. A scaled ratio of the (perimeter)2 to the area is used to quantify the extent of departure from the equilibrium shape

A Cache-Aware Approach to Domain Decomposition for Stencil-Based Codes

Partial Differential Equations (PDEs) lie at the heart of numerous scientific simulations depicting physical phenomena. The parallelization of such simulations introduces additional performance penalties in the form of local and global synchronization among cooperating processes. Domain decomposition partitions the largest shareable data structures into sub-domains and attempts to achieve perfect load balance and minimal communication. Up to now research efforts to optimize spatial and temporal cache reuse for stencil-based PDE discretizations (e.g. finite difference and finite element) have considered sub-domain operations after the domain decomposition has been determined. We derive a cache-oblivious heuristic that minimizes cache misses at the sub-domain level through a quasi-cache-directed analysis to predict families of high performance domain decompositions in structured 3-D grids. To the best of our knowledge this is the first work to optimize domain decompositions by analyzing cache misses - thus connecting single core parameters (i.e. cache-misses) to true multicore parameters (i.e. domain decomposition). We analyze the trade-offs in decreasing cache-misses through such decompositions and increasing the dynamic bandwidth-per-core. The limitation of our work is that currently, it is applicable only to structured 3-D grids with cuts parallel to the Cartesian Axes. We emphasize and conclude that there is an imperative need to re-think domain decompositions in this constantly evolving multicore era

Towards a 3-dimensional phase-field model of non-isothermal alloy solidification

We review the application of advanced numerical techniques such as adaptive mesh refinement, implicit time-stepping, multigrid solvers and massively parallel implementations as a route to obtaining solutions to the 3-dimensional phase-field problem for coupled heat and solute transport during non-isothermal alloy solidification. Using such techniques it is shown that such models are tractable for modest values of the Lewis number (ratio of thermal to solutal diffusivities). Solutions to the 3-dimensional problem are compared with existing solutions to the equivalent 2-dimensional problem

An efficient numerical algorithm for a multiphase tumour model

This paper is concerned with the development and application of optimally efficient numerical methods for the simulation of vascular tumour growth. This model used involves the flow and interaction of four different, but coupled, phases which are each treated as incompressible fluids, Hubbard and Byrne (2013). A finite volume scheme is used to approximate mass conservation, with conforming finite element schemes to approximate momentum conservation and an associated equation. The principal contribution of this paper is the development of a novel block preconditioner for solving the linear systems arising from the discrete momentum equations at each time step. In particular, the preconditioned system has both a solution time and a memory requirement that is shown to scale almost linearly with the problem size

MeshingNet: A New Mesh Generation Method based on Deep Learning

We introduce a novel approach to automatic unstructured mesh generation using machine learning to predict an optimal finite element mesh for a previously unseen problem. The framework that we have developed is based around training an artificial neural network (ANN) to guide standard mesh generation software, based upon a prediction of the required local mesh density throughout the domain. We describe the training regime that is proposed, based upon the use of a posteriori error estimation, and discuss the topologies of the ANNs that we have considered. We then illustrate performance using two standard test problems, a single elliptic partial differential equation (PDE) and a system of PDEs associated with linear elasticity. We demonstrate the effective generation of high quality meshes for arbitrary polygonal geometries and a range of material parameters, using a variety of user-selected error norms

Energy Efficiency Optimization of Superhydrophobic Surfaces for Enhanced Condensation Heat Transfer

The process of droplets jumping, against adhesive forces, from a solid surface upon coalescence has been studied in detail using experimentally-validated CFD modelling. Both Lattice Boltzmann and Volume of Fluid methods have been used to evaluate different kinematic conditions of coalescence inducing a jump velocity. Design of experiment techniques were used to establish near-optimal initial process parameters around which to focus the study. This multidisciplinary approach allows us to evaluate the jumping phenomenon for super-hydrophobic surfaces for which several input parameters may be varied, so as to improve the heat transfer exchange rate on the surface during condensation. Reliable conditions were found to occur for droplets within initial radius range of r=20-40 μm and static contact angle θs~160º. Moreover, the jumping phenomenon was observed for droplets with initial radius of up to 500 μm. Our study also shows that a critical contact angle for droplets to jump upon coalescence is θc~140º

Towards a Physically Consistent Phase-Field Model for Alloy Solidification

We give an overview of contributions made to the computational phase-field modelling of alloy solidification from the University of Leeds as part of the LiME project (EPSRC Advanced Manufacturing Hub in Liquid Metal Engineering). The broader look at the more salient features from our research allows the individual contributions to be seen in a wider context than can be seen from each contribution separately. We begin with a general introduction to phase-field and then reference the numerical issues that arise from the solution of the model before outlining contributions to phase-field modelling that we found most interesting or significant. These range from controlling and developing interface-width independent modelling; controlling morphology in both single and multiphase settings; generalising from single to multiphase models; and creating a thermodynamically consistent framework for modelling entropy flow and thereby postulating a temperature field consistent with the concepts of, and applicable in, multiphase and density-dependent settings

A vertex based approach to crystal facet modelling in phase field

This paper seeks a vertex based approach to faceted anisotropy in phase field modelling of crystal growth. We examine Wulff shapes and the connection they have with phase field formulations. On inspecting current approaches to modelling facets within phase field we observe that there are two distinct approaches: one implements the faceting purely in the kinetic parameter thus avoiding the complications of taking gradients of discontinuous functions; while the second is based upon regularisation of the anisotropy function within the free energy function. Armed with our new insight into the operation of anisotropy within phase field we refine the second of these and advocate a vertex based approach to facet anisotropy modelling. Results include regular and irregular morphologies and hill-valley growth. We also present high undercooling effects on faceting, which can cause breaks in facets and, in the case of irregular shapes, distortion of the underlying Wulff shape

A numerical approach to compensate for phase field interface effects in alloy solidification

The use of a phase field approach to simulate solidification of metallic alloys has many computational advantages, but if obtaining quantitative results relies on the interface between phases being physically realistic, the computational advantage is much reduced. We propose here a method for compensating for a computationally convenient large interface width by simply transferring a numerically derived 1D steady state anti-trapping current to a general non-steady 2D simulation. The method proposed is not restricted to dilute or ideal materials and has a high degree of interface width independence, illustrated here with two models, illustrating a broad applicability for the approach