# Peter K JimackUniversity of Leeds · School of Computing

Peter K Jimack

## About

222

Publications

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## Publications

Publications (222)

A surrogate-enabled multi-objective optimisation methodology for a continuous flow Polymerase Chain Reaction (CFPCR) systems is presented, which enables the effect of the applied PCR protocol and the channel width in the extension zone on four practical objectives of interest, to be explored. High fidelity, conjugate heat transfer (CHT) simulations...

Numerical simulations of groundwater flow are used to analyze and predict the response of an aquifer system to its change in state by approximating the solution of the fundamental groundwater physical equations. The most used and classical methodologies, such as Finite Difference (FD) and Finite Element (FE) Methods, use iterative solvers which are...

Numerical simulations of groundwater flow are used to analyze and predict the response of an aquifer system to its change in state by approximating the solution of the fundamental groundwater physical equations. The most used and classical methodologies, such as Finite Difference (FD) and Finite Element (FE) Methods, use iterative solvers which are...

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 wide...

The development of Polymerase Chain Reaction Mullis et al. in 1986 [1] (PCR) has played an important role in the progress of molecular diagnostics, enabling the rapid DNA amplification through a series of repeated cycles. Considering the wide use of PCR devices in research, there is a great need to optimize their performance. This study focuses on...

We summarise contributions made to the computational phase-field modelling of alloy solidification from the University of Leeds spoke of the LiME project. We begin with a general introduction to phase-field, and then reference the numerical issues that arise from solution of the model, before detailing each contribution to the modelling itself. The...

In this article, we derive an adjoint Fluid-Structure Interaction (FSI) system in an Arbitrary Lagrangian-Eulerian (ALE) framework, based upon a one-field finite element method. A key feature of this approach is that the interface condition is automatically satisfied and the problem size is reduced since we only solve for one-velocity field for bot...

We describe a new algorithm for the generation of high quality tetrahedral meshes using artificial neural networks. The goal is to generate close-to-optimal meshes in the sense that the error in the computed finite element (FE) solution (for a target system of partial differential equations (PDEs)) is as small as it could be for a prescribed number...

Polymerase Chain Reaction (PCR) is widely used in biological research labs in order to detect hereditary diseases, diagnose infectious diseases, clone genes and other purposes. This work focuses on combining CFD and response surface modelling to explore the dependence of DNA amplification on two design parameters in a single phase, continuous flow...

We describe a new algorithm for the generation of high quality tetrahedral meshes using artificial neural networks. The goal is to generate close-to-optimal meshes in the sense that the error in the computed finite element (FE) solution (for a target system of partial differential equations (PDEs)) is as small as it could be for a prescribed number...

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 i...

The invention and development of Polymerase Chain Reaction (PCR) technology have revolutionised molecular biology and molecular diagnostics. There is an urgent need to optimise the performance of these devices while reducing the total construction and operation costs. This study proposes a CFD-enabled optimisation methodology for continuous flow (C...

jats:p>The invention and development of Polymerase Chain Reaction (PCR) technology have revolutionised molecular biology and molecular diagnostics. There is an urgent need to optimise the performance of these devices while reducing the total construction and operation costs. This study proposes a CFD-enabled optimisation methodology for continuous...

In this article we present a one-field monolithic finite element method in the Arbitrary Lagrangian–Eulerian (ALE) formulation for Fluid–Structure Interaction (FSI) problems. The method only solves for one velocity field in the whole FSI domain, and it solves in a monolithic manner so that the fluid solid interface conditions are satisfied automati...

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...

In this article we consider the three-dimensional numerical simulation of Fluid-Structure Interaction (FSI) problems involving large solid deformations. The one-field Fictitious Domain Method (FDM) is introduced in the framework of an operator splitting scheme. Three-dimensional numerical examples are presented in order to validate the proposed app...

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...

In this article we present a one-field monolithic finite element method in the Arbitrary Lagrangian-Eulerian (ALE) formulation for Fluid-Structure Interaction (FSI) problems. The method only solves for one velocity field in the whole FSI domain, and it solves in a monolithic manner so that the fluid solid interface conditions are satisfied automati...

AtChem is an open-source zero-dimensional box model for atmospheric chemistry. Any general set of chemical reactions can be used with AtChem, but the model was designed specifically for use with the Master Chemical Mechanism (MCM, http://mcm.york.ac.uk/, last access: 16 January 2020). AtChem was initially developed within the EUROCHAMP project as a...

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of these methods, based upon an operator splitting scheme, in order to demonstrate that both the explicit IFEM a...

AtChem is an open source zero-dimensional box-model for atmospheric chemistry. Any general set of chemical reactions can be used with AtChem, but the model was designed specifically for use with the Master Chemical Mechanism (MCM, http://mcm.york.ac.uk/). AtChem was initially developed within the EUROCHAMP project as a web application (AtChem-onlin...

We present an approach to alloy solidification modelling that incorporates binary interface energies in a manner that correctly reproduces the associated theoretical angles at triple junctions in eutectic solidification. We find that simply applying the principle that the correct binary junction behaviour is recovered when only two phases are prese...

Molecular dynamic simulations, ab initio (DFT) calculations and experimental evidence suggests that
there is a liquid-solid transition region which may be characterised by an order parameter. In this interface
region the order parameter is not observed to be symmetrical, rather it tends to be steep on the solid
side and exponentially decreasing on...

There is a large literature of numerical methods for phase field models from materials science. The prototype models are the Allen-Cahn and Cahn-Hilliard equations. We present four benchmark problems for these equations, with numerical results validated using several computational methods with different spatial and temporal discretizations. Our goa...

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of these methods, based upon an operator splitting scheme, in order to demonstrate that both the explicit IFEM a...

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. A finite volume scheme is used to approximate mass conservation,...

Molecular dynamic simulations, {\it ab initio} (DFT) calculations and experimental evidence suggests that there is a liquid-solid transition region which may be characterised by an order parameter. In this interface region the order parameter is not observed to be symmetrical, rather it tends to be steep on the solid side and exponentially decreasi...

Unless corrected by so called anti-trapping currents, phase field models of solidification display a dependence upon the diffuse interface width, δ , used in the simulation. This is most commonly manifest as a reduction in solute partitioning, which is both growth velocity and interface width dependent, resulting in a serious impediment to quantita...

We present current ideas towards developing a phase-field model appropriate to the solidification of intermetallic phases. Such simulation presents two main challenges (i) dealing with faceted interfaces and (ii) the complex sub-lattice models used to describe the thermodynamics of such phases. Although models are already existent for the simulatio...

We review and compare the [Wheeler-Boettinger-McFadden Phys. Rev A 45, 1992] (WBM), free energy based, phase field formulation of alloy solidification, with the grand potential energy formulation (GPF) of [Plapp Phys. Rev E 84 2011] and so, by association, the two phase approach of [Kim-Kim-Suzuki Phys. Rev. E 60 1999]. We ask what the effective di...

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 inte...

Unless corrected by so called anti-trapping currents, phase-field models of solidification display a dependence upon the diffuse interface width, δ, used in the simulation. This is most commonly manifest as a reduction in solute partitioning, which is both growth velocity and interface width dependent, resulting in a serious impediment to quantitat...

Understanding the sedimentation behaviour of colloidal suspensions is crucial in determining their stability. Since sedimentation rates are often very slow, centrifugation is used to expedite sedimentation experiments. The effect of centrifugal acceleration on sedimentation behaviour is not fully understood. Furthermore, in sedimentation models, in...

In this paper we assess the performance of a selection of load balancing strategies for a parallel, adaptive multigrid solver that has been developed for the implicit solution of phase-field problems. The strategies considered include a number of standard approaches and a new technique that we propose specifically for multigrid solvers. This techni...

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 conti...

In this article, the energy stability of a one-field fictitious domain method is proved and validated by numerical tests in two and three dimensions. The distinguishing feature of this method is that it only solves for one velocity field for the whole fluid-structure domain; the interactions remain decoupled until solving the final linear algebraic...

We present methods and results for the simulation of faceted and dendritic crystal growth. Using a thermodynamically realistic isothermal alloy model for AlSi we demonstrate, in confirmation of experimental observations, a change in morphology from perfectly faceted hexagons at smaller undercooling to dendritic growth at larger undercoolings. We al...

Stencil computations form the heart of numerical simulations to solve Partial Differential Equations using Finite Difference, Finite Element, and Finite Volume methods. Geometric Multigrid is an optimal O(N), hierarchical tool employing stencil computations in its chief constituents, namely, smoothing, restriction, and interpolation. When Multigrid...

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 conti...

In prior-research the authors have demonstrated that, for stencil-based numerical solvers for Partial Differential Equations (PDEs), the parallel performance can be significantly improved by selecting sub-domains that are not cubic in shape (Saxena et. al., HPCS 2016, pp. 875-885). This is achieved through accounting for cache utilization in both t...

Storage requirement and computational efficiency have always been challenges for the efficient implementation of discontinuous Galerkin (DG) methods for real life applications. In this paper, a fully implicit Jacobian-Free Newton-Krylov (JFNK) method is developed in the context of DG discretizations for the three-dimensional compressible Euler and...

We present a phase field approach to modelling the growth of faceted crystals, illustrated for hexagonal platelets growing in hypereutectic Al-Si alloy. Simulation results confirm experimental evidence that there is a marked change from perfectly faceted morphology to dendritic structures if the temperature at which nucleation occurs is reduced suf...

In this article, we analyze and numerically assess a new fictitious domain method for fluid-structure interactions in two and three dimensions. The distinguishing feature of the proposed method is that it only solves for one velocity field for the whole fluid-structure domain; the interactions remain decoupled until solving the final linear algebra...

In this article, we present a one-field monolithic fictitious domain (FD) method for simulation of general fluid-structure interactions (FSI). One-field 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...

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs...

We present a method for coupling current phase field models of alloy solidification into general continuum modelling. The advantages of this approach are to provide a generic framework for phase field modelling , give a natural and thermodynamically consistent extension to non-isothermal modelling, and to see phase field models in a wider context....

In this article, we present a new unified finite element method (UFEM) for simulation of general Fluid-Structure interaction (FSI) which has the same generality and robustness as monolithic methods but is significantly more computationally efficient and easier to implement. Our proposed approach has similarities with classical immersed finite eleme...

This paper describes a new software tool that has been developed for the efﬁcient solution of systems of linear and nonlinear partial differential equations (PDEs) of parabolic type. Speciﬁcally, the software is designed to provide optimal computational performance for multiscale problems, which require highly stable, implicit, time-stepping scheme...

Dropwise condensation has superior heat transfer efficiency than filmwise condensation; however condensate evacuation from the surface still remains a significant technological challenge. The process of droplets jumping, against adhesive forces, from a solid surface upon coalescence has been studied using both experimental and Computational Fluid D...

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...

Using a phase field model, which fully couples the thermal and solute concentration field, we present simulation results in three dimensions of the rapid dendritic solidification of a class of dilute alloys at the meso scale. The key results are the prediction of steady state tip velocity and radius at varying undercooling and thermal diffusivities...

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...

We present our computational method for binary alloy solidification which takes advantage of high performance computing where up to 1024 cores are employed. Much of the simulation at a sufficiently fine resolution is possible on a modern 12 core PC and the 1024 core simulation is only necessary for very mature dendrite and convergence testing where...

A major challenge in undertaking high resolution numerical simulations for engineering problems comes from the growth in the computational work that occurs as the underlying finite difference or the finite element meshes are refined in order to improve accuracy. For most solution algorithms this growth in work is super-linear with the number of deg...

The first half of the paper provides an overview of a new engineering software tool that is designed for the efficient solution of problems that may be modeled as systems of linear and nonlinear partial differential equations (PDEs) of parabolic type. Our tool is built upon the PARAMESH library, [15], which provides hierarchical mesh adaptivity in...

This paper presents an automatic locally adaptive finite element solver for the fully-coupled EHL point contact problems. The proposed algorithm uses a posteriori error estimation in the stress in order to control adaptivity in both the elasticity and the lubrication domains. The implementation is based on the fact that the solution of the linear e...

Nonlinear multigrid methods such as the Full Approximation Scheme (FAS) and Newton-multigrid (Newton-MG) are well established as fast solvers for nonlinear PDEs of elliptic and parabolic type. In this paper we consider Newton-MG and FAS iterations applied to second order differential operators with nonlinear diffusion coefficient. Under mild assump...

We employ adaptive mesh refinement, implicit time stepping, a nonlinear
multigrid solver and parallel computation, to solve a multi-scale, time
dependent, three dimensional, nonlinear set of coupled partial differential
equations for three scalar field variables. The mathematical model represents
the non-isothermal solidification of a metal alloy i...

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 techniqu...

This paper shows how to move from a specification of free energy for the solidification of a binary alloy to the dynamical equations using the elegance of a dissipative bracket analogous to the Poisson bracket of Hamiltonian mechanics. A key new result is the derivation of the temperature equation for single-phase thermal-solutal models, which cont...

This paper shows how to move from a specification of free energy for the solidification of a binary alloy to the dynamical equations using the elegance of a dissipative bracket analogous to the Poisson bracket of Hamiltonian mechanics. A key new result is the derivation of the tempera-ture equation for single-phase thermal-solutal models, which con...

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 with a domain size and interface resolution previously possible only in 2-dimensions. Using such tech...

A distributed Lagrangian moving-mesh finite element method is applied to problems
involving changes of phase. The algorithm uses a distributed conservation principle to de-
termine nodal mesh velocities, which are then used to move the nodes. The nodal values are
obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a gene...

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 three-dimensional phase-field problem with a domain size and interface resolution previously possible only in two dimensions. Using suc...