David Moxey

• MMath, PhD
• Professor of Computational Engineering at King's College London

High-order discontinuous Galerkin spectral element methods (DGSEM) have received growing attention and development, especially in the regime of computational fluid dynamics in recent years. The inherent flexibility of the discontinuous Galerkin approach in handling non-conforming interfaces, such as those encountered in moving geometries or hp-refi...

The Atout SMARTTS (SMART Tanks for Space) system allows the propellant mass distribution in a storage vessel to be measured accurately under several motion and gravity conditions and at any fill level. Based on Electrical Capacitance Tomography (ECT), SMARTTS systems incorporate electrodes on the inside of the tank, electrical connections to these...

We present a proof-of-concept methodology for generating curvilinear polygonal meshes suitable for high-order discretizations by the Virtual Element Method (VEM). A VEM discretization requires the definition of a set of boundary and internal points that are used to interpolate the approximation functions and to evaluate integrals by means of suitab...

Due to the proprietary nature of modern motorsport and Formula 1, current scientific literature lacks relevant studies and benchmarks that can be used to understand flow physics in this area, as well as to test and validate new simulation methodology. With the release of a new, open-source geometry (the Imperial Front Wing), we present a computatio...

We develop efficient kernels for elemental operators of matrix-free solvers of the Helmholtz equation, which are the core operations for incompressible Navier-Stokes solvers, for use on graphics-processing units (GPUs). Our primary concern in this work is the extension of matrix-free routines to efficiently evaluate this elliptic operator on regula...

Due to the proprietary nature of modern motorsport and Formula 1, current scientific literature lacks relevant studies and benchmarks that can be used to test and validate new methods. Due to the release of a free geometry - the Imperial Front Wing - we present a computational study of a multi-element aerofoil at a ride height of 0.36 h/c and a Rey...

As the use of spectral/hp element methods, and high-order finite element methods in general, continues to spread, community efforts to create efficient, optimized algorithms associated with fundamental high-order operations have grown. Core tasks such as solution expansion evaluation at quadrature points, stiffness and mass matrix generation, and m...

Emerging commercial and academic tools are regularly being applied to the design of road and race cars, but there currently are no well-established benchmark cases to study the aerodynamics of race car wings in ground effect. In this paper we propose a new test case, with a relatively complex geometry, supported by the availability of CAD model and...

Quantifying the uncertainty in model parameters and output is a critical component in model-driven decision support systems for groundwater management. This paper presents a novel algorithmic approach which fuses Markov Chain Monte Carlo (MCMC) and Machine Learning methods to accelerate uncertainty quantification for groundwater flow models. We for...

The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations). With an incr...

As the use of spectral/hp element methods, and high-order finite element methods in general, continues to spread, community efforts to create efficient, optimized algorithms associated with fundamental high-order operations have grown. Core tasks such as solution expansion evaluation at quadrature points, stiffness and mass matrix generation, and m...

The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. The fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations). With an...

Quantifying the uncertainty in model parameters and output is a critical component in model-driven decision support systems for groundwater management. This paper presents a novel algorithmic approach which fuses Markov Chain Monte Carlo (MCMC) and Machine Learning methods to accelerate uncertainty quantification for groundwater flow models. We for...

We present an rp‐adaptation strategy for high‐fidelity simulation of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimiser to r‐adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resolution t...

We present a successful deployment of high-fidelity Large-Eddy Simulation (LES) technologies based on spectral/hp element methods to industrial flow problems, which are characterized by high Reynolds numbers and complex geometries. In particular, we describe the numerical methods, software development and steps that were required to perform the imp...

Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/ element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, there...

At high Reynolds numbers the use of explicit in time compressible flow simulations with spectral/hp element discretization can become significantly limited by time step. To alleviate this limitation we extend the capability of the spectral/hp element open-source software framework, Nektar++, to include an implicit discontinuous Galerkin compressibl...

We consider the application of three performance-portable programming models in the context of a high-order spectral element, implicit time-stepping solver for the Navier–Stokes equations. We aim to evaluate whether the use of these models allows code developers to deliver high-performance solvers for computational fluid dynamics simulations that a...

At high Reynolds numbers, the use of explicit in time compressible flow simulations with spectral/$hp$ element discretization can become significantly limited by time step. To alleviate this limitation we extend the capability of the spectral/$hp$ element open-source software framework, Nektar++, to include an implicit discontinuous Galerkin compre...

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the ext...

We present an rp-adaptation strategy for the high-fidelity simulation of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimiser to r-adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resoluti...

Emerging commercial and academic tools are regularly being applied to the design of road and race cars, but there currently are no well-established benchmark cases to study the aerodynamics of race car wings in ground effect. In this paper we propose a new test case, with a relatively complex geometry, supported by the availability of CAD model and...

We have performed direct numerical simulations of a transitional flow in a pipe for \(Re_m=2250\) when turbulence manifests in the form of fleshes (puffs). From experiments and simulations, \(Re_m \approx 2250\) has been estimated as a threshold when the average speeds of upstream and downstream fronts of a puff are identical (Song et al. in J Flui...

Nektar++ is an open-source framework that provides a flexible, performant and scalable platform for the development of solvers for partial differential equations using the high-order spectral/hp element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby a...

We have performed direct numerical simulations of a spatio-temporally intermittent flow in a pipe for Rem = 2250. From previous experiments and simulations of pipe flow, this value has been estimated as a threshold when the average speeds of upstream and downstream fronts of a puff are identical (Barkley et al., Nature 526, 550–553, 2015; Barkley e...

Computational modelling is now tightly integrated into many fields of research in science and industry. Computational fluid dynamics software, for example, gives engineers the ability to model fluid flow around complex geometries defined in Computer-Aided Design (CAD) packages, without the expense of constructing large wind tunnel experiments. Howe...

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain – groups of elements that support a piecewise-polynomial continuous expansion. This step allows us to identify a new...

Mesh generation and adaptive refinement are largely driven by the objective of minimizing the bounds on the interpolation error of the solution of the partial differential equation (PDE) being solved. Thus, the characterization and analysis of interpolation error bounds for curved, high-order finite elements is often desired to efficiently obtain t...

We present an approach for robust high-order mesh generation specially tailored to streamlined bodies. The method is based on a semi-sructured approach which combines the high quality of structured meshes in the near-field with the flexibility of unstructured meshes in the far-field. We utilise medial axis technology to robustly partition the near-...

We present an approach for robust high-order mesh generation specially tailored to streamlined bodies. The method is based on a semi-sructured approach which combines the high quality of structured meshes in the near-field with the flexibility of unstructured meshes in the far-field. We utilise medial axis technology to robustly partition the near-...

We describe a semi-structured method for the generation of high-order hybrid meshes suited for the simulation of high Reynolds number flows. This is achieved through the use of highly stretched elements in the viscous boundary layers near the wall surfaces. CADfix is used to first repair any possible defects in the CAD geometry and then generate a...

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain - groups of elements that support a piecewise-polynomial continuous expansion. This step allows us to identify a~new...

Heterogeneous manycore performance-portable programming models and libraries, such as Kokkos, have been developed to facilitate portability and maintainability of high-performance computing codes and enhance their resilience to architectural changes. Here we investigate the suitability of the Kokkos programming model for optimizing the performance...

In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS dat...

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain-groups of elements that support a piecewise-polynomial continuous expansion. This step allows us to identify a new we...

We describe a semi-structured method for the generation of high-order hybrid meshes suited for the simulation of high Reynolds number flows. This is achieved through the use of highly stretched elements in the viscous boundary layers near the wall surfaces. CADfix is used to first repair any possible defects in the CAD geometry and then generate a...

We present a pipeline of state-of-the-art techniques for the generation of high-order meshes that contain highly stretched elements in viscous boundary layers, and are suitable for flow simulations at high Reynolds numbers. The pipeline uses CADfix to generate a medial object based decomposition of the domain, which wraps the wall boundaries with p...

We aim to tackle the challenge of generating unstructured high-order meshes of complex three-dimensional bodies, which remains a significant bottleneck in the wider adoption of high-order methods. In particular we show that by adopting a variational approach to the generation process, many of the current popular high-order generation methods can be...

A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the initial mesh are manipulated using metric tensors to obtain target elements. The nonlinear optimisation in turns ad...

A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the initial mesh are manipulated using metric tensors to obtain target elements. The nonlinear optimisation in turns ad...

There is an increasing requirement from both academia and industry for high-fidelity flow simulations that are able to accurately capture complicated and transient flow dynamics in complex geometries. Coupled with the growing availability of high-performance, highly parallel computing resources, there is therefore a demand for scalable numerical me...

The generation of sufficiently high quality unstructured high-order meshes remains a significant obstacle in the adoption of high-order methods. However, there is little consensus on which approach is the most robust, fastest and produces the ‘best’ meshes. We aim to provide a route to investigate this question, by examining popular high-order mesh...

As computing hardware evolves, increasing core counts mean that memory bandwidth is becoming the deciding factor in attaining peak performance of numerical methods. High-order finite element methods, such as those implemented in the spectral/hp framework Nektar++, are particularly well-suited to this environment. Unlike low-order methods that typic...

The generation of suitable, good quality high-order meshes is a significant obstacle in the academic and industrial uptake of high-order CFD methods. These methods have a number of favourable characteristics such as low dispersion and dissipation and higher levels of numerical accuracy than their low-order counterparts, however the methods are high...

An accurate calculation of aerodynamic force coefficients for a given geometry is of fundamental importance for aircraft design. High-order spectral/hp element methods, which use a discontinuous Galerkin discretisation of the compressible Navier–Stokes equations, are now increasingly being used to improve the accuracy of flow simulations and thus t...

A hybrid parallelisation technique for distributed memory systems is investigated for a coupled Fourier-spectral/hp element discretisation of domains characterised by geometric homogeneity in one or more directions. The performance of the approach is mathematically modelled in terms of operation count and communication costs for identifying the mos...

In this article, recent developments in numerical methods for performing a large-eddy simulation of the formation and evolution of a wingtip vortex are presented. The development of these vortices in the near wake, in combination with the large Reynolds numbers present in these cases, makes these types of test cases particularly challenging to inve...

High-order methods are becoming increasingly attractive in both academia and industry, especially in the context of computational fluid dynamics. However, before they can be more widely adopted, issues such as lack of robustness in terms of numerical stability need to be addressed, particularly when treating industrial-type problems where challengi...

With high-order methods becoming increasingly popular in both academia and industry, generating curvilinear meshes that align with the boundaries of complex geometries continues to present a significant challenge. Whereas traditional low-order methods use planar-faced elements, high-order methods introduce curvature into elements that may, if added...

Generating and managing input data for large-scale scientific computations has, for many classes of application, always been a challenging process. The emergence of new hardware platforms and increasingly complex scientific models compounds this problem as configuration data can change depending on the underlying hardware and properties of the comp...

Since the inception of discontinuous Galerkin (DG) methods for elliptic problems, there has existed a question of whether DG methods can be made more computationally efficient than continuous Galerkin (CG) methods. Fewer degrees of freedom, approximation properties for elliptic problems together with the number of optimization techniques, such as s...

In this article we present recent developments in numerical methods for performing a Large Eddy Simulation (LES) of the formation and evolution of a wingtip vortex. The development of these vortices in the near wake, in combination with the large Reynolds numbers present in these cases, make these types of test cases particularly challenging to inv...

Nektar++ is an open-source software framework designed to support the development of high-performance scalable solvers for partial differential equations using the spectral/ element method. High-order methods are gaining prominence in several engineering and biomedical applications due to their improved accuracy over low-order techniques at reduced...

Recently, a new mesh generation technique based on the isoparametric representation of curvilinear elements has been developed in order to address the issue of generating high-order meshes with highly stretched elements. Given a valid coarse mesh comprising of a prismatic boundary layer, this technique uses the shape functions that define the geome...

Accurate visualization of high-order meshes and flow fields is a fundamental tool for the verification, validation, analysis and interpretation of high-order flow simulations. Standard visualization tools based on piecewise linear approximations can be used for the display of highorder fields but their accuracy is restricted by computer memory and...

In this article, we give an overview of a new technique for unstructured curvilinear boundary layer grid generation, which uses the isoparametric mappings that define elements in an existing coarse prismatic grid to produce a refined mesh capable of resolving arbitrarily thin boundary layers. We demonstrate that the technique always produces valid...

In recent years, techniques for the generation of high-order curvilinear mesh have frequently adopted mesh deformation procedures to project the curvature of the surface onto the mesh, thereby introducing curvature into the interior of the domain and lessening the occurrence of self-intersecting elements. In this article, we propose an extension of...

With high-order methods becoming more widely adopted throughout the field of computational fluid dynamics, the development of new computationally efficient algorithms has increased tremendously in recent years. One of the most recent methods to be developed is the flux reconstruction approach, which allows various well-known high-order schemes to b...

This paper presents limits for stability of projection type schemes when using high order pressure-velocity pairs of same degree. Two high order h/p variational methods encompassing continuous and discontinuous Galerkin formulations are used to explain previously observed lower limits on the time step for projection type schemes to be stable [18],...

The generation of high-order curvilinear meshes for complex three-dimensional geometries is presently a challenging topic, particularly for meshes used in simulations at high Reynolds numbers where a thin boundary layer exists near walls and elements are highly stretched in the direction normal to flow. In this paper, we present a conceptually simp...

Developing software to undertake complex, compute-intensive scientific processes requires a challenging combination of both specialist domain knowledge and software development skills to convert this knowledge into efficient code. As computational platforms become increasingly heterogeneous and newer types of platform such as Infrastructure-as-a-Se...

As the capabilities and diversity of computational platforms continue to grow, scientific software is becoming ever more complex in order to target resources effectively. In the libhpc project we are developing a suite of tools and services to simplify job description and execution on heterogeneous infrastructures. This paper presents Nekkloud, a w...

Shear flows undergo a sudden transition from laminar to turbulent motion as the velocity increases, and the onset of turbulence radically changes transport efficiency and mixing properties. Even for the well-studied case of pipe flow, it has not been possible to determine at what Reynolds number the motion will be either persistently turbulent or u...

Lifetime measurements of localized states have been the focus of many recent studies of transitional turbulence. We argue that the transition to infinite-lifetime turbulence must be understood as a transition to spatiotemporal chaos, similar to directed percolation (although the transition may not be strictly DP). While such arguments were first ma...

When fluid flows through a channel, pipe, or duct, there are two basic forms of motion: smooth laminar motion and complex turbulent motion. The discontinuous transition between these states is a fundamental problem that has been studied for more than 100 yr. What has received far less attention is the large-scale nature of the turbulent flows near...

Over a century, and thousands of articles, after Reynolds' description of the transition to turbulence in pipe flow, a predictive theory of transition is still unavailable. One of the most intriguing phenomena observed near transition ishe coexistence of well-defined and long-lived laminar and turbulent regions, first observed in counter-rotating T...

We report on numerical simulations of flow in pipes at Reynolds numbers 1800 to 3000 - near the minimum Reynolds numbers that supports turbulence. The computational domains are periodic in the streamwise direction with lengths up to 150 pipe diameters. We find both intermittent and equilibrium puffs. More particularly we find that, just as with oth...

In this report, a number of basic Monte Carlo methods for modelling polymer chains are presented (including configurational-bias Monte Carlo and the pruned-enriched Rosenbluth method). These are then used to investigate the behaviour of the collapse of polymer chains around the well-studied θ-point. Additionally, a flat-histogram version of PERM is...