Gerard J. Gorman

Anisotropic mesh adaptivity for multi-scale ocean modelling

Research into the use of unstructured mesh methods in oceanography has been growing steadily over the past decade. The advantages of this approach for domain representation and non-uniform resolution are clear. However, a number of issues remain, in particular those related to the computational cost of models produced using unstructured mesh methods compared with their structured mesh counterparts. Mesh adaptivity represents an important means to improve the competitiveness of unstructured mesh models, where high resolution is only used when and where necessary. In this paper, an optimization-based approach to mesh adaptivity is described where emphasis is placed on capturing anisotropic solution characteristics. Comparisons are made between the results obtained with uniform isotropic resolution, isotropic adaptive resolution and fully anisotropic adaptive resolution.

Anisotropic Mesh Adaptivity and Control Volume Finite Element Methods for Numerical Simulation of Multiphase Flow in Porous Media

Numerical simulation of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. The governing equations are the continuity equation and Darcy’s law. A novel control volume finite element (CVFE) approach is developed to discretize the governing equations in which a node-centered control volume approach is applied for the saturation equation, while a CVFE method is used for discretization of the pressure equation. We embed the discrete continuity equation into the pressure equation and ensure that the continuity equation is exactly enforced. Furthermore, the scheme is equipped with dynamic anisotropic mesh adaptivity which uses a metric tensor field approach, based on the curvature of fields of interest, to control the size and shape of elements in the metric space. This improves the resolution of the mesh in the zones of dynamic interest. Moreover, the mesh adaptivity algorithm employs multi-constraints on element size in different regions of the porous medium to resolve multi-scale transport phenomena. The advantages of mesh adaptivity and the capability of the scheme are demonstrated for simulation of flow in several challenging computational domains. The scheme captures the key features of flow while preserving the initial geometry and can be applied for efficient simulation of flow in heterogeneous porous media and geological formations.

Parallel anisotropic mesh adaptivity with dynamic load balancing for cardiac electrophysiology

Abstract Simulations in cardiac electrophysiology generally use very fine meshes and small time steps to resolve highly localized wavefronts. This expense motivates the use of mesh adaptivity, which has been demonstrated to reduce the overall computational load. However, even with mesh adaptivity performing such simulations on a single processor is infeasible. Therefore, the adaptivity algorithm must be parallelised. Rather than modifying the sequential adaptive algorithm, the parallel mesh adaptivity method introduced in this paper focuses on dynamic load balancing in response to the local refinement and coarsening of the mesh. In essence, the mesh partition boundary is perturbed away from mesh regions of high relative error, while also balancing the computational load across processes. The parallel scaling of the method when applied to physiologically realistic heart meshes is shown to be good as long as there are enough mesh nodes to distribute over the available parallel processes. It is shown that the new method is dominated by the cost of the sequential adaptive mesh procedure and that the parallel overhead of inter-process data migration represents only a small fraction of the overall cost.

Coupled FEMDEM/Fluids for coastal engineers with special reference to armour stability and breakage

Sea-level rise and increased storminess present huge challenges to coastal engineers worldwide. The seaward slope of many breakwaters and shoreline defence structures consists of thousands of interlocking units of concrete or rock making up a massive granular defence against wave attack. The units are placed freely to form an armour layer which is intended to both dissipate wave energy and remain structurally stable. Design guidance on the mass and shape of these units is based on empirical equations derived from Froude scale physical model tests. The two main failure modes for concrete armour layers are displacement (hydraulic instability) and breakage (structural instability) which are strongly coupled. Breakage mechanisms cannot all be faithfully reproduced under scaled physical models. Fundamental understanding of the forces governing such wave-structure interaction remains poor and unit breakages continue to baffle the designers of concrete armour units. This paper illustrates a range of DEM and FEMDEM methods being developed to model the granular solid skeleton of freely packed brittle units. Such discrete element methods are increasingly being used by engineers for solids modelling. They are especially powerful when coupled with a CFD model which can resolve ocean wave dynamics. The aim is to describe a framework for coupled modelling technologies applicable to coastal engineering problems. Preliminary simulation test cases, still at proof of concept stage, but based on a wealth of validation studies are presented. Thus, we report a snap-shot of progress towards a future where designers combine multi-physics numerical technology with knowledge from scaled physical models for a better understanding of wave energy turbulence, block movement, and internal stresses within armour units.

A systematic approach to unstructured mesh generation for ocean modelling using GMT and Terreno

A systematic approach to unstructured mesh generation for ocean modelling is presented. The method optimises unstructured meshes to approximate bathymetry to a user specified accuracy which may be defined as a function of longitude, latitude and bathymetry. GMT (Generic Mapping Tools) is used to perform the initial griding of the bathymetric data. Subsequently, the Terreno meshing package combines automated shoreline approximation, mesh gradation and optimisation methods to generate high-quality bathymetric meshes. The operation of Terreno is based upon clearly defined error measures and this facilitates the automation of unstructured mesh generation while minimising user intervention and the subjectivity that this can introduce.

Hybrid OpenMP/MPI Anisotropic Mesh Smoothing

Abstract Mesh smoothing is an important algorithm for the improvement of element quality in unstructured mesh finite element methods. A new optimisation based mesh smoothing algorithm is presented for anisotropic mesh adaptivity. It is shown that this smoothing kernel is very effective at raising the minimum local quality of the mesh. A number of strategies are employed to reduce the algorithms cost while maintaining its effectiveness in improving overall mesh quality. The method is parallelised using hybrid OpenMP/MPI programming methods, and graph colouring to identify independent sets. Different approaches are explored to achieve good scaling performance within a shared memory compute node.

Adjoint A Posteriori Error Measures for Anisotropic Mesh Optimisation

In this paper an adjoint- (or sensitivity-) based error measure is formulated which measures the error contribution of each solution variable to an overall goal The goal is typically embodied in an integral functional, e.g., the solution in a small region of the domain of interest. The resulting a posteriori error measures involve the solution of both primal and adjoint problems. A comparison of a number of important a posteriori error measures is made in this work. There is a focus on developing relatively simple methods that refer to information from the discretised equation sets (often readily accessible in simulation codes) and do not explicitly use equation residuals. This method is subsequently used to guide anisotropic mesh adaptivity of tetrahedral finite elements. Mesh adaptivity is achieved here with a series of optimisation heuristics of the landscape defined by mesh quality. Mesh quality is gauged with respect to a Riemann metric tensor embodying an a posteriori error measure, such that an ideal element has sides of unit length when measured with respect to this metric tensor. This results in meshes in which each finite-element node has approximately equal (subject to certain boundary-conforming constraints and the performance of the mesh optimisation heuristics) error contribution to the functional (goal).

Tidal circulation in an ancient epicontinental sea: The Early Jurassic Laurasian Seaway

We model tides and associated bed shear stress in the Early Jurassic Laurasian Seaway of northwest Europe. Sensitivity tests with different water depths highlight those regions that are least affected by paleobathymetric uncertainty. Results show that although the vast seaway was largely microtidal, the tides were still capable of affecting sediment transport more than 2000 km from the open ocean. Flow constriction associated with shallow platforms and straits produced elevated bed shear stresses (a direct proxy for the entrainment and transport of sediment) that were decoupled from tidal range and were capable of transporting sand. Areas of increased bed shear stress broadly correlate with published geological data. Varying the water depth in the basin provides an insight into the effects of an idealized transgression. Increasing the water level leads to a net reduction in the bed shear stress at the shelf edge, but promotes further penetration of tidal energy into the basin interior, although it is still focused into areas of flow constriction. Further drowning of the seaway eventually widens the straits to the point that they fail to constrict the flow and bed shear stress is reduced. Increasing water level counterintuitively leads to an increase in bed shear stress in a small number of locations.

PyRDM: A Python-based library for automating the management and online publication of scientific software and data

The recomputability and reproducibility of results from scientific software requires access to both the source code and all associated input and output data. However, the full collection of these resources often does not accompany the key findings published in journal articles, thereby making it difficult or impossible for the wider scientific community to verify the correctness of a result or to build further research on it. This paper presents a new Python-based library, PyRDM, whose functionality aims to automate the process of sharing the software and data via online, citable repositories such as Figshare. The library is integrated into the workflow of an open-source computational fluid dynamics package, Fluidity, to demonstrate an example of its usage.

A Fast and Scalable Graph Coloring Algorithm for Multi-core and Many-core Architectures

Irregular computations on unstructured data are an important class of problems for parallel programming. Graph coloring is often an important preprocessing step, e.g. as a way to perform dependency analysis for safe parallel execution. The total run time of a coloring algorithm adds to the overall parallel overhead of the application whereas the number of colors used determines the amount of exposed parallelism. A fast and scalable coloring algorithm using as few colors as possible is vital for the overall parallel performance and scalability of many irregular applications that depend upon runtime dependency analysis.