Matthew D. Piggott

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.

The Effect of Meltwater Plumes on the Melting of a Vertical Glacier Face

AbstractFreshwater produced by the surface melting of ice sheets is commonly discharged into ocean fjords from the bottom of deep fjord-terminating glaciers. The discharge of the freshwater forms upwelling plumes in front of the glacier calving face. This study simulates the meltwater plumes emanated into an unstratified environment using a nonhydrostatic ocean model with an unstructured mesh and subgrid-scale mixing calibrated by comparison to established plume theory. The presence of an ice face reduces the entrainment of seawater into the meltwater plumes, so the plumes remain attached to the ice front, in contrast to previous simple models. Ice melting increases with height above the discharge, also in contrast to some simple models, and the authors speculate that this “overcutting” may contribute to the tendency of icebergs to topple inwards toward the ice face upon calving. The overall melt rate is found to increase with discharge flux only up to a critical value, which depends on the channel size. ...

Modelling of fluid–solid interactions using an adaptive mesh fluid model coupled with a combined finite–discrete element model

Fluid–structure interactions are modelled by coupling the finite element fluid/ocean model ‘Fluidity-ICOM’ with a combined finite–discrete element solid model ‘Y3D’. Because separate meshes are used for the fluids and solids, the present method is flexible in terms of discretisation schemes used for each material. Also, it can tackle multiple solids impacting on one another, without having ill-posed problems in the resolution of the fluid’s equations. Importantly, the proposed approach ensures that Newton’s third law is satisfied at the discrete level. This is done by first computing the action–reaction force on a supermesh, i.e. a function superspace of the fluid and solid meshes, and then projecting it to both meshes to use it as a source term in the fluid and solid equations. This paper demonstrates the properties of spatial conservation and accuracy of the method for a sphere immersed in a fluid, with prescribed fluid and solid velocities. While spatial conservation is shown to be independent of the mesh resolutions, accuracy requires fine resolutions in both fluid and solid meshes. It is further highlighted that unstructured meshes adapted to the solid concentration field reduce the numerical errors, in comparison with uniformly structured meshes with the same number of elements. The method is verified on flow past a falling sphere. Its potential for ocean applications is further shown through the simulation of vortex-induced vibrations of two cylinders and the flow past two flexible fibres.

Large sea, small tides: the Late Carboniferous seaway of NW Europe

Debate surrounds the extent of tidal influence in Palaeozoic shallow epi-continental seas. In the absence of analogical reasoning, numerical modelling provides a quantitative means of investigating tidality in the geological record. Herein a new finite element model, tested for accuracy on the present-day Mediterranean, is used to predict an exceedingly low tidal range (<10 cm) in the epi-continental seaway that covered much of NW Europe during the Late Carboniferous. This small bulge may have been amplified to c. 1 m in estuaries, leading to the localized deposition of cyclic rhythmites, agreeing with geological observations. Extremely low tidal ranges in ancient epi-continental seas may be one mechanism to prevent water-body mixing, enhancing stratification and promoting anoxia.

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.

Shoreline approximation for unstructured mesh generation

A new method for approximating shorelines (polygons and polylines) is presented. The algorithm differs from the commonly used Douglas-Peucker type algorithms as the method can approximate to some feature error given the constraint that edge-lengths must satisfy some minimum-edge-length criteria. This constraint is necessary for the shoreline approximation to be useful for unstructured mesh generation for ocean modelling. In addition the method applies local optimisations to iteratively improve the shoreline approximation. Applications of the method are presented.

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).