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Numerical modelling frequently involves a diagnostic quantity of interest (QoI) - often of greater importance than the PDE solution - which we seek to accurately approximate. In the case of coastal ocean modelling the power output of a tidal turbine farm is one such example. Goal-oriented error estimation and mesh adaptation can be used to provide meshes which are well-suited to achieving this goal, using fewer computational resources than required by other methods, such as uniform refinement. A mixed discontinuous/continuous Galerkin approach is applied to solve the nonlinear shallow water equations within the Thetis coastal ocean finite element model. An implementation of goal-oriented mesh adaptation is outlined, including an error estimate which takes account of the discontinuities in the discrete solution and a method for approximating the adjoint error. Results are presented for simulations of two model tidal farm configurations. Convergence analysis indicates that the anisotropic goal-oriented adaptation strategy yields meshes which permit accurate QoI estimation using fewer computational resources than uniform refinement.

Purpose: To examine the accuracy and sensitivity of tidal array performance assessment by numerical techniques applying goal-oriented mesh adaptation.Methods: The goal-oriented framework is designed to give rise to adaptive meshes upon which a given diagnostic quantity of interest (QoI) can be accurately captured, whilst maintaining a low overall computational cost. We seek to improve the accuracy of the discontinuous Galerkin method applied to a depth-averaged shallow water model of a tidal energy farm, where turbines are represented using a drag parametrisation and the energy output is specified as the QoI. Two goal-oriented adaptation strategies are considered, which give rise to meshes with isotropic and anisotropic elements.Results: We present both fixed mesh and goal-oriented adaptive mesh simulations for an established test case involving an idealised tidal turbine array positioned in a channel. With both the fixed meshes and the goal-oriented methodologies, we reproduce results from the literature which demonstrate how a staggered array configuration extracts moreenergy than an aligned array. We also make detailed qualitative and quantitative comparisons between the fixed mesh and adaptive outputs.Conclusion: The proposed goal-oriented mesh adaptation strategies are validated for the purposes of tidal energy resource assessment. Using 10% as many degrees of freedom as a high resolution fixed mesh benchmark, they are shown to enable energy output differences smaller than 10%. Applied to a tidal array with aligned rows of turbines, the anisotropic adaptation scheme is shown to yield differences smaller than 1%.

International audience; This paper applies metric-based mesh adaptation methods to advection-dominated tracer transport modelling problems in two and three dimensions, using the finite element package Firedrake. In particular, the mesh adaptation methods considered are built upon goal-oriented estimates for the error incurred in evaluating a diagnostic quantity of interest (QoI). In the motivating example of modelling to support desalination plant outfall design, such a QoI could be the salinity at the plant inlet, which could be negatively impacted by the transport of brine from the plant’s outfall. Four approaches are considered, one of which yields isotropic meshes. The focus on advection-dominated problems means that flows are often anisotropic; thus, three anisotropic approaches are also considered. Meshes resulting from each of the four approaches yield solutions to the tracer transport problem which give better approximations to QoI values than uniform meshing, for a given mesh size. The methodology is validated using an existing 2D tracer transport test case with a known analytical solution. Goal-oriented meshes for an idealised time-dependent desalination outfall scenario are also presented.

The modelling of a tidal array farm is an inherently multi-scale endeavour. It requires the simultaneous resolution of tidal processes across tens or hundreds of kilometres of coastal ocean (including estuaries, or even entire seas), the hydrodynamics in the neighbourhood of the farm (hundreds of metres), the wakes of individual turbines (metres, or tens of metres) and device hydrodynamics (sub-metre). As such, the construction of an accurate, computationally efficient numerical model requires careful consideration of the underlying discretisation. In this paper, we apply time-dependent mesh adaptation techniques based on the Riemannian metric framework to an idealised tidal array and assess the quality of the resulting approximations. Whilst classical hierarchical mesh adaptation methods modify mesh element/cell size in order to improve resolution locally, the metric-based approach also allows for control of element shape and orientation, which can be especially advantageous for advection-dominated problems. Metrics are normalised in such a way that the resulting discretisation is multi-scale in both space and time as per Alauzet and Olivier (2010). Typically, metrics are constructed from recovered derivatives of solution fields, such as fluid vorticity. Alternatively, metrics may be derived from goal-oriented error estimates, enabling accurate estimation of a diagnostic quantity of interest (QoI). In the context of tidal farm modelling, one clear QoI is the power output. Building upon the idealised steady-state test case considered in Wallwork et al. (2020), which represents turbines using a drag parametrisation in a depth-averaged shallow water model, we demonstrate here that goal-oriented mesh adaptation can be used to obtain an accurate approximation of tidal farm power output using relatively few overall degrees of freedom.

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations.

International audience; This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displace-ments on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabili-ties in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations.

Unstructured grid adaptation is a technology that holds the potential to improve the automation and accuracy of computational fluid dynamics and other computational disciplines. Difficulty producing the highly anisotropic elements necessary for simulation on complex curved geometries that satisfies a resolution request has limited this technology's widespread adoption. The Unstructured Grid Adaptation Working Group is an open gathering of researchers working on adapting simplicial meshes to conform to a metric field. Current members span a wide range of institutions including academia, industry, and national laboratories. The purpose of this group is to create a common basis for understanding and improving mesh adaptation. We present our first major contribution: a common set of benchmark cases, including input meshes and analytic metric specifications, that are publicly available to be used for evaluating any mesh adaptation code. We also present the results of several existing codes on these benchmark cases, to illustrate their utility in identifying key challenges common to all codes and important differences between available codes. Future directions are defined to expand this benchmark to mature the technology necessary to impact practical simulation workflows.

International audience; Unstructured grid adaptation is a tool to control Computational Fluid Dynamics (CFD) discretization error. However, adaptive grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Issues that prevent the use of adaptive grid methods are identified by applying unstructured grid adaptation methods to a series of benchmark cases. Once identified, these challenges to existing adaptive workflows can be addressed. Unstructured grid adaptation is evaluated for test cases described on the Turbulence Modeling Resource (TMR) web site, which documents uniform grid refinement of multiple schemes. The cases are turbulent flow over a Hemisphere Cylinder and an ONERA M6 Wing. Adaptive grid force and moment trajectories are shown for three integrated grid adaptation processes with Mach interpolation control and output error based metrics. The integrated grid adaptation process with a finite element (FE) discretization produced results consistent with uniform grid refinement of fixed grids. The integrated grid adaptation processes with finite volume schemes were slower to converge to the reference solution than the FE method. Metric conformity is documented ongrid/metric snapshots for five grid adaptation mechanics implementations. These tools produce anisotropic boundary conforming grids requested by the adaptation process.

Anisotropic metric based mesh adaptation has proved its efficiency to reduce the CPU time of steady simulations while improving their accuracy. However its extension to timedependent problems is far from straightforward, and the introduction of moving meshes adds new problems. This paper presents updates regarding mesh adaptation for unsteady problems with moving boundaries. A new space-time analysis of the interpolation error in the continuous mesh framework is proposed, which enables enhancements of the fixedpoint unsteady mesh adaptation algorithm. The analysis is then extended to the case of moving geometries, within the range of body-fitted moving meshes and ALE simulations, and the appropriate modifications are made to the adaptation algorithm. Finally, three dimensional adaptative simulations with moving boundaries are exhibited to validate our approach.

International audience; This paper deals with numerical simulations involving three-dimensional moving geometries with large displacements. Such simulations are much valued by industries, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations is proposed, that allows to avoid remeshing while performing large displacements. However, this is done at the cost of relaxing the fixed-topology constraint imposed by the classical Arbitrary-Lagrangian-Eulerian (ALE) framework. An ALE compressible flow solver is integrated to this process. This solver lies on the strict interpretation of the Discrete Geometrical Conservation Law to preserve the order of accuracy of the time integration. For fluid-structure interaction (FSI) simulations, the six degrees of freedom (6-DOF) approach for rigid bodies is considered. Finally, 3D imposed-motion and FSI examples are given, to validate the proposed approach