Adrian Umpleby

Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations

A method for optimising a pre-existing mesh of tetrahedral finite elements is described. It is based on a series of mesh connectivity and node position searches of the landscape defining mesh quality. A Riemannian metric, reflecting the a posteriori error measure, is used to calculate element size and shape. A functional is defined which embodies both shape and size quality of an element with respect to the metric, and is used to gauge mesh quality. A heuristic-based local search strategy is adopted – local in the sense that it has no hill-climbing abilities. The paper presents applications of the method to complex, steady-state and time-dependent problems which highlight its anisotropic, feature-capturing abilities. Numerical evidence is provided which suggests that the computational complexity (time) of the proposed algorithm varies linearly with the number of elements or nodes of the finite element mesh.

Full waveform inversion: A North Sea OBC case study

Full Waveform Inversion (FWI) aims to obtain superior velocity models by minimizing the difference between observed and modelled seismic waveforms. We apply FWI to a North Sea OBC field data set with wide azimuths and more than 10 km long offsets. We discuss the methodology used and the associated practical issues. Our FWI result has revealed detailed velocity features associated with thin, gas-charged layers and faulting in the shallow sections of the model. We demonstrate that this velocity update has improved the imaging of the deeper structures.

Transient Criticality in Fissile Solutions - Compressibility Effects

Abstract Research on the incorporation of compressibility effects, for both the liquid and radiolytic gas phases, into the Finite Element Transient Criticality (FETCH) coupled neutronics/computational fluid dynamics code is described. The code has been developed to simulate criticality transients in multiphase media and is applied here to fissile solution transient criticality. The predicted fission and pressure transients obtained by the enhanced numerical model are benchmarked against the results from the SILENE series of experiments on criticality transients in uranium solutions. The amplitude and the form of the first pressure peak, following a step reactivity change, are well represented, and insight is gained into the form of subsequent pressure oscillations. An explanation is given on the absence of these oscillations in more energetic transients.

Space-dependent kinetics simulation of a gas-cooled fluidized bed nuclear reactor

In this paper we present numerical simulations of a conceptual helium-cooled fluidized bed thermal nuclear reactor. The simulations are performed using the coupled neutronics/multi-phase computational fluid dynamics code finite element transient criticality which is capable of modelling all the relevant non-linear feedback mechanisms. The conceptual reactor consists of an axi-symmetric bed surrounded by graphite moderator inside which 0.1 cm diameter TRISO-coated nuclear fuel particles are fluidized. Detailed spatial/temporal neutron flux and temperature profiles have been obtained providing valuable insight into the power distribution and fluid dynamics of this complex system. The numerical simulations show that the unique mixing ability of the fluidized bed gives rise, as expected, to uniform temperature and particle distribution. This uniformity enhances the heat transfer and therefore the power produced by the reactor.

Finite element-spherical harmonics solutions of the 3D Kobayashi benchmarks with ray-tracing void treatment

The finite element spherical-harmonics method is applied to the solution of the Kobayashi 3D benchmark problems. In particular, we evaluate the surface radiation exchange method based on raytracing which has been developed to circumvent the difficulty caused to the second-order, even-parity formulation by low-density regimes. This method brings several advantages which include obviating the need to explicitly solve the problem in voided regions and improving accuracy of the solution for a given order of angular approximation. Results produced by the computer code EVENT are presented for the six cases proposed. Comparisons with reference solutions show that the hybrid scheme can solve to reasonable accuracy most cases with relatively modest space-angle resolution. For the more difficult cases involving streaming in purely absorbing media, noticeable discrepancies were observed, but this indicated the need for a more judicious space-angle refinement (not attempted) rather than any deficiency of the hybrid scheme itself.

3D full-wavefield tomography: imaging beneath heterogeneous overburden

We have developed computer codes and work-flows for 3D acoustic waveform inversion in both the frequency and time domains. We have applied these methods to several 3D field datasets with a variety of acquisition geometries and target depths. In each case, wavefield tomography was able to obtain a high-resolution high-fidelity velocity model of the heterogeneous overburden, and consequently to improve subsequent depth imaging of an underlying target.

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).

Non-linear space-dependent kinetics for the criticality assessment of fissile solutions

Abstract A deterministic model for calculating the time dependent fission yield from solutions has been developed. The model is based on transient finite element methods and couples radiation transport modelling with computational fluid dynamics. Non-linear space dependent kinetic equations are derived, in which the non-linearities arise due to radiolytic gas generation, geometical changes in the liquid, the temperature dependent densities, cross sections and thermally/gas induced fluid motion. The latter advects the delayed neutron precursor concentrations together with the energy fields. Applications focus on the role of radiolytic gas evolution and buoyancy induced fluid motion on the criticality of fissile liquids with delayed and prompt supercritical step reactivity insertions. The analysis is performed with uranyl nitrate solutions. The theory behind the modelling is presented, together with numerical results, to validate the approach. The resulting computer code, which we call FETCH (finite element transient criticality), is validated against point kinetics based models for right cylinders and against experiment for both low (delayed supercritical) and high powered (usually prompt supercritical) transients. The term ‘low powered’ in this context will be used to describe transients in fissile liquids in which the rate of radiolytic gas generation is so small that it can be ignored without sacrificing the accuracy of the simulations. Modelling can then be conducted in a single fluid phase. The term “high powered’ refers to transients in which gas evolution and ensuing free surface motion play an important part in their dynamics and are thus solved using the multi-phase mode of FETCH. The simulations presented here provided extensive insights into the dynamics of these transients which can be difficult to study in detail with experiment.

A Strategy for Waveform Inversion without an Accurate Starting Model

SUMMARY A key limitation of waveform inversion as currently implemented is the need for a starting model of high accuracy or field data with low frequencies. Here we present a new approach - staged waveform inversion - designed to mitigate this need and thereby permit the application of waveform inversion to a much wider range of datasets.

Finite Element Based Riemann Solvers for Time-Dependent and Steady-State Radiation Transport

Abstract A high-order, nonoscillatory scheme is described which solves the transient and steady-state Boltzmann transport equation on unstructured Finite Element (FE) meshes. Flux limiters are applied in the space and time domains resulting in a scheme which is both free from oscillations and globally high-order accurate in space and time. The method described is finite volume based and uses a consistent FE representation of the solution variables to obtain a high-order solution along the control volume boundaries. Careful inspection of the eigenstructure of the Riemann problem allows one to switch smoothly between a high-order and a low-order nonoscillatory solution.