Numerical Computation of Moving Boundary Phenomena

When matter is subjected to a gradient of: temperature, pressure, concentration, voltage or chemical potential a phase change may occur, which for dynamic processes will be separated by moving boundaries between the adjacent phases. Transport properties vary considerably between phases, consequently any change in phase modifies the rate of transport of: energy, momentum, charge or matter which are fundamental to the behaviour of many physical systems. Such dynamic multi-phase problems have, for historical and mathematical reasons, become known as either: Stefan problems or Moving Boundary Problems (MBPs). In most engineering applications the analysis of these problems is often impossible without recourse to numerical schemes which utilise either: finite difference or finite element methods. The success of finite element methods is their ability to handle complex geometries; however, they are time consuming and less amenable to vectorisation than finite difference techniques which, because of their greater simplicity in formulation and programming, continue to be the more popular choice. Several finite difference schemes are available for the solution of moving boundary problems; however, there are some difficulties associated with each method. Each time a new numerical scheme is developed, it has the aim of improving either, or both, the accuracy and the computational performance. For solving one-dimensional moving boundary problems, the variable time step grid is the best approach in terms of simplicity and computational efficiency. Due to the fact that the time step is variable the implicit recurrence formulae, which are stable for any mesh size, have always been used with this type of discretisation of the space time domain. It will be shown in the course of this thesis that the implicit methods are very inaccurate when used with relatively large time steps; hence, the immediate conclusion may be made - that implicit variable time step methods may not be sufficiently accurate to solve moving boundary problems where the boundary is moving with a relatively slow velocity. The proposed idea, of combining real and virtual grid networks and using new explicit finite difference equations, eliminates the loss of accuracy associated with implicit methods, when the time step is large, and offers higher computational performance. The new finite difference equations are based on the approach of making the finite difference substitution into the solution of the partial differential equation rather than into the partial differential equation itself, which is the classical approach. A new numerical scheme for two-phase Stefan problems which will be referred to as the EVTS method is developed and the solution is compared to other numerical methods as well as the analytic solution. Furthermore, the EVTS method is modified to solve implicit moving boundary problems (oxygen diffusion problem), in which an explicit relation containing the velocity of the moving boundary is absent. The resulting method achieves similar results to other more complex and time consuming methods. A further numerical scheme referred to as the ZC method is developed to deal with heat transfer problems involving three phases (or 2 moving boundaries) which appear and disappear during the process. To the knowledge of the author, a finite difference method for such a problem does not exist. For validation, numerical results are compared with those of the conservative finite element method of Bonnerot and Jamet, which is the only other method available to solve two-moving boundary problems. Finally, a new finite difference solution for non-linear problems is developed and applied to laser heat treatment of materials. The numerical results are in good agreement with published experimental results

Simulations of idealised 3D atmospheric flows on terrestrial planets using LFRic-Atmosphere

We demonstrate that LFRic-Atmosphere, a model built using the Met Office's GungHo dynamical core, is able to reproduce idealised large-scale atmospheric circulation patterns specified by several widely-used benchmark recipes. This is motivated by the rapid rate of exoplanet discovery and the ever-growing need for numerical modelling and characterisation of their atmospheres. Here we present LFRic-Atmosphere's results for the idealised tests imitating circulation regimes commonly used in the exoplanet modelling community. The benchmarks include three analytic forcing cases: the standard Held-Suarez test, the Menou-Rauscher Earth-like test, and the Merlis-Schneider Tidally Locked Earth test. Qualitatively, LFRic-Atmosphere agrees well with other numerical models and shows excellent conservation properties in terms of total mass, angular momentum and kinetic energy. We then use LFRic-Atmosphere with a more realistic representation of physical processes (radiation, subgrid-scale mixing, convection, clouds) by configuring it for the four TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI) scenarios. This is the first application of LFRic-Atmosphere to a possible climate of a confirmed terrestrial exoplanet. LFRic-Atmosphere reproduces the THAI scenarios within the spread of the existing models across a range of key climatic variables. Our work shows that LFRic-Atmosphere performs well in the seven benchmark tests for terrestrial atmospheres, justifying its use in future exoplanet climate studies.Comment: 34 pages, 9(12) figures; Submitted to Geoscientific Model Development; Comments are welcome (see Discussion tab on the journal's website: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-647

UKESM1: description and evaluation of the UK Earth System Model

We document the development of the first version of the United Kingdom Earth System Model UKESM1. The model represents a major advance on its predecessor HadGEM2‐ES, with enhancements to all component models and new feedback mechanisms. These include: a new core physical model with a well‐resolved stratosphere; terrestrial biogeochemistry with coupled carbon and nitrogen cycles and enhanced land management; tropospheric‐stratospheric chemistry allowing the holistic simulation of radiative forcing from ozone, methane and nitrous oxide; two‐moment, five‐species, modal aerosol; and ocean biogeochemistry with two‐way coupling to the carbon cycle and atmospheric aerosols. The complexity of coupling between the ocean, land and atmosphere physical climate and biogeochemical cycles in UKESM1 is unprecedented for an Earth system model. We describe in detail the process by which the coupled model was developed and tuned to achieve acceptable performance in key physical and Earth system quantities, and discuss the challenges involved in mitigating biases in a model with complex connections between its components. Overall the model performs well, with a stable pre‐industrial state, and good agreement with observations in the latter period of its historical simulations. However, global mean surface temperature exhibits stronger‐than‐observed cooling from 1950 to 1970, followed by rapid warming from 1980 to 2014. Metrics from idealised simulations show a high climate sensitivity relative to previous generations of models: equilibrium climate sensitivity (ECS) is 5.4 K, transient climate response (TCR) ranges from 2.68 K to 2.85 K, and transient climate response to cumulative emissions (TCRE) is 2.49 K/TtC to 2.66 K/TtC

NERC UKESM1.ice-LL model output prepared for CMIP6 ISMIP6

Coupled Model Intercomparison Project Phase 6 (CMIP6) datasets: These data include all datasets published for 'CMIP6.ISMIP6.NERC.UKESM1-ice-LL' with the full Data Reference Syntax following the template 'mip_era.activity_id.institution_id.source_id.experiment_id.member_id.table_id.variable_id.grid_label.version'. The UKESM1.ice-N96ORCA1 climate model, released in 2019, includes the following components: aerosol: UKCA-GLOMAP-mode, atmos: MetUM-HadGEM3-GA7.1 (N96; 192 x 144 longitude/latitude; 85 levels; top level 85 km), land: JULES-ISMIP6-1.0, landIce: BISICLES-UKESM-ISMIP6-1.0, ocean: NEMO-HadGEM3-GO6.0 (eORCA1 tripolar primarily 1 deg with meridional refinement down to 1/3 degree in the tropics; 360 x 330 longitude/latitude; 75 levels; top grid cell 0-1 m), seaIce: CICE-HadGEM3-GSI8 (eORCA1 tripolar primarily 1 deg; 360 x 330 longitude/latitude). The model was run by the Natural Environment Research Council, STFC-RAL, Harwell, Oxford, OX11 0QX, UK (NERC) in native nominal resolutions: aerosol: 250 km, atmos: 250 km, land: 250 km, landIce: 5 km, ocean: 100 km, seaIce: 100 km. Project: These data have been generated as part of the internationally-coordinated Coupled Model Intercomparison Project Phase 6 (CMIP6; see also GMD Special Issue: http://www.geosci-model-dev.net/special_issue590.html). The simulation data provides a basis for climate research designed to answer fundamental science questions and serves as resource for authors of the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC-AR6). CMIP6 is a project coordinated by the Working Group on Coupled Modelling (WGCM) as part of the World Climate Research Programme (WCRP). Phase 6 builds on previous phases executed under the leadership of the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and relies on the Earth System Grid Federation (ESGF) and the Centre for Environmental Data Analysis (CEDA) along with numerous related activities for implementation. The original data is hosted and partially replicated on a federated collection of data nodes, and most of the data relied on by the IPCC is being archived for long-term preservation at the IPCC Data Distribution Centre (IPCC DDC) hosted by the German Climate Computing Center (DKRZ). The project includes simulations from about 120 global climate models and around 45 institutions and organizations worldwide. - Project website: https://pcmdi.llnl.gov/CMIP6

NERC HadGEM3-GC31-LL model output prepared for CMIP6 PMIP

Coupled Model Intercomparison Project Phase 6 (CMIP6) datasets: These data include all datasets published for 'CMIP6.PMIP.NERC.HadGEM3-GC31-LL' with the full Data Reference Syntax following the template 'mip_era.activity_id.institution_id.source_id.experiment_id.member_id.table_id.variable_id.grid_label.version'. The HadGEM3-GC3.1-N96ORCA1 climate model, released in 2016, includes the following components: aerosol: UKCA-GLOMAP-mode, atmos: MetUM-HadGEM3-GA7.1 (N96; 192 x 144 longitude/latitude; 85 levels; top level 85 km), land: JULES-HadGEM3-GL7.1, ocean: NEMO-HadGEM3-GO6.0 (eORCA1 tripolar primarily 1 deg with meridional refinement down to 1/3 degree in the tropics; 360 x 330 longitude/latitude; 75 levels; top grid cell 0-1 m), seaIce: CICE-HadGEM3-GSI8 (eORCA1 tripolar primarily 1 deg; 360 x 330 longitude/latitude). The model was run by the Natural Environment Research Council, STFC-RAL, Harwell, Oxford, OX11 0QX, UK (NERC) in native nominal resolutions: aerosol: 250 km, atmos: 250 km, land: 250 km, ocean: 100 km, seaIce: 100 km. Project: These data have been generated as part of the internationally-coordinated Coupled Model Intercomparison Project Phase 6 (CMIP6; see also GMD Special Issue: http://www.geosci-model-dev.net/special_issue590.html). The simulation data provides a basis for climate research designed to answer fundamental science questions and serves as resource for authors of the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC-AR6). CMIP6 is a project coordinated by the Working Group on Coupled Modelling (WGCM) as part of the World Climate Research Programme (WCRP). Phase 6 builds on previous phases executed under the leadership of the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and relies on the Earth System Grid Federation (ESGF) and the Centre for Environmental Data Analysis (CEDA) along with numerous related activities for implementation. The original data is hosted and partially replicated on a federated collection of data nodes, and most of the data relied on by the IPCC is being archived for long-term preservation at the IPCC Data Distribution Centre (IPCC DDC) hosted by the German Climate Computing Center (DKRZ). The project includes simulations from about 120 global climate models and around 45 institutions and organizations worldwide. - Project website: https://pcmdi.llnl.gov/CMIP6

NERC HadGEM3-GC31-LL model output prepared for CMIP6 PMIP

Coupled Model Intercomparison Project Phase 6 (CMIP6) datasets: These data include all datasets published for 'CMIP6.PMIP.NERC.HadGEM3-GC31-LL' with the full Data Reference Syntax following the template 'mip_era.activity_id.institution_id.source_id.experiment_id.member_id.table_id.variable_id.grid_label.version'. The HadGEM3-GC3.1-N96ORCA1 climate model, released in 2016, includes the following components: aerosol: UKCA-GLOMAP-mode, atmos: MetUM-HadGEM3-GA7.1 (N96; 192 x 144 longitude/latitude; 85 levels; top level 85 km), land: JULES-HadGEM3-GL7.1, ocean: NEMO-HadGEM3-GO6.0 (eORCA1 tripolar primarily 1 deg with meridional refinement down to 1/3 degree in the tropics; 360 x 330 longitude/latitude; 75 levels; top grid cell 0-1 m), seaIce: CICE-HadGEM3-GSI8 (eORCA1 tripolar primarily 1 deg; 360 x 330 longitude/latitude). The model was run by the Natural Environment Research Council, STFC-RAL, Harwell, Oxford, OX11 0QX, UK (NERC) in native nominal resolutions: aerosol: 250 km, atmos: 250 km, land: 250 km, ocean: 100 km, seaIce: 100 km. Project: These data have been generated as part of the internationally-coordinated Coupled Model Intercomparison Project Phase 6 (CMIP6; see also GMD Special Issue: http://www.geosci-model-dev.net/special_issue590.html). The simulation data provides a basis for climate research designed to answer fundamental science questions and serves as resource for authors of the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC-AR6). CMIP6 is a project coordinated by the Working Group on Coupled Modelling (WGCM) as part of the World Climate Research Programme (WCRP). Phase 6 builds on previous phases executed under the leadership of the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and relies on the Earth System Grid Federation (ESGF) and the Centre for Environmental Data Analysis (CEDA) along with numerous related activities for implementation. The original data is hosted and partially replicated on a federated collection of data nodes, and most of the data relied on by the IPCC is being archived for long-term preservation at the IPCC Data Distribution Centre (IPCC DDC) hosted by the German Climate Computing Center (DKRZ). The project includes simulations from about 120 global climate models and around 45 institutions and organizations worldwide. - Project website: https://pcmdi.llnl.gov/CMIP6