Browsing by Author "Kok, Schalk"

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    Efficient and robust partitioned solution schemes for fluid-structure interactions
    (2015) Bogaers, Alfred Edward Jules; Reddy, B Daya; Kok, Schalk; Franz, Thomas
    In this thesis, the development of a strongly coupled, partitioned fluid-structure interactions (FSI) solver is outlined. Well established methods are analysed and new methods are proposed to provide robust, accurate and efficient FSI solutions. All the methods introduced and analysed are primarily geared towards the solution of incompressible, transient FSI problems, which facilitate the use of black-box sub-domain field solvers. In the first part of the thesis, radial basis function (RBF) interpolation is introduced for interface information transfer. RBF interpolation requires no grid connectivity information, and therefore presents an elegant means by which to transfer information across a non-matching and non-conforming interface to couple finite element to finite volume based discretisation schemes. The transfer scheme is analysed, with particular emphasis on a comparison between consistent and conservative formulations. The primary aim is to demonstrate that the widely used conservative formulation is a zero order method. Furthermore, while the consistent formulation is not provably conservative, it yields errors well within acceptable levels and converges within the limit of mesh refinement. A newly developed multi-vector update quasi-Newton (MVQN) method for implicit coupling of black-box partitioned solvers is proposed. The new coupling scheme, under certain conditions, can be demonstrated to provide near Newton-like convergence behaviour. The superior convergence properties and robust nature of the MVQN method are shown in comparison to other well-known quasi-Newton coupling schemes, including the least squares reduced order modelling (IBQN-LS) scheme, the classical rank-1 update Broyden's method, and fixed point iterations with dynamic relaxation. Partitioned, incompressible FSI, based on Dirichlet-Neumann domain decomposition solution schemes, cannot be applied to problems where the fluid domain is fully enclosed. A simple example often provided in the literature is that of balloon inflation with a prescribed inflow velocity. In this context, artificial compressibility (AC) will be shown to be a useful method to relax the incompressibility constraint, by including a source term within the fluid continuity equation. The attractiveness of AC stems from the fact that this source term can readily be added to almost any fluid field solver, including most commercial solvers. AC/FSI is however limited in the range of problems it can effectively be applied to. To this end, the combination of the newly developed MVQN method with AC/FSI is proposed. In so doing, the AC modified fluid field solver can continue to be treated as a black-box solver, while the overall robustness and performance are significantly improved. The study concludes with a demonstration of the modularity offered by partitioned FSI solvers. The analysis of the coupled environment is extended to include steady state FSI, FSI with free surfaces and an FSI problem with solid-body contact.
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    Empirical methods for the estimation of Southern Ocean CO2: support vector and random forest regression
    (2017) Gregor, Luke; Kok, Schalk; Monteiro, Pedro M S
    The Southern Ocean accounts for 40 % of oceanic CO2 uptake, but the estimates are bound by large uncertainties due to a paucity in observations. Gap-filling empirical methods have been used to good effect to approximate pCO2 from satellite observable variables in other parts of the ocean, but many of these methods are not in agreement in the Southern Ocean. In this study we propose two additional methods that perform well in the Southern Ocean: support vector regression (SVR) and random forest regression (RFR). The methods are used to estimate ΔpCO2 in the Southern Ocean based on SOCAT v3, achieving similar trends to the SOM-FFN method by LandschYtzer et al. (2014). Results show that the SOM-FFN and RFR approaches have RMSEs of similar magnitude (14.84 and 16.45 µatm, where 1 atm = 101 325 Pa) where the SVR method has a larger RMSE (24.40 µatm). However, the larger errors for SVR and RFR are, in part, due to an increase in coastal observations from SOCAT v2 to v3, where the SOM-FFN method used v2 data. The success of both SOM-FFN and RFR depends on the ability to adapt to different modes of variability. The SOM-FFN achieves this by having independent regression models for each cluster, while this flexibility is intrinsic to the RFR method. Analyses of the estimates shows that the SVR and RFR's respective sensitivity and robustness to outliers define the outcome significantly. Further analyses on the methods were performed by using a synthetic dataset to assess the following: which method (RFR or SVR) has the best performance? What is the effect of using time, latitude and longitude as proxy variables on ΔpCO2? What is the impact of the sampling bias in the SOCAT v3 dataset on the estimates? We find that while RFR is indeed better than SVR, the ensemble of the two methods outperforms either one, due to complementary strengths and weaknesses of the methods. Results also show that for the RFR and SVR implementations, it is better to include coordinates as proxy variables as RMSE scores are lowered and the phasing of the seasonal cycle is more accurate. Lastly, we show that there is only a weak bias due to undersampling. The synthetic data provide a useful framework to test methods in regions of sparse data coverage and show potential as a useful tool to evaluate methods in future studies.
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    Improved estimates and understanding of interannual trends of CO₂ fluxes in the Southern Ocean
    (2017) Gregor, Luke; Monteiro, Pedro M S; Vichi, Marcello; Kok, Schalk
    The Southern Ocean plays an important role in mitigating the effects of anthropogenically driven climate change. The region accounts for 43% of oceanic uptake of anthropogenic carbon dioxide (CO₂). This is foreseen to change with increasing greenhouse gas emissions due to ocean chemistry and climate feedbacks that regulate the carbon cycle in the Southern Ocean. Studies have already shown that Southern Ocean CO₂ is subject to interannual variability. Measuring and understanding this change has been difficult due to sparse observational data that is biased toward summer. This leaves a crucial gap in our understanding of the Southern Ocean CO₂ seasonal cycle, which needs to be resolved to adequately monitor change and gain insight into the drivers of interannual variability. Machine learning has been successful in estimating CO₂ in may parts of the ocean by extrapolating existing data with satellite measurements of proxy variables of CO₂. However, in the Southern Ocean machine learning has proven less successful. Large differences between machine learning estimates stem from the paucity of data and complexity of the mechanisms that drive CO₂. In this study the aim is to reduce the uncertainty of estimates, advance our understanding of the interannual drivers, and optimise sampling of CO₂ in the Southern Ocean. Improving the estimates of CO₂ was achieved by investigating: the impact of increasing the gridding resolution of input data and proxy variables, and Support vector regression (SVR) and Random Forest Regression (RFR) as alternate machine learning methods. It was found that the improvement gained by increasing gridding resolution was minimal and only RFR was able to improve on existing error estimates. Yet, there was good agreement of the seasonal cycle and interannual trends between RFR, SVR and estimates from the literature. The ensemble mean of these methods was used to investigate the variability and interannual trends of CO₂ in the Southern Ocean. The interannual trends of the ensemble confirmed trends reported in the literature. A weakening of the sink in the early 2000's, followed by a strengthening a strengthening of the sink into the early 2010's. Wind was the overall driver of dominant decadal interannual trends, being more important during winter due to the increased efficacy of entrainment processes. Summer interannual variability of CO₂ was driven primarily by chlorophyll, which responded to basin scale changes in drivers by the complex interaction with underlying physics and possibly sub-mesoscale processes. Lastly CO₂ sampling platforms, namely ships, profiling floats and moorings, were tested in an idealised simulated model environment using a machine learning approach. Ships, simulated from existing cruise tracks, failed to adequately resolve CO₂ below the uncertainty threshold that is required to resolve the seasonal cycle of Southern Ocean CO₂. Eight high frequency sampling moorings narrowly outperformed 200 profiling floats, which were both able to adequately resolve the seasonal cycle. Though, a combination of ships and profiling floats achieved the smallest error.