Synthesis of novel and stable g-C3N4/N-doped SrTiO3 hybrid nanocomposites with improved photocurrent and photocatalytic activity under visible light irradiation

Hybrid nanocomposites based on N-doped SrTiO3 nanoparticles wrapped in g-C3N4 nanosheets were successfully prepared by a facile and reproducible polymeric citrate and thermal exfoliation method. The results clearly indicated that the N-doped SrTiO3 nanoparticles are successfully wrapped in layers of the g-C3N4 nanosheets. The g-C3N4/N-doped SrTiO3 nanocomposites showed absorption edges at longer wavelengths compared with the pure g-C3N4 as well as N-doped SrTiO3. The hybrid nanocomposites exhibit an improved photocurrent response and photocatalytic activity under visible light irradiation. Interestingly, the hybrid nanocomposite possesses high photostability and reusability. Based on experimental results, the possible mechanism for prolonged lifetime of the photoinduced charge carrier was also discussed. The high performance of the g-C3N4/N-doped SrTiO3 photocatalysts is due to the synergic effect at the interface of g-C3N4 and N-doped SrTiO3 hetero/nanojunction including the high separation efficiency of the charge carrier, band energy matching and the suppressed recombination rate. Therefore, the hybrid photocatalyst could be of potential interest for water splitting and environmental remediation under natural sunlight.

Synthesis of highly efficient and recyclable visible-light responsive mesoporous g-C3N4 photocatalyst via facile template-free sonochemical route

Herein we demonstrate a facile template-free sonochemical strategy to synthesize mesoporous g-C3N4 with a high surface area and enhanced photocatalytic activity. The TEM and nitrogen adsorption–desorption studies confirm mesoporous structure in g-C3N4 body. The photocatalytic activity of mesoporous g-C3N4 is almost 5.5 times higher than that of bulk g-C3N4 under visible-light irradiation. The high photocatalytic performance of the mesoporous g-C3N4 was attributed to the much higher specific surface area, efficient adsorption ability and the unique interfacial mesoporous structure which can favour the absorption of light and separation of photoinduced electron–hole pairs more effectively. A possible photocatalytic mechanism was discussed by the radicals and holes trapping experiments. Interestingly, the synthesized mesoporous g-C3N4 possesses high reusability. Hence the mesoporous g-C3N4 can be a promising photocatalytic material for practical applications in water splitting as well as environmental remediation.

Nanostructured Metal Oxide Coatings for Electrochemical Energy Conversion and Storage Electrodes

The realization of an energy future based on safe, clean, sustainable, and economically viable technologies is one of the grand challenges facing modern society. Electrochemical energy technologies underpin the potential success of this effort to divert energy sources away from fossil fuels, whether one considers alternative energy conversion strategies through photoelectrochemical (PEC) production of chemical fuels or fuel cells run with sustainable hydrogen, or energy storage strategies, such as in batteries and supercapacitors. This dissertation builds on recent advances in nanomaterials design, synthesis, and characterization to develop novel electrodes that can electrochemically convert and store energy.

Chapter 2 of this dissertation focuses on refining the properties of TiO2-based PEC water-splitting photoanodes used for the direct electrochemical conversion of solar energy into hydrogen fuel. The approach utilized atomic layer deposition (ALD); a growth process uniquely suited for the conformal and uniform deposition of thin films with angstrom-level thickness precision. ALD’s thickness control enabled a better understanding of how the effects of nitrogen doping via NH3 annealing treatments, used to reduce TiO2’s bandgap, can have a strong dependence on TiO2’s thickness and crystalline quality. In addition, it was found that some of the negative effects on the PEC performance typically associated with N-doped TiO2 could be mitigated if the NH3-annealing was directly preceded by an air-annealing step, especially for ultrathin (i.e., < 10 nm) TiO2 films. ALD was also used to conformally coat an ultraporous conductive fluorine-doped tin oxide nanoparticle (nanoFTO) scaffold with an ultrathin layer of TiO2. The integration of these ultrathin films and the oxide nanoparticles resulted in a heteronanostructure design with excellent PEC water oxidation photocurrents (0.7 mA/cm2 at 0 V vs. Ag/AgCl) and charge transfer efficiency.

In Chapter 3, two innovative nanoarchitectures were engineered in order to enhance the pseudocapacitive energy storage of next generation supercapacitor electrodes. The morphology and quantity of MnO2 electrodeposits was controlled by adjusting the density of graphene foliates on a novel graphenated carbon nanotube (g-CNT) scaffold. This control enabled the nanocomposite supercapacitor electrode to reach a capacitance of 640 F/g, under MnO2 specific mass loading conditions (2.3 mg/cm2) that are higher than previously reported. In the second engineered nanoarchitecture, the electrochemical energy storage properties of a transparent electrode based on a network of solution-processed Cu/Ni cores/shell nanowires (NWs) were activated by electrochemically converting the Ni metal shell into Ni(OH)2. Furthermore, an adjustment of the molar percentage of Ni plated onto the Cu NWs was found to result in a tradeoff between capacitance, transmittance, and stability of the resulting nickel hydroxide-based electrode. The nominal area capacitance and power performance results obtained for this Cu/Ni(OH)2 transparent electrode demonstrates that it has significant potential as a hybrid supercapacitor electrode for integration into cutting edge flexible and transparent electronic devices.

Catalytic Processes Mediated by Metal−Organic Frameworks : Reactivity and Mechanistic Studies

The present thesis describes the development of heterogeneous catalytic methodologies using metal−organic frameworks (MOFs) as porous matrices for supporting transition metal catalysts. A wide spectrum of chemical reactions is covered. Following the introductory section (Chapter 1), the results are divided between one descriptive part (Chapter 2) and four experimental parts (Chapters 3–6). Chapter 2 provides a detailed account of MOFs and their role in heterogeneous catalysis. Specific synthesis methods and characterization techniques that may be unfamiliar to organic chemists are illustrated based on examples from this work. Pd-catalyzed heterogeneous C−C coupling and C−H functionalization reactions are studied in Chapter 3, with focus on their practical utility. A vast functional group tolerance is reported, allowing access to substrates of relevance for the pharmaceutical industry. Issues concerning the recyclability of MOF-supported catalysts, leaching and operation under continuous flow are discussed in detail. The following chapter explores puzzling questions regarding the nature of the catalytically active species and the pathways of deactivation for Pd@MOF catalysts. These questions are addressed through detailed mechanistic investigations which include in situ XRD and XAS data acquisition. For this purpose a custom reaction cell is also described in Chapter 4. The scope of Pd@MOF-catalyzed reactions is expanded in Chapter 5. A strategy for boosting the thermal and chemical robustness of MOF crystals is presented. Pd@MOF catalysts are coated with a protecting SiO2 layer, which improves their mechanical properties without impeding diffusion. The resulting nanocomposite is better suited to withstand the harsh conditions of aerobic oxidation reactions. In this chapter, the influence of the nanoparticles’ geometry over the catalyst’s selectivity is also investigated. While Chapters 3–5 dealt with Pd-catalyzed processes, Chapter 6 introduces hybrid materials based on first-row transition metals. Their reactivity is explored towards light-driven water splitting. The heterogenization process leads to stabilized active sites, facilitating the spectroscopic probing of intermediates in the catalytic cycle.

Functional alkali tantalate 2D structures for microelectronics and related applications

Alkali tantalates and niobates, including K(Ta / Nb)O3, Li(Ta / Nb)O3 and Na(Ta / Nb)O3, are a very promising ferroic family of lead-free compounds with perovskite-like structures. Their versatile properties make them potentially interesting for current and future application in microelectronics, photocatalysis, energy and biomedics. Among them potassium tantalate, KTaO3 (KTO), has been raising interest as an alternative for the well-known strontium titanate, SrTiO3 (STO). KTO is a perovskite oxide with a quantum paraelectric behaviour when electrically stimulated and a highly polarizable lattice, giving opportunity to tailor its properties via external or internal stimuli. However problems related with the fabrication of either bulk or 2D nanostructures makes KTO not yet a viable alternative to STO. Within this context and to contribute scientifically to the leverage tantalate based compounds applications, the main goals of this thesis are: i) to produce and characterise thin films of alkali tantalates by chemical solution deposition on rigid Si based substrates, at reduced temperatures to be compatible with Si technology, ii) to fulfil scientific knowledge gaps in these relevant functional materials related to their energetics and ii) to exploit alternative applications for alkali tantalates, as photocatalysis. In what concerns the synthesis attention was given to the understanding of the phase formation in potassium tantalate synthesized via distinct routes, to control the crystallization of desired perovskite structure and to avoid low temperature pyrochlore or K-deficient phases. The phase formation process in alkali tantalates is far from being deeply analysed, as in the case of Pb-containing perovskites, therefore the work was initially focused on the process-phase relationship to identify the driving forces responsible to regulate the synthesis. Comparison of phase formation paths in conventional solid-state reaction and sol-gel method was conducted. The structural analyses revealed that intermediate pyrochlore K2Ta2O6 structure is not formed at any stage of the reaction using conventional solid-state reaction. On the other hand in the solution based processes, as alkoxide-based route, the crystallization of the perovskite occurs through the intermediate pyrochlore phase; at low temperatures pyrochlore is dominant and it is transformed to perovskite at >800 °C. The kinetic analysis carried out by using Johnson-MehlAvrami-Kolmogorow model and quantitative X-ray diffraction (XRD) demonstrated that in sol-gel derived powders the crystallization occurs in two stages: i) at early stage of the reaction dominated by primary nucleation, the mechanism is phase-boundary controlled, and ii) at the second stage the low value of Avrami exponent, n ~ 0.3, does not follow any reported category, thus not permitting an easy identification of the mechanism. Then, in collaboration with Prof. Alexandra Navrotsky group from the University of California at Davis (USA), thermodynamic studies were conducted, using high temperature oxide melt solution calorimetry. The enthalpies of formation of three structures: pyrochlore, perovskite and tetragonal tungsten bronze K6Ta10.8O30 (TTB) were calculated. The enthalpies of formation from corresponding oxides, ∆Hfox, for KTaO3, KTa2.2O6 and K6Ta10.8O30 are -203.63 ± 2.84 kJ/mol, - 358.02 ± 3.74 kJ/mol, and -1252.34 ± 10.10 kJ/mol, respectively, whereas from elements, ∆Hfel, for KTaO3, KTa2.2O6 and K6Ta10.8O30 are -1408.96 ± 3.73 kJ/mol, -2790.82 ± 6.06 kJ/mol, and -13393.04 ± 31.15 kJ/mol, respectively. The possible decomposition reactions of K-deficient KTa2.2O6 pyrochlore to KTaO3 perovskite and Ta2O5 (reaction 1) or to TTB K6Ta10.8O30 and Ta2O5 (reaction 2) were proposed, and the enthalpies were calculated to be 308.79 ± 4.41 kJ/mol and 895.79 ± 8.64 kJ/mol for reaction 1 and reaction 2, respectively. The reactions are strongly endothermic, indicating that these decompositions are energetically unfavourable, since it is unlikely that any entropy term could override such a large positive enthalpy. The energetic studies prove that pyrochlore is energetically more stable phase than perovskite at low temperature. Thus, the local order of the amorphous precipitates drives the crystallization into the most favourable structure that is the pyrochlore one with similar local organization; the distance between nearest neighbours in the amorphous or short-range ordered phase is very close to that in pyrochlore. Taking into account the stoichiometric deviation in KTO system, the selection of the most appropriate fabrication / deposition technique in thin films technology is a key issue, especially concerning complex ferroelectric oxides. Chemical solution deposition has been widely reported as a processing method to growth KTO thin films, but classical alkoxide route allows to crystallize perovskite phase at temperatures >800 °C, while the temperature endurance of platinized Si wafers is ~700 °C. Therefore, alternative diol-based routes, with distinct potassium carboxylate precursors, was developed aiming to stabilize the precursor solution, to avoid using toxic solvents and to decrease the crystallization temperature of the perovskite phase. Studies on powders revealed that in the case of KTOac (solution based on potassium acetate), a mixture of perovskite and pyrochlore phases is detected at temperature as low as 450 °C, and gradual transformation into monophasic perovskite structure occurs as temperature increases up to 750 °C, however the desired monophasic KTaO3 perovskite phase is not achieved. In the case of KTOacac (solution with potassium acetylacetonate), a broad peak is detected at temperatures <650 °C, characteristic of amorphous structures, while at higher temperatures diffraction lines from pyrochlore and perovskite phases are visible and a monophasic perovskite KTaO3 is formed at >700 °C. Infrared analysis indicated that the differences are due to a strong deformation of the carbonate-based structures upon heating. A series of thin films of alkali tantalates were spin-coated onto Si-based substrates using diol-based routes. Interestingly, monophasic perovskite KTaO3 films deposited using KTOacac solution were obtained at temperature as low as 650 °C; films were annealed in rapid thermal furnace in oxygen atmosphere for 5 min with heating rate 30 °C/sec. Other compositions of the tantalum based system as LiTaO3 (LTO) and NaTaO3 (NTO), were successfully derived as well, onto Si substrates at 650 °C as well. The ferroelectric character of LTO at room temperature was proved. Some of dielectric properties of KTO could not be measured in parallel capacitor configuration due to either substrate-film or filmelectrode interfaces. Thus, further studies have to be conducted to overcome this issue. Application-oriented studies have also been conducted; two case studies: i) photocatalytic activity of alkali tantalates and niobates for decomposition of pollutant, and ii) bioactivity of alkali tantalate ferroelectric films as functional coatings for bone regeneration. Much attention has been recently paid to develop new type of photocatalytic materials, and tantalum and niobium oxide based compositions have demonstrated to be active photocatalysts for water splitting due to high potential of the conduction bands. Thus, various powders of alkali tantalates and niobates families were tested as catalysts for methylene blue degradation. Results showed promising activities for some of the tested compounds, and KNbO3 is the most active among them, reaching over 50 % degradation of the dye after 7 h under UVA exposure. However further modifications of powders can improve the performance. In the context of bone regeneration, it is important to have platforms that with appropriate stimuli can support the attachment and direct the growth, proliferation and differentiation of the cells. In lieu of this here we exploited an alternative strategy for bone implants or repairs, based on charged mediating signals for bone regeneration. This strategy includes coating metallic 316L-type stainless steel (316L-SST) substrates with charged, functionalized via electrical charging or UV-light irradiation, ferroelectric LiTaO3 layers. It was demonstrated that the formation of surface calcium phosphates and protein adsorption is considerably enhanced for 316L-SST functionalized ferroelectric coatings. Our approach can be viewed as a set of guidelines for the development of platforms electrically functionalized that can stimulate tissue regeneration promoting direct integration of the implant in the host tissue by bone ingrowth and, hence contributing ultimately to reduce implant failure.

Electrocatalytic oxidation enhancement at the surface of InGaN films and nanostructures grown directly on Si(111)

Pronounced electrocatalytic oxidation enhancement at the surface of InGaN layers and nanostructures directly grown on Si by plasma-assisted molecular beam epitaxy is demonstrated. The oxidation enhancement, probed with the ferro/ferricyanide redox couple increases with In content and proximity of nanostructure surfaces and sidewalls to the c-plane. This is attributed to the corresponding increase of the density of intrinsic positively charged surface donors promoting electron transfer. Strongest enhancement is for c-plane InGaN layers functionalized with InN quantum dots (QDs). These results explain the excellent performance of our InN/InGaN QD biosensors and water splitting electrodes for further boosting efficiency.

Synthesis of porous graphene/TiO2 by use of recycled graphite

Graphene-based nanomaterials are a kind of new technological materials with high interest for physicists, chemists and materials scientists. Graphene is a two-dimensional (2-D) sheet of carbon atoms in a hexagonal configuration with atoms bonded by sp2 bonds. These bonds and this electron configuration provides the extraordinary properties of graphene, such as very large surface area, a tunable band gap, high mechanical strength and high elasticity and thermal conductivity [1]. Graphene has also been investigated for preparation of composites with various semiconductors like TiO2, ZnO, CdS aiming at enhanced photocatalytic activity for their use for photochemical reaction as water splitting or CO2 to methanol conversion [2-3]. In this communication, the synthesis of porous graphene@TiO2 obtained from a powder graphite recycled, supplied by ECOPIBA, is presented. This graphite was exfoliated, using a nonionic surfactant (Triton X-100) and sonication. Titanium(IV) isopropoxide was used as TiO2 source. After removing the surfactant with a solution HCl/n-propanol, a porous solid is obtained with a specific area of 358 m2g-1. The solid was characterized by XRD, FTIR, XPS, EDX and TEM. Figure 1 shows the graphene 2D layer bonded with nanoparticles of TiO2. When a water suspension of this material is exposed with UV-vis radiation, water splitting reaction is carried out and H2/O2 bubbles are observed (Figure 2)

Light & Electron beam - the perfect combination for the observation and application of photo active materials

The aim of the present PhD thesis is to investigate the properties of innovative nanomaterials for energy conversion. The materials have been deeply studied by means of a wide spectrum of different techniques based on both light and electron sources, in order to get an insight into the correlation between the properties of each material and the activity towards different energy conversion applications. The activity has been carried out in the framework of a collaboration between the “G.Ciamician” Chemistry Department of the University of Bologna and the CNR-IMM Bologna. Four main topics have been explored: in the first part, luminescent silicon nanocrystals (SiNCs) have been discussed, suggesting a new approach to improve their optical properties as active material in complementary optoelectronic devices and photovoltaic cells. The luminescence of SiNCs have been exploited to increase the efficiency of conventional photovoltaic cells by means of an innovative architecture. Specifically, SiNCs were shown to be very promising light emitters in luminescent solar concentrators (LSC). The second part of the work has been focused on the study of high phosphorescent molecular chromophores, suggesting a new approach in their use as optical sensors successfully applied to the field of polymeric materials. This is due to the enhanced emission of light that appears in rigid, constrained or crystalline state, that is commonly called: "Aggregation-Induced Emission (AIE)". Such phenomenon is characteristic for molecular structures such as persulfurated benzene chromophores, hereafter named asterisks. The last two parts were focused on conventional and in-situ Transmission Electron Microscopy (TEM) morphological and structural characterization of photoactive and catalytic materials for energetic applications and in particular water splitting.

Caratterizzazione ottica e fotoelettrochimica di fotoanodi di triossido di tungsteno e bismuto vanadato (WO3/BiVO4) con catalizzatore (CoFe-PB)

Il presente lavoro di tesi si propone di illustrare il meccanismo di funzionamento delle celle fotoelettrochimiche (PEC cell) per la produzione di idrogeno, grazie allo studio di diversi semiconduttori, attraverso il cosiddetto fenomeno del water splitting. Nella cella `e stata testata un’eterogiunzione di Triossido di Tungsteno (WO3), una di Triossido di Tungsteno e Bismuto Vanadato (BiVO4) e una terza analoga alla precedente con l’aggiunta di un catalizzatore (CoFe–PB, cobalto-ferro blu di Prussia) per diminuire l’effetto della ricombinazione delle coppie elettrone - lacuna. All’interno della cella il campione era immerso in una soluzione di Acetato (CH3 COO – ) 0.2 M a pH 5. Le principali grandezze misurate sono la fotocorrente prodotta all’interno della cella e il tasso di riduzione e ossidazione dell’acqua.

Fabrication by magnetron sputtering and characterization of electrodes based on CuIn0.7Ga0.3Se2 (CIGS)

This thesis work aims to produce and test multilayer electrodes for their use as photocathode in a PEC device. The electrode developed is based on CIGS, a I-III-VI2 semiconductor material composed of copper (Cu), indium (In), Gallium (Ga) and selenium (Se). It has a bandgap in the range of 1.0-2.4 eV and an absorption coefficient of about 105cm−1, which makes it a promising photocathode for PEC water splitting. The idea of our multilayer electrode is to deposit a thin layer of CdS on top of CIGS to form a solid-state p–n junction and lead to more efficient charge separation. In addition another thin layer of AZO (Aluminum doped zinc oxide) is deposit on top of CdS since it would form a better alignment between the AZO/CdS/CIGS interfaces, which would help to drive the charge transport further and minimize charge recombination. Finally, a TiO2 layer on top of the electrodes is used as protective layer during the H2 evolution. FTO (Fluorine doped tin oxide) and Molybdenum are used as back-contact. We used the technique of RF magnetron sputtering to deposit the thin layers of material. The structural characterization performed by XDR measurement confirm a polycrystalline chalcopyrite structural with a preferential orientation along the (112) direction for the CIGS. From linear fit of the Tauc plot, we get an energy gap of about 1.16 eV. In addition, from a four points measurements, we get a resistivity of 0.26 Ωcm. We performed an electrochemical characterization in cell of our electrodes. The results show that our samples have a good stability but produce a photocurrent of the order of μA, three orders of magnitude smaller than our targets. The EIS analysis confirm a significant depletion of the species in front of the electrode causing a lower conversion of the species and less current flows.

Splitting rivers at their seams: bifurcations and avulsion

River bifurcations are critical but poorly understood elements of many geomorphological systems. They are integral elements of alluvial fans, braided rivers, fluvial lowland plains, and deltas and control the partitioning of water and sediment through these systems. Bifurcations are commonly unstable but their lifespan varies greatly. In braided rivers bars and channels migrate, split and merge at annual or shorter timescales, thereby creating and abandoning bifurcations. This behaviour has been studied mainly by geomorphologists and fluid dynamicists. Bifurcations also exist during avulsion, the process of a river changing course on a floodplain or in a delta, which may take 102103 years and has been studied mainly by sedimentologists. This review synthesizes our current understanding of bifurcations and brings together insights from different research communities and different environmental settings. We consider the causes and initiation of bifurcations and avulsion, the physical mechanisms controlling bifurcation and avulsion evolution, mathematical and numerical modelling of these processes, and the possibility of stable bifurcations. We end the review with some open questions. Copyright (c) 2012 John Wiley & Sons, Ltd.

Investigations into the extraction and the determination of polycyclic aromatic hydrocarbons (PAHs) from water by solid-phase extraction and capillary gas chromatography/ mass spectrometry

Factors affecting the detennination of PAHs by capillary GC/MS were studied. The effect of the initial column temperature and the injection solvent on the peak areas and heights of sixteen PAHs, considered as priority pollutants, USillg crosslinked methyl silicone (DB!) and 5% diphenyl, 94% dimethyl, 1% vinyl polysiloxane (DBS) columns was examined. The possibility of using high boiling point alcohols especially butanol, pentanol, cyclopentanol, and hexanol as injection solvents was investigated. Studies were carried out to optimize the initial column temperature for each of the alcohols. It was found that the optimum initial column temperature is dependent on the solvent employed. The peak areas and heights of the PAHs are enhanced when the initial column temperature is 10-20 c above the boiling point of the solvent using DB5 column, and the same or 10 C above the boiling point of the solvent using DB1 column. Comparing the peak signals of the PAHs using the alcohols, p-xylene, n-octane, and nonane as injection solvents, hexanol gave the greatest peak areas and heights of the PAHs particularly the late-eluted peaks. The detection limits were at low pg levels, ranging from 6.0 pg for fluorene t9 83.6 pg for benzo(a)pyrene. The effect of the initial column temperature on the peak shape and the separation efficiency of the PARs was also studied using DB1 and DB5 columns. Fronting or splitting of the peaks was obseIVed at very low initial column temperature. When high initial column temperature was used, tailing of the peaks appeared. Great difference between DB! and.DB5 columns in the range of the initial column temperature in which symmetrical.peaks of PAHs can be obtained is observed. Wider ranges were shown using DB5 column. Resolution of the closely-eluted PAHs was also affected by the initial column temperature depending on the stationary phase employed. In the case of DB5, only the earlyeluted PAHs were affected; whereas, with DB1, all PAHs were affected. An analytical procedure utilizing solid phase extraction with bonded phase silica (C8) cartridges combined with GC/MS was developed to analyze PAHs in water as an alternative method to those based on the extraction with organic solvent. This simple procedure involved passing a 50 ml of spiked water sample through C8 bonded phase silica cartridges at 10 ml/min, dried by passing a gentle flow of nitrogen at 20 ml/min for 30 sec, and eluting the trapped PAHs with 500 Jll of p-xylene at 0.3 ml/min. The recoveries of PAHs were greater than 80%, with less than 10% relative standard deviations of nine determinations. No major contaminants were present that could interfere with the recognition of PAHs. It was also found that these bonded phase silica cartridges can be re-used for the extraction of PAHs from water.

Approximate Riemann solutions of the two-dimensional shallow-water equations

A finite-difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow-water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gasdynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. An extension to the two-dimensional equations with source terms, is included. The scheme is applied to a dam-break problem with cylindrical symmetry.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

An algorithm for the shallow water equations with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations in a generalised coordinate system. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The scheme has good jump capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for flow past a circular obstruction.