Yes / The existing analytical solutions of dam-break flow do not consider simultaneously the effects of wet downstream bottom and bed slope on the dam-break wave propagation. In this study, a new analytical solution for the shallow-water equations (SWE) is developed to remove this limitation to simulate the wave caused by an instantaneous dam-break. The approach adopts the method of characteristics and has been applied to simulate the dam-break flows with different downstream water depths and slopes. The analytical solutions have been compared with predictions by the lattice Boltzmann method and the agreement is good. Although the proposed analytical solution treats an idealized case, it is nonetheless suitable for assessing the robustness and accuracy of numerical models based on the SWE without the frictional slope. / The National Key Research and Development Program of China (Grant No: 2018YFC1505000), National Natural Science Foundation of China (Grant Nos: 51879179; 51579166) and Sichuan Science and Technology Program (No. 2019JDTD0007); Open Fund from the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University (SKHL1809). .

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-10T18:01:20Z No. of bitstreams: 1 KEYTT AMARAL DA SILVA - DISSERTAÇÃO PPGMAT 2015..pdf: 1966719 bytes, checksum: d55ff8700252c9540c54209c808e22a3 (MD5) / Made available in DSpace on 2018-08-10T18:01:20Z (GMT). No. of bitstreams: 1 KEYTT AMARAL DA SILVA - DISSERTAÇÃO PPGMAT 2015..pdf: 1966719 bytes, checksum: d55ff8700252c9540c54209c808e22a3 (MD5) Previous issue date: 2015-08 / Neste trabalho apresentamos a construção detalhada da solução do Problema de Riemann associado à um sistema de leis de conservação de um problema não estritamente hiperbólico, proveniente da modelagem matemática de um escoamento unidimensional bifásico num meio poroso em que as fases são óleo e água com polímero dissolvido, para dados iniciais arbitrários no espaço de estados. A construção da solução do sistema é baseada na solução da equação de Buckley−Leverett para cada nível de concentração constante de polímero e nas curvas integrais de uma campo característico linearmente degenerado que dá origem as chamadas ondas de contato. / We present the detailed construction of the Riemann problem solution associate to a system of conservation laws of a non−strictly hyperbolic problem, from mathematical modeling of a one-dimensional two-flow in a porous medium filled by oil and water with dissolved polymer, for arbitrary initial data in the state space. The construction of the system solution is based on the solution Buckley−Leverett equation for each level constant polymer concentration and on the integral curves of a linearly degenerated field characteristic that gives rise to the so-called contact waves.

Underwater explosions (UNDEX) and a ship's vulnerability to them are problems of interest in early-stage ship design. A series of events occur sequentially in an UNDEX scenario in both the fluid and structural domains and these events happen over a wide range of time and spatial scales. Because of the complexity of the physics involved, it is a common practice to separate the description of UNDEX into early-time and late-time, and far-field and near-field. The research described in this dissertation is focused on the simulation of near-field and early-time UNDEX. It assembles a hybrid framework of algorithms to provide results while maintaining computational efficiency. These algorithms include Runge-Kutta, Discontinuous Galerkin, Level Set, Direct Ghost Fluid and Embedded Boundary methods. Computational fluid dynamics (CFD) solvers are developed using this framework of algorithms to demonstrate the computational methods and their ability to effectively and efficiently solve UNDEX problems. Contributions, made in the process of satisfying the objective of this research include: the derivation of eigenvectors of flux Jacobians and their application to the implementation of the slope limiter in the fluid discretization; the three-dimensional extension of Direct Ghost Fluid Method and its application to the multi-fluid treatment in UNDEX flows; the enforcement of an improved non-reflecting boundary condition and its application to UNDEX simulations; and an improvement to the projection-based embedded boundary method and its application to fluid-structure interaction simulations of UNDEX problems. / Doctor of Philosophy / Underwater explosions (UNDEX) and a ship's vulnerability to them are problems of interest in early-stage ship design. A series of events occur sequentially in an UNDEX scenario in both the fluid and structural domains and these events happen over a wide range of time and spatial scales. Because of the complexity of the physics involved, it is a common practice to separate the description of UNDEX into early-time and late-time, and far-field and near-field. The research described in this dissertation is focused on the simulation of near-field and early-time UNDEX. It assembles a hybrid framework of algorithms to provide results while maintaining computational efficiency. These algorithms include Runge-Kutta, Discontinuous Galerkin, Level Set, Direct Ghost Fluid and Embedded Boundary methods. Computational fluid dynamics (CFD) solvers are developed using this framework of algorithms to demonstrate these computational methods and their ability to effectively and efficiently solve UNDEX problems.

In the Thesis, two important theoretical problems arising in the theory of one-dimensional defocusing nonlinear Schrödinger (NLS) flows are investigated analytically and numerically: (i) the resonant generation of dispersive shock waves (DSWs) in one-dimensional NLS flow past a broad repulsive penetrable barrier; and (ii) the interaction of counter-propagating DSW and a simple rarefaction wave (RW), which is referred to as the DSW refraction problem. The first problem is motivated by the recent experimental observations of dark soliton radiation in a cigar-shaped BEC by sweeping through it a localised repulsive potential; the second problem represents a dispersive-hydrodynamic counterpart of the classical gas-dynamics problem of the shock wave refraction on a RW, and, apart from its theoretical significance could also find applications in superfluid dynamics. Both problems also naturally arise in nonlinear optics, where the NLS equation is a standard mathematical model and the `superfluid dynamics of light' can be used for an all-optical modelling of BEC flows. The main results of the Thesis are as follows: (i) In the problem of the transcritical flow of a BEC through a wide repulsive penetrable barrier an asymptotic analytical description of the arising wave pattern is developed using the combination of the localised ``hydraulic'' solution of the 1D Gross-Pitaevskii (GP) equation with repulsion (the defocusing NLS equation with an added external potential) and the appropriate exact solutions of the Whitham-NLS modulation equations describing the resolution of the upstream and downstream discontinuities through DSWs. We show that the downstream DSW effectively represents the train of dark solitons, which can be associated with the excitations observed experimentally by Engels and Atherton (2008). (ii) The refraction of a DSW due to its head-on collision with the centred RW is considered in the frameworks of two one-dimensional defocusing NLS models: the standard cubic NLS equation and the NLS equation with saturable nonlinearity, the latter being a standard model for the light propagation through photorefractive optical crystals. For the cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain key parameters of the DSW refraction. In both problems, we undertake a detailed analysis of the flow structure for different parametric regimes and calculate physical quantities characterising the output flows in terms of relevant input parameters. Our modulation theory analytical results are supported by direct numerical simulations of the corresponding full dispersive initial value problems (IVP).

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-11T13:32:15Z No. of bitstreams: 1 ERIVALDO DINIZ DE LIMA - DISSERTAÇÃO PPGMAT 2015..pdf: 2368610 bytes, checksum: 3db3b8e45efcb83c955dae60371f8f4b (MD5) / Made available in DSpace on 2018-08-11T13:32:15Z (GMT). No. of bitstreams: 1 ERIVALDO DINIZ DE LIMA - DISSERTAÇÃO PPGMAT 2015..pdf: 2368610 bytes, checksum: 3db3b8e45efcb83c955dae60371f8f4b (MD5) Previous issue date: 2015-08 / Neste trabalho consideramos um sistema de leis de conservação proveniente da modelagem matemática de um escoamento bifásico unidimensional num meio poroso, preenchido de óleo e água com polímero dissolvido nela e levando em conta a adsorção de parte do polímero pela rocha. Usando a técnica das curvas de onda apresentamos a construção detalhada da solução do problema de Riemann para dados iniciais arbitrários no espaço de estados. Usamos a condição de entropia do per l viscoso para as ondas de choque com salto na concentração do polímero e a condição de Oleinik-Liu para os choques com concentração constante do polímero e salto na saturação da água / In this work we consider a system of conservation laws from the mathematical modeling of a one-dimensional two-phase flow in porous media, filled with oil and water with dissolved polymer in it and taking into account the adsorption of part of the polymer by the rock. Using the wave curves technique, we present a detailed construction of the Riemann problem solution for arbitrary initial data on the state space. We use the entropy condition of the viscous pro le for the shock waves with jumps in the polymer concentration and Oleynik-Liu condition for the shocks with constant concentration of polymer and jumps on the water saturation.