Surface-only simulation methods for fluid dynamics are those that perform computation only on a surface representation, without relying on any volumetric discretization. Such methods have superior asymptotic complexity in time and memory than the traditional volumetric discretization approaches, and thus are more tractable for simulation of complex fluid phenomena. Although for most computer graphics applications and many engineering applications, the interior flow inside the fluid phases is typically not of interest, the vast majority of existing numerical techniques still rely on discretization of the volumetric domain. My research first tackles the mesh-based surface tracking problem in the multimaterial setting, and then proposes surface-only simulation solutions for two scenarios: the soap-films and bubbles, and the general 3D liquids. Throughout these simulation approaches, all computation takes place on the surface, and volumetric discretization is entirely eliminated.

Relationships between structure and dynamics in fluids have a wide variety of applications. Because theories for fluid structure are now well developed, such relationships can be used to “predict” dynamic properties. Also, recasting dynamic properties in terms of structure may provide new insights. In this thesis, we explore whether some of the relationships between structure and dynamics that have proven useful for understanding simple atomic liquids can also be applied to complex fluid systems. In particular, we focus on model fluid systems with particles that interact with attractive forces that are shortranged (relative to the particle diameter), and display properties that are anomalous when compared to those of simple liquids. Examples of fluids with short-range attractive (SRA) interactions include colloidal suspensions and solutions of micelles or proteins. We show via simulations that common assumptions regarding free volume and dynamics do not apply for SRA fluids, and propose a revision to the traditional free volume perspective of dynamics. We also develop a model which can predict the free volume behavior for hard-sphere and SRA fluids. Next, we demonstrate that the dynamic properties of SRA fluids can be related to structural order. In terms of structural order, the properties of SRA fluids can be related to those of another anomalous fluid, liquid water. In both fluids, anomalous dynamics are closely related to anomalous structure, which can be traced to changes in second and higher coordination shells. We also find that a similar relationship between structural order and dynamics approximately holds for fluids under shear. Motivated by previous work, we explore via simulation how tuning the particle-wall interactions to flatten or enhance the particle layering in a confined fluid impacts its self-diffusivity, viscosity, and entropy. We find that the excess entropy explains the observed trends. Finally, we present preliminary simulation data regarding the relationship between heterogeneous dynamics and structure. We show that the mobility of particles is related in a simple way to the structure of the particles surrounding them. In particular, our results suggest that a critical amount of local disorder allows a particle to be mobile on intermediate time scales. / text

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In this dissertation, we introduce a framework for simulating the dynamics between liquid and thin structures, including the effects of buoyancy, drag, capillary cohesion, dripping, and diffusion. After introducing related works, Part I begins with a discussion on the interactions between Newtonian fluid and fabrics. In this discussion, we treat both the fluid and the fabrics as continuum media; thus, the physical model is built from mixture theory. In Part II, we discuss the interactions between Newtonian fluid and hairs. To have more detailed dynamics, we no longer treat the hairs as continuum media. Instead, we treat them as discrete Kirchhoff rods. To deal with the thin layer of liquid that clings to the hairs, we augment each hair strand with a height field representation, through which we introduce a new reduced-dimensional flow model to solve the motion of liquid along the longitudinal direction of each hair. In addition, we develop a faithful model for the hairs' cohesion induced by surface tension, where a penalty force is applied to simulate the collision and cohesion between hairs. To enable the discrete strands interact with continuum-based, shear-dependent liquid, in Part III, we develop models that account for the volume change of the liquid as it passes through strands and the momentum exchange between the strands and the liquid. Accordingly, we extend the reduced-dimensional flow model to simulate liquid with elastoviscoplastic behavior. Furthermore, we use a constraint-based model to replace the penalty-force model to handle contact, which enables an accurate simulation of the frictional and adhesive effects between wet strands. We also present a principled method to preserve the total momentum of a strand and its surface flow, as well as an analytic plastic flow approach for Herschel-Bulkley fluid that enables stable semi-implicit integration at larger time steps. We demonstrate a wide range of effects, including the challenging animation scenarios involving splashing, wringing, and colliding of wet clothes, as well as flipping of hair, animals shaking, spinning roller brushes from car washes being dunked in water, and intricate hair coalescence effects. For complex liquids, we explore a series of challenging scenarios, including strands interacting with oil paint, mud, cream, melted chocolate, and pasta sauce.

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A thesis submitted to the faculty of Engineering, University of the Witwatersrand, Johannesburg , in fulfillment of the requirements for the degree of Doctor of Philosophy. Johannesburg, November 1994 / Organ function is often characterised using imaging techniques. In particular a tracer is often used which does not react with tissue, is low in concentration, follows body fluid flows and is distinguishable from the observed system and thus measurable. These requirements ensure linear characteristics of the tracer. In this thesis, these linear characteristics are used to develop a generalised mathematical theory to determine organ function from imaged tracer experiments. The theory is based on anatomical and physiological information for single and multiple input organs. [Abbreviated Abstract. Open document to view full version] / MT2018

Formulamos um modelo simplificado para o estudo do processo de injeção de solvente em reservatórios de petróleo, onde o fluido injetado (um ácido) tem a capacidade de dissolver parcialmente a matriz sólida. Como hipóteses principais, consideramos que o solvente e o soluto (componente químico que constitui o meio poroso) são espécies totalmente miscíveis, a viscosidade da mistura solvente + soluto não varia com a concentração de soluto, há significativa transferência de massa entre as fases e a permeabilidade do meio poroso varia linearmente com a porosidade. O modelo é formado por duas Equações Diferenciais Parciais, uma do tipo Convecção-Difusão a outra é do tipo Convecção-Reação. Para resolução numérica, desenvolvemos uma metodologia que denominamos de EPEC (Explícita Porosidade e Explícita Concentração). Tal metodologia se baseia em um limitador de fluxo do tipo TVD e em diferenças finitas centradas de segunda ordem. Em adição, o EPEC emprega uma técnica de separação de operadores. Deste modo, em cada passo de tempo, realizamos inicialmente o cálculo explícito da porosidade seguido do cálculo explícito da concentração do solvente. Assim, obtemos um desacoplamento natural das equações que descrevem o problema. Resultados de simulações são apresentados para um meio poroso bidimensional, após sessenta dias de injeção de solvente. / We formulate a simplified Model to study the process of solvent injection in petroleum Reservoir, where the injected fluid (an acid) can partially dissolve a solid matrix. As prime hypotheses, we considered that solvent an soluble component are completely mixed, the viscosity of the fluid does not vary with the concentration of the soluble component, theres significant transfer of mass between the parts and, the permeability of media porous changes linearly with porosity. The model is formed by two Partial Differential Equation, one is convection-diffusion type and another is a convection-reaction type. The Numerical Resolution weve developed a method called EPEC (Explicit Porosity Explicit Concentration). Such methodology is based upon a Limiting of Flow of TVD type and, used Centered Finite Differences of second order. In addition, the EPEC use a operators separation technique. This way, every time, first we clearly calculate the porosity and then the concentration of solvent is calculated. Thus we obtain a natural decoupling of the equations that describe the problem. Simulation results are presented to a two dimensional media porous after sixty days of solvent injection.

Técnicas de injeção de traçadores são bastante utilizadas nos estudos de escoamentos em meios porosos heterogêneos, principalmente em problemas relacionados à simulação numérica de escoamentos miscíveis em reservatórios de petróleo e à dispersão de contaminantes em aqüíferos. Neste trabalho apresentamos novos algoritmos para a aproximação numérica do problema de injeção de traçadores. Apresentaremos desenvolvimentos recentes do método Forward Integral-Tube Tracking (FIT) que foi originalmente apresentado em Aquino et al. (2007a). O FIT é um método lagrangeano localmente conservativo utilizado na resolução de problemas de transporte linear. Este método não faz o uso de soluções de problemas de Riemann e baseia-se na construção dos tubos integrais introduzidas em Douglas Jr. et al. (2000b). Além disso, ele possui excelente eficiência computacional e é virtualmente livre de difusão numérica. Resultados numéricos são apresentados com o objetivo de comparar a precisão das soluções fornecidas por novas implementações do método FIT na resolução do problema do traçador em reservatórios de petróleo. / The injection of tracers are used in the investigation of flows in heterogeneous porous media, in studies related to the simulation of miscible dispacements in petroleum reservoirs and the dispersion of contaminants in aquifers. In this work we present new algorithms for the numerical approximation of tracer injection problems. We discuss recent developments of the Forward Integral-Tube Tracking (FIT) scheme which was introduced in Aquino et al. (2007a). The FIT is a locally conservative lagrangian scheme for the approximation of the linear transport problems. This scheme does not use analytic solutions of Riemann problems and is based on the construction of the integral tubes introduced in Douglas Jr. et al. (2000b). The FIT scheme is computationally very eficient and is virtually free of numerical diffusion. Numerical results are presented to compare the accuracy of the solutions provided by new implementation of the FIT scheme for the injection of tracers in petroleum reservoirs.

Formulamos um modelo simplificado para o estudo do processo de injeção de solvente em reservatórios de petróleo, onde o fluido injetado (um ácido) tem a capacidade de dissolver parcialmente a matriz sólida. Como hipóteses principais, consideramos que o solvente e o soluto (componente químico que constitui o meio poroso) são espécies totalmente miscíveis, a viscosidade da mistura solvente + soluto não varia com a concentração de soluto, há significativa transferência de massa entre as fases e a permeabilidade do meio poroso varia linearmente com a porosidade. O modelo é formado por duas Equações Diferenciais Parciais, uma do tipo Convecção-Difusão a outra é do tipo Convecção-Reação. Para resolução numérica, desenvolvemos uma metodologia que denominamos de EPEC (Explícita Porosidade e Explícita Concentração). Tal metodologia se baseia em um limitador de fluxo do tipo TVD e em diferenças finitas centradas de segunda ordem. Em adição, o EPEC emprega uma técnica de separação de operadores. Deste modo, em cada passo de tempo, realizamos inicialmente o cálculo explícito da porosidade seguido do cálculo explícito da concentração do solvente. Assim, obtemos um desacoplamento natural das equações que descrevem o problema. Resultados de simulações são apresentados para um meio poroso bidimensional, após sessenta dias de injeção de solvente. / We formulate a simplified Model to study the process of solvent injection in petroleum Reservoir, where the injected fluid (an acid) can partially dissolve a solid matrix. As prime hypotheses, we considered that solvent an soluble component are completely mixed, the viscosity of the fluid does not vary with the concentration of the soluble component, theres significant transfer of mass between the parts and, the permeability of media porous changes linearly with porosity. The model is formed by two Partial Differential Equation, one is convection-diffusion type and another is a convection-reaction type. The Numerical Resolution weve developed a method called EPEC (Explicit Porosity Explicit Concentration). Such methodology is based upon a Limiting of Flow of TVD type and, used Centered Finite Differences of second order. In addition, the EPEC use a operators separation technique. This way, every time, first we clearly calculate the porosity and then the concentration of solvent is calculated. Thus we obtain a natural decoupling of the equations that describe the problem. Simulation results are presented to a two dimensional media porous after sixty days of solvent injection.

Técnicas de injeção de traçadores são bastante utilizadas nos estudos de escoamentos em meios porosos heterogêneos, principalmente em problemas relacionados à simulação numérica de escoamentos miscíveis em reservatórios de petróleo e à dispersão de contaminantes em aqüíferos. Neste trabalho apresentamos novos algoritmos para a aproximação numérica do problema de injeção de traçadores. Apresentaremos desenvolvimentos recentes do método Forward Integral-Tube Tracking (FIT) que foi originalmente apresentado em Aquino et al. (2007a). O FIT é um método lagrangeano localmente conservativo utilizado na resolução de problemas de transporte linear. Este método não faz o uso de soluções de problemas de Riemann e baseia-se na construção dos tubos integrais introduzidas em Douglas Jr. et al. (2000b). Além disso, ele possui excelente eficiência computacional e é virtualmente livre de difusão numérica. Resultados numéricos são apresentados com o objetivo de comparar a precisão das soluções fornecidas por novas implementações do método FIT na resolução do problema do traçador em reservatórios de petróleo. / The injection of tracers are used in the investigation of flows in heterogeneous porous media, in studies related to the simulation of miscible dispacements in petroleum reservoirs and the dispersion of contaminants in aquifers. In this work we present new algorithms for the numerical approximation of tracer injection problems. We discuss recent developments of the Forward Integral-Tube Tracking (FIT) scheme which was introduced in Aquino et al. (2007a). The FIT is a locally conservative lagrangian scheme for the approximation of the linear transport problems. This scheme does not use analytic solutions of Riemann problems and is based on the construction of the integral tubes introduced in Douglas Jr. et al. (2000b). The FIT scheme is computationally very eficient and is virtually free of numerical diffusion. Numerical results are presented to compare the accuracy of the solutions provided by new implementation of the FIT scheme for the injection of tracers in petroleum reservoirs.