Truncation errors and computational cost are obstacles that still hinder large-scale applications of the Computational Fluid Dynamics method. The discontinuous Galerkin method is one of the high-order schemes utilized extensively in recent years, which is locally conservative, stable, and high-order accurate. Besides that, it can handle complex geometries and irregular meshes with hanging nodes. In this document, the nondimensional compressible Euler equations and Reynolds- Averaged Navier-Stokes equations are discretized by discontinuous Galerkin methods with a two-equations turbulence model on both structured and unstructured meshes. The traditional equation of state for an ideal gas model is substituted by a multispecies thermodynamics model in order to complete the governing equations. An approximate Riemann solver is used for computing the convective flux, and the diffusive flux is approximated with some internal penalty based schemes. The temporal discretization of the partial differential equations is either performed explicitly with the aid of Rung-Kutta methods or with semi-implicit methods. Inspired by the artificial viscosity diffusion based limiter for shock-capturing method, which has been extensively studied, a novel and robust technique based on the introduction of mass diffusion to the species governing equations to guarantee that the species mass fractions remain positive has been thoroughly investigated. This contact-surface-capturing method is conservative and a high order of accuracy can be maintained for the discontinuous Galerkin method. For each time step of the algorithm, any trouble cell is first caught by the contact-surface discontinuity detector. Then some amount of mass diffusions are added to the governing equations to change the gas mixtures and arrive at an equilibrium point satisfying some conditions. The species properties are reasonable without any oscillations. Computations are performed for many steady and unsteady flow problems. For general non-mixing fluid flows, the classical air-helium shock bubble interaction problem is the central test case for the high-order discontinuous Galerkin method with a mass diffusion based limiter chosen. The computed results are compared with experimental, exact, and empirical data to validate the fluid dynamic solver.

[pt] O processo de tratamento de tumores por embolização vascular é sensível ao conjunto de partículas poliméricas empregado, ditos agentes embólicos, cujos fatores como tamanho e morfologia influenciam no sucesso do procedimento e podem ocasionar complicações quando mal dimensionados. Partículas esféricas de poli(acetato de vinila-co-metacrilato de metila) apresentam a maioria das características desejadas após tratamento por hidrólise alcalina. Este material é relativamente novo, o que significa que há uma lacuna de conhecimento em relação ao estudo dos fenômenos que regem sua cinética. Dessa forma, o presente trabalho investigou a cinética de copolimerização responsável pela sua produção. No desenvolvimento matemático, o método dos momentos foi utilizado assumindo estado quase-estacionário para as espécies radicalares. Além disso, o modelo considera difusão das moléculas no meio para contabilização dos efeitos viscosos, comumente determinados empiricamente. Constatou-se que as características físicas dos monômeros, assim como os parâmetros cinéticos da homopolimerização, puderam ser utilizados na copolimerização. Entretanto, como relatado na literatura para outros sistemas, os efeitos viscosos se comportam de forma consideravelmente diferente na copolimerização, sendo necessário a reestimação de alguns parâmetros relativos aos mesmos. Assim, foi possível reproduzir de forma adequada perfis de conversão, massas molares médias e composição do copolímero. Concluiu-se que o modelo proposto é capaz de representar a cinética da copolimerização em suspensão do poli(acetato de vinila-co-metacrilato de metila), possibilitando um melhor controle das características do copolímero aplicado ao procedimento de embolização vascular. Até onde se tem conhecimento, este é o primeiro trabalho que investiga e implementa com sucesso a modelagem cinética desse sistema. / [en] The treatment of vascularized tumors through vascular embolization is sensible to the polymeric particles used during procedure. These embolic agents have attributes, like size and morphology, which play a significant role on the success of this technique and can promote complications when not well dimensioned. Among the many options available, spherical particles of poly(vinyl acetate-co-methyl methacrylate) present most desired characteristics after alkalyne hydrolysis treatment. Being relatively new, the literature lack studies related to the kinetics of production of this material. Therefore, this research investigated the copolymerization kinetics of poly(vinyl acetate-co-methyl methacrylate) production. In the mathematical development, the method of moments was used assuming quasi-steady state for the free radical species. Additionally, the model includes the viscous effects through the diffusion of the involved molecules, which is usually accounted empirically. It was possible to use the physical properties of the monomers as well as the homopolymerization kinetic parameters in the copolymerization. However, as reported in the literature, some parameters are sensible to the system and some viscous effects affect the copolymerization differently. Therefore, some parameters were reestimated. It was possible to predict the conversion, average molecular weights and composition. Consequently, the model was capable of representing the kinetics of the suspension copolymerization of poly(vinyl acetate-co-methyl methacrylate), meaning it could be used to improve the production of this polymer as an embolic agent for vascular embolization procedure. As far as known by the author, this is the first study to successfully perform the kinetic modeling of this specific system.