Esta dissertação investiga numericamente a influência dos efeitos viscosos e elásticos em escoamentos de materiais viscoplásticos no interior de uma cavidade dirigida. O modelo mecânico empregado é constituído pelas equações de conservação de massa e pelo princípio da quantidade de movimento linear, para fluidos incompressíveis, acoplado à equação constitutiva. Esta equação modifica o modelo viscoelástico de Oldroyd-B de modo a acomodar que os tempos de relaxação e retardo do material, bem como sua viscosidade viscoplástica, dependam das mudanças de sua microestrutura. A aproximação numérica do modelo emprega o método multi-campos de Galerkin mínimos-quadrados em termos do tensor de tensão extra, do vetor velocidade e do campo de pressão. Os resultados objetivam a determinção do tamanho e localização das regiões aparentemente não-escoadas do material, bem como sua deformação elástica, intensidade de tensão, e a sua vorticidade no interior da cavidade. Os resultados claramente indicam que o padrão do escoamento é fortemente influenciado pela variação dos efeitos elásticos (variação do tempo de relaxação adimensional, θ0 * ), viscosos (variação do índice de power-law, n) e cinemáticos (variação da velocidade adimensional, U* , do escoamento) no interior da cavidade. / This dissertation investigated numerically the influence of viscous and elastic effects on flows of viscoplastic materials within a lid-driven cavity. The mechanical model used is made up of mass and momentum balance equations, coupled with the constitutive equation. This equation modifies the viscoelastic Oldroyd-B model to accommodate both relaxation and retardation times, and viscosity function, dependent on the microstructure changes. Numerical approximations of the model make use a three-field Galerkin least squares method in terms of the extra stress tensor, velocity vector and pressure field. Computations focus on the determination of the size and position of apparently unyielded regions as well as the elastic deformation, stress intensity, and the vorticity within of the cavity. Results clearly indicate that the flow pattern is strongly influenced by the elastic (variation of the dimensionless relaxation time, θ0 * ), viscous (variation of the power-law index, n) and kinematic (variation of the dimensionless flow velocity, U* ) effects within the cavity.

Esta dissertação investiga numericamente a influência dos efeitos viscosos e elásticos em escoamentos de materiais viscoplásticos no interior de uma cavidade dirigida. O modelo mecânico empregado é constituído pelas equações de conservação de massa e pelo princípio da quantidade de movimento linear, para fluidos incompressíveis, acoplado à equação constitutiva. Esta equação modifica o modelo viscoelástico de Oldroyd-B de modo a acomodar que os tempos de relaxação e retardo do material, bem como sua viscosidade viscoplástica, dependam das mudanças de sua microestrutura. A aproximação numérica do modelo emprega o método multi-campos de Galerkin mínimos-quadrados em termos do tensor de tensão extra, do vetor velocidade e do campo de pressão. Os resultados objetivam a determinção do tamanho e localização das regiões aparentemente não-escoadas do material, bem como sua deformação elástica, intensidade de tensão, e a sua vorticidade no interior da cavidade. Os resultados claramente indicam que o padrão do escoamento é fortemente influenciado pela variação dos efeitos elásticos (variação do tempo de relaxação adimensional, θ0 * ), viscosos (variação do índice de power-law, n) e cinemáticos (variação da velocidade adimensional, U* , do escoamento) no interior da cavidade. / This dissertation investigated numerically the influence of viscous and elastic effects on flows of viscoplastic materials within a lid-driven cavity. The mechanical model used is made up of mass and momentum balance equations, coupled with the constitutive equation. This equation modifies the viscoelastic Oldroyd-B model to accommodate both relaxation and retardation times, and viscosity function, dependent on the microstructure changes. Numerical approximations of the model make use a three-field Galerkin least squares method in terms of the extra stress tensor, velocity vector and pressure field. Computations focus on the determination of the size and position of apparently unyielded regions as well as the elastic deformation, stress intensity, and the vorticity within of the cavity. Results clearly indicate that the flow pattern is strongly influenced by the elastic (variation of the dimensionless relaxation time, θ0 * ), viscous (variation of the power-law index, n) and kinematic (variation of the dimensionless flow velocity, U* ) effects within the cavity.

A new combination of techniques for the numerical computation of incompressible flow is presented. The temporal discretization bases on the discontinuous Galerkin-formulation. Both constant (DG(0)) and linear approximation (DG(1)) in time is discussed. In case of DG(1) an iterative method reduces the problem to a sequence of problems each with the dimension of the DG(0) approach. For the semi-discrete problems a Galerkin/least-squares method is applied. Furthermore a non-overlapping domain decomposition method can be used for a parallelized computation. The main advantage of this approach is the low amount of information which must be exchanged between the subdomains. Due to the slight bandwidth a workstation-cluster is a suitable platform. Otherwise this method is efficient only for a small number of subdomains. The interface condition is of the Robin/Robin-type and for the Navier-Stokes equation a formulation introducing a further pressure interface condition is used. Additionally a suggestion for the implementation of the standard k-epsilon turbulence model with special wall function is done in this context. All the features mentioned above are implemented in a code called ParallelNS. Using this code the verification of this approach was done on a large number of examples ranging from simple advection-diffusion problems to turbulent convection in a closed cavity.

A new combination of techniques for the numerical computation of incompressible flow is presented. The temporal discretization bases on the discontinuous Galerkin-formulation. Both constant (DG(0)) and linear approximation (DG(1)) in time is discussed. In case of DG(1) an iterative method reduces the problem to a sequence of problems each with the dimension of the DG(0) approach. For the semi-discrete problems a Galerkin/least-squares method is applied. Furthermore a non-overlapping domain decomposition method can be used for a parallelized computation. The main advantage of this approach is the low amount of information which must be exchanged between the subdomains. Due to the slight bandwidth a workstation-cluster is a suitable platform. Otherwise this method is efficient only for a small number of subdomains. The interface condition is of the Robin/Robin-type and for the Navier-Stokes equation a formulation introducing a further pressure interface condition is used. Additionally a suggestion for the implementation of the standard k-epsilon turbulence model with special wall function is done in this context. All the features mentioned above are implemented in a code called ParallelNS. Using this code the verification of this approach was done on a large number of examples ranging from simple advection-diffusion problems to turbulent convection in a closed cavity.