Doctoral Dissertation, University of Pittsburgh. This thesis is concerned with one of the most promising approaches to the numerical simulation of turbulent flows, the subgrid eddy viscosity models. We analyze both continuous and discontinuous finite element approximation of the new subgrid eddy viscosity model introduced in , , . First, we present a new subgrid eddy viscosity model introduced in a variationally consistent manner and acting only on the small scales of the fluid flow. We give complete convergence of themethod.
Department of Mechanical and Aerospace Engineering
Department of Mechanical and Aerospace Engineering < Case Western Reserve University
This paper proposes a study of Reinforcement Learning RL for continuous state-space and time control problems, based on the theoretical framework of viscosity solutions VSs. We use the method of dynamic programming DP which introduces the value function VF , expectation of the best future cumulative reinforcement. In the continuous case, the value function satisfies a non-linear first or second order depending on the deterministic or stochastic aspect of the process differential equation called the Hamilton-Jacobi-Bellman HJB equation. It is well known that there exists an infinity of generalized solutions differentiable almost everywhere to this equation, other than the VF. We show that gradient-descent methods may converge to one of these generalized solutions, thus failing to find the optimal control.
Using recent measurements of the velocity of ice on the surface of Helheim Glacier, located on the south-east coast of Greenland, the variation of viscosity, a material property of the ice, is investigated. The investigation focuses on determining the value of a parameter in Glen's flow law, a constitutive equation widely used in numerical models of ice sheets. Three different approaches are used: 1 Finite differences are used in a direct approach, 2 A finite element model is used in an approach involving an inverse problem, and 3 Nonlinear least squares fits of the velocity are used. The parameter focused on, the exponent in Glen's flow law, is assigned a value of three in most ice sheet models but the results presented in this thesis suggest that the behavior of ice at least that in the fast moving portion of Helheim Glacier might be more accurately modeled using a significantly smaller value, 1. Advanced Search.
Bowey, Alan William Predictions of soil behaviour using finite element analysis. PhD thesis, University of Glasgow. Measured data from five geotechnical structures have been back analysed to determine, in each case, the set of material parameters that will permit a reasonable match to the observed pre-failure foundation response.