The Hard-Constraint PINNs for Interface Optimal Control Problems

We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations (PDEs) with interfaces and some control constraints. The resulting algorithm is mesh-free and scalable to different PDEs, and it ensures the control constraints rigorously. Since the boundary and interface conditions, as well as the PDEs, are all treated as soft constraints by lumping them into a weighted loss function, it is necessary to learn them simultaneously and there is no guarantee that the boundary and interface conditions can be satisfied exactly. This immediately causes difficulties in tuning the weights in the corresponding loss function and training the neural networks. To tackle these difficulties and guarantee the numerical accuracy, we propose to impose the boundary and interface conditions as hard constraints in PINNs by developing a novel neural network architecture. The resulting hard-constraint PINNs approach guarantees that both the boundary and interface conditions can be satisfied exactly and they are decoupled from the learning of the PDEs. Its efficiency is promisingly validated by some elliptic and parabolic interface optimal control problems

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Analytical and Numerical Aspects of Porous Media Flow

The Brinkman equations model fluid flow through porous media and are particularly interesting in regimes where viscous shear effects cannot be neglected. Two model parameters in the momentum balance function as weights for the terms related to inter-particle friction and bulk resistance. If these are not in balance, then standard finite element methods might suffer from instabilities or error estimates might deteriorate. In particular the limit case, where the Brinkman problem reduces to a Darcy problem, demands for special attention. This thesis proposes a low-order finite element method which is uniformly stable with respect to the flow regimes captured by the Brinkman model, including the Darcy limit. To that end, linear equal-order approximations are combined with a pressure stabilization technique, a grad-div stabilization, and a penalty-free non-symmetric Nitsche method. The combination of these ingredients allows to develop a robust method, which is proven to be well-posed for the whole family of problems in two spatial dimensions, even if any Brinkman parameter vanishes. An a priori error analysis reveals optimal convergence in the considered norm. A convergence study based on problems with known analytic solutions confirms the robust first order convergence for reasonable ranges of numerical (stabilization) parameters. Further, numerical investigations that partly extend the theoretical framework are considered, revealing strengths and weaknesses of the approach. An application motivated by the optimization of geothermal energy production completes the thesis. Here, the proposed method is included in a multi-physics discrete model, appropriate to describe the thermo-hydraulics in hot, sedimentary, essentially horizontal aquifers. An immersed boundary method is adopted in order to allow a flexible, automatic optimization without regenerating the computational mesh. Utilizing the developed computational framework, the optimized multi-well arrangements with respect to the net energy gain are presented and discussed for different geothermal and hydrogeological setups. The results show that taking into account heterogeneous permeability structures and variable aquifer temperatures might drastically affect the optimal configuration of the wells

Pore-scale Direct Numerical Simulation of Flow and Transport in Porous Media

This dissertation presents research on the pore-scale simulation of flow and transport in porous media and describes the application of a new numerical approach based on the discontinuous Galerkin (DG) finite elements to pore-scale modelling. In this approach, the partial differential equations governing the flow at the pore-scale are solved directly where the main advantage is that it does not require a body fitted grid and works on a structured partition of the domain. Furthermore this approach is locally mass conservative, a desirable property for transport simulation. This allows the investigation of pore-scale processes and their effect on macroscopic behaviour more efficiently. The Stokes flow in two and three dimensional disordered packing was solved and the flow field was used in a random-walk particle tracking model to simulate the transport through the packing. The permeabilities were computed and asymptotic behaviour of solute dispersion for a wide range of Péclet numbers was studied. The simulated results agree well with the data reported in the literature, which indicates that the approach chosen here is well suited for pore-scale simulation

Multi-phase thermal cavitation flow in rough conforming and partially conforming conjunctions

The main aim of this research was to investigate the mechanism of cavitation in conforming and partially conforming tribological conjunctions. The effect of cavitation on load carrying capacity and frictional performance of is also investigated. This is important with regards to fuel efficiency in internal combustion (IC) engines. Friction accounts for 15–20% of IC engine losses. The piston–cylinder system contributes to 40–50% of these, with the compression ring(s) being responsible for most of this. This is because the primary function of the ring is to seal the combustion chamber, thus small emerging gaps lead to increased friction. In fact, compression ring(s) expend 3–5% of engine input fuel energy. The share of frictional losses of engine bearings is approximately 20–25%. Traditionally, prediction of performance of tribological conjunctions has been studied using Reynolds equation. When the effect of cavitation is considered, various cavitation algorithms with associated boundary conditions for lubricant rupture and reformation are proposed. These include Elrod, and Elrod and Coyne algorithms, as well as boundary conditions such as Swift-Stieber, JFO and Prandtl-Hopkins. There are a number of assumptions embodied in these approaches, as well as the use of Reynolds equation itself. These approaches do not uphold the continuity of mass and momentum in multi-phase flow, in cavitation beyond the lubricant film rupture. A detailed methodology for multi-phase flow, comprising simultaneous solution of Navier-Stokes, energy and lubricant rheological state equations is developed. [Continues.

Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer

PERFORMANCE BASED EVALUATION OF CRACKING IN ASPHALT CONCRETE USING VISCOELASTIC AND FRACTURE PROPERTIES

Cracking is one of the major distresses encountered in pavements. Pavements that fail prematurely due to cracking precipitate lower ride quality, elevate the chance of road accidents, and cause agencies to spend considerable amount of public funds on pavement maintenance and rehabilitation. As part of the concerted endeavor to ensure high performing pavements, extensive research is being undertaken throughout the United States to develop more effective and efficient performance based materials selection and specification procedures as well as mechanistic-empirical (M-E) methods for pavement cracking performance evaluation. However, agencies have been hesitant to introduce the methods to their specifications, pavement evaluation protocols and design procedures for reasons related to complexity and uncertainty associated to precisions and accuracy of these methods. This dissertation contributes to the ongoing performance based specifications and design efforts by addressing known gaps related to linear viscoelastic and fracture characterization of asphalt concrete. Overarching goals of this dissertation research has been enhancement of performance property determination processes and increased confidence in asphalt pavement performance predictions. Specific research contributions include, a simple and robust method is provided to determine phase angle from stiffness data and BBR low temperature specification parameters, stiffness (S) and relaxation properties (m-value), from DSR measurement for linear viscoelastic characterization of asphalt concrete. The ability of dynamic modulus and phase angle master curve parameters to capture the changes in mixture properties is investigated. Finally, increased understanding is achieved regarding fracture properties of asphalt mixtures as it relates to the effect of mix variables and number of replicates to be tested to obtain representative measurement to help agencies make informed decision during mix design and production