Geometry Modeling for Unstructured Mesh Adaptation

The quantification and control of discretization error is critical to obtaining reliable simulation results. Adaptive mesh techniques have the potential to automate discretization error control, but have made limited impact on production analysis workflow. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic mesh adaptation mechanics. However, the poor integration of initial mesh generation and adaptive mesh mechanics to typical sources of geometry has hindered adoption of adaptive mesh techniques, where these geometries are often created in Mechanical Computer- Aided Design (MCAD) systems. The difficulty of this coupling is compounded by two factors: the inherent complexity of the model (e.g., large range of scales, bodies in proximity, details not required for analysis) and unintended geometry construction artifacts (e.g., translation, uneven parameterization, degeneracy, self-intersection, sliver faces, gaps, large tolerances be- tween topological elements, local high curvature to enforce continuity). Manual preparation of geometry is commonly employed to enable fixed-grid and adaptive-grid workflows by reducing the severity and negative impacts of these construction artifacts, but manual process interaction inhibits workflow automation. Techniques to permit the use of complex geometry models and reduce the impact of geometry construction artifacts on unstructured grid workflows are models from the AIAA Sonic Boom and High Lift Prediction are shown to demonstrate the utility of the current approach

A parallel nearly implicit time-stepping scheme

Across-the-space parallelism still remains the most mature, convenient and natural way to parallelize large scale problems. One of the major problems here is that implicit time stepping is often difficult to parallelize due to the structure of the system. Approximate implicit schemes have been suggested to circumvent the problem. These schemes have attractive stability properties and they are also very well parallelizable.\ud The purpose of this article is to give an overall assessment of the parallelism of the method

No pressure? Energy-consistent ROMs for the incompressible Navier-Stokes equations with time-dependent boundary conditions

This work presents a novel reduced-order model (ROM) for the incompressible Navier-Stokes equations with time-dependent boundary conditions. This ROM is velocity-only, i.e. the simulation of the velocity does not require the computation of the pressure, and preserves the structure of the kinetic energy evolution. The key ingredient of the novel ROM is a decomposition of the velocity into a field with homogeneous boundary conditions and a lifting function that satisfies the mass equation with the prescribed inhomogeneous boundary conditions. This decomposition is inspired by the Helmholtz-Hodge decomposition and exhibits orthogonality of the two components. This orthogonality is crucial to preserve the structure of the kinetic energy evolution. To make the evaluation of the lifting function efficient, we propose a novel method that involves an explicit approximation of the boundary conditions with POD modes, while preserving the orthogonality of the velocity decomposition and thus the structure of the kinetic energy evolution. We show that the proposed velocity-only ROM is equivalent to a velocity-pressure ROM, i.e., a ROM that simulates both velocity and pressure. This equivalence can be generalized to other existing velocity-pressure ROMs and reveals valuable insights in their behaviour. Numerical experiments on test cases with inflow-outflow boundary conditions confirm the correctness and efficiency of the new ROM, and the equivalence with the velocity-pressure formulation

Investigation and development of implicit numerical methods for building energy simulation

A variety of building energy analysis and simulation tools are increasingly used to determine peak heating and cooling loads, size thermal plant, anticipate annual energy consumption and analyse thermal comfort. Numerical solution techniques are considered the most flexible for building energy simulation. When applied to the differential equations modelling energy flows in buildings, they give rise to a system of non-linear algebraic (difference) equations. In order to evaluate numerical methods for building energy simulation, the problem has been characterized mathematically and comprehensive test problems (equation sets) with these characteristics have been prepared. The principal attribute of the problem was found to be a stifiess ratio of the order of lo4. Candidate methods have been programmed and their outputs compared, in numerical experiments, with highly accurate (converged) solutions for the test problems. The accepted validation methods, empirical validation, analytical verification and inter-modal comparison were considered inappropriate. The first estimates total and not just numerical error, the second is too confined and the third lacks an absolute standard. The main evaluation parameter used was computational efficiency which is defined as accuracy attained per unit (computational) effort expended. An improved difference equation solver has been proposed and compared with the one used in the European reference model (ESP) and elsewhere. It was found to produce 27% less error than the currently used method. A fundamental method for estimating the pre-conditioning period of a building has been put forward in this part of the work. The trapezoidal rule (TR) is currently used in a number of building energy simulation packages including ESP. A known instability associated with the method is described and an implicit member of the Runge-Kutta family, possessing the necessary strong stability, has been shown, using the test problems, to be more efficient than TR by a factor of 4.27

Statistical and Mechanistic Approaches to Study Cell Signaling Dynamics

Cells use complex signaling systems to constantly detect environmental changes, relay extracellular information from the cell membrane to the nucleus, and drive cell responses, such as transcription. The ability of each single cell to dynamically respond to changes in its environment is the basis for healthy, functioning, multicellular beings. Diseases often arise from dysregulated signaling, and our ability to manipulate cell responses, that stems from our growing understanding of signaling processes, is often the basis for disease treatments. Computational approaches can complement experimental studies of cellular systems, allowing us to formalize our growing body of knowledge of cellular biochemistry. Mechanistic modeling provides a natural framework to describe and simulate complex systems with many system components and causal interactions that often lead to non-intuitive emergent behavior, lending itself well to the analysis of signaling systems. Statistical approaches can complement mechanistic modeling by enabling an analysis of complex input-output relationships in the data, providing insight into how cells translate input environmental cues into output responses, even when the underlying mechanisms are only partially understood. In this thesis, we explore both mechanistic and statistical approaches and address several challenges in modeling signaling processes within a cell, and signaling heterogeneity between cells, using the NF-kB pathway as a model system. First, we evaluate methods to efficiently determine numerical values of model parameters, enabling model simulations that are comparable to experimental data. Second, we develop methods to identify reduced submodels that are sufficient for the data, highlighting simple mechanisms that drive emergent behavior. Third, switching gears to study signaling heterogeneity, we use information-theoretic analyses to evaluate the capabilities of the NF-kB pathway to effectively transduce cytokine dosage information in the presence of biochemical noise. Finally, we develop a framework to calibrate mechanistic models to heterogeneous signaling data, enabling simulation-based analyses of single-cell signaling capabilities