Spatially Adaptive Stochastic Multigrid Methods for Fluid-Structure Systems with Thermal Fluctuations

In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic numerical methods are developed based on multigrid which allow for the efficient computation of both the hydrodynamic interactions in the presence of walls and the thermal fluctuations. The presented stochastic multigrid approach provides efficient real-space numerical methods for generating the required stochastic driving fields with long-range correlations consistent with statistical mechanics. The presented approach also allows for the use of spatially adaptive meshes in resolving the hydrodynamic interactions. Numerical results are presented which show the methods perform in practice with a computational complexity of O(N log(N))

Hierarchical Parallelism in Finite Difference Analysis of Heat Conduction

Based on the concept of hierarchical parallelism, this research effort resulted in highly efficient parallel solution strategies for very large scale heat conduction problems. Overall, the method of hierarchical parallelism involves the partitioning of thermal models into several substructured levels wherein an optimal balance into various associated bandwidths is achieved. The details are described in this report. Overall, the report is organized into two parts. Part 1 describes the parallel modelling methodology and associated multilevel direct, iterative and mixed solution schemes. Part 2 establishes both the formal and computational properties of the scheme

An arbitrary grid CFD algorithm for configuration aerodynamics analysis. Volume 1: Theory and validations

This report documents the user input and output data requirements for the FEMNAS finite element Navier-Stokes code for real-gas simulations of external aerodynamics flowfields. This code was developed for the configuration aerodynamics branch of NASA ARC, under SBIR Phase 2 contract NAS2-124568 by Computational Mechanics Corporation (COMCO). This report is in two volumes. Volume 1 contains the theory for the derived finite element algorithm and describes the test cases used to validate the computer program described in the Volume 2 user guide

Mixed finite element and stochastic Galerkin methods for groundwater flow modelling: efficiency analysis and real-life application

The thesis concludes with the development of a numerical model for a real case study in the United Kingdom, which is one of the first examples of formal characterization of model uncertainty for an actual site

A higher order numerical method for transonic flows

This thesis presents and verifies a numerical method for solving the compressible Euler equations. The method is based on a finite volume method with an upwind type TVD dissipation terms originally developed by Harten ( 1983 ) for scalar hyperbolic conservation law and extended to Euler equations by using Roe's approximate Riemann solver. The present method has second-order accurate in smooth region of the solution and intelligently switches the scheme to first-order accurate in the vicinity of shocks to presents a sharp and smooth shock wave profile. The present method contains no user-dependent and problem-dependent parameters. An explicit multistage Runge-Kutta time stepping is used to integrate the system. A multigrid method is employed in the present method to accelerate to convergence. Meanwhile a fully implicit time integration scheme is also investigated and adopted in this method. The explicit multistage time stepping with the multigrid acceleration is modified to solve the fully implicit system. The present method is programmed in two-dimensions for the Euler equations aiming at the application to internal flows. Numerical experiments are carried out to test the accuracy and the efficiency of the present method. Results compare well with exact solutions and perform better than some well-documented results. The desired efficiency is obtained. The connection between central difference and upwind difference is investigated. It is found that the widely used Jameson's central differencing plus explicit adaptive artificial viscosity can be interpreted as a hybrid scheme by a weighted average of a first order upwind scheme and a second order upwind scheme

Numerical evaluation of aerodynamic roughness of the built environment and complex terrain

Aerodynamic drag in the atmospheric boundary layer (ABL) is affected by the structure and density of obstacles (surface roughness) and nature of the terrain (topography). In building codes and standards, average roughness is usually determined somewhat subjectively by examination of aerial photographs. For detailed wind mapping, boundary layer wind tunnel (BLWT) testing is usually recommended. This may not be cost effective for many projects, in which case numerical studies become good alternatives. This thesis examines Computational Fluid Dynamics (CFD) for evaluation of aerodynamic roughness of the built environment and complex terrain. The present study started from development of an in-house CFD software tailored for ABL simulations. A three-dimensional finite-volume code was developed using flexible polyhedral elements as building blocks. The program is parallelized using MPI to run on clusters of processors so that micro-scale simulations can be conducted quickly. The program can also utilize the power of latest technology in high performance computing, namely GPUs. Various turbulence models including mixing-length, RANS, and LES models are implemented, and their suitability for ABL simulations assessed. Then the effect of surface roughness alone on wind profiles is assessed using CFD. Cases with various levels of complexity are considered including simplified models with roughness blocks of different arrangement, multiple roughness patches, semi-idealized urban model, and real built environment. Comparison with BLWT data for the first three cases showed good agreement thereby justifying explicit three-dimensional numerical approach. Due to lack of validation data, the real built environment case served only to demonstrate use of CFD for such purposes. Finally, the effect of topographic features on wind profiles was investigated using CFD. This work extends prior work done by the research team on multiple idealized two-dimensional topographic features to more elaborate three-dimensional simulations. It is found that two-dimensional simulations overestimate speed up over crests of hills and also show larger recirculation zones. The current study also emphasized turbulence characterization behind hills. Finally a real complex terrain case of the well-known Askervein hill was simulated and the results validated against published field observations. In general the results obtained from the current simulations compared well with those reported in literature

A combined immersed boundary/phase-field method for simulating two-phase pipe flows

The investigation of the flow in a pipe is a major issue for the pipeline capacity but also plays an important role for the control and prevention of phenomena that could damage the pipe, such as corrosion, erosion, and the potential formation of wax or their deposits. Therefore, the characterization of the flow patterns is also a major issue for the prediction of the distribution over the cross-section of the pipe, in order to understand any problems that may interrupt or shut down the operation of the production line. The main purpose of the present effort is to develop an appropriate numerical method for simulating two-phase pipe flows. Advanced Computational Fluid Dynamics (CFD) methods are employed as Navier-Stokes solver, while a Phase-Field method is used to simulate the interfacial region between the two fluids. A Ghost-Cell Immersed Boundary Method (GCIBM) was developed and implemented for the reconstruction of smooth rigid boundaries (pipe wall) based on the work of Tseng and Ferziger (2003). The method was also modified in order to incorporate appropriate boundary conditions for coupling the Phase-Field and Navier-Stokes solvers for two-phase pipe flows. Tseng and Ferziger (2003) used the GCIBM for turbulent single-phase flows; the present modified version comprises a continuation of the method for handling two-phase pipe flows. The computational model is capable of handling large density and viscosity ratios with good accuracy. The developed GCIBM algorithm was validated against analytical solutions for single and two-phase pipe flow, presenting very good agreement. The computational model was compared to available experimental data from the literature for single rising bubbles and bubble coalescence in vertical pipe also with good agreement. The numerical method was used to investigate the lateral wall effects of a 3-D single bubble in a viscous liquid for different pipe diameters and bubble flow regimes. The dynamics of 3-D Taylor bubbles was also examined in vertical pipes for different properties of fluids (e.g. air-water system) and dimensionless parameters relevant to the problem (e.g. ReB, Eo, Mo). The numerical results were compared with available experimental and numerical data from the literature, presenting good agreement.Open Acces

Engineering geology and geohydrology of the magnesian limestone of Northern England

Not availabl