Three-Dimensional Bedrock Channel Evolution with Smoothed Particle Hydrodynamics

Bedrock channels are responsible for balancing and communicating tectonic and climatic signals across landscapes, but it is difficult and dangerous to observe and measure the flows responsible for removing weakly-attached blocks of bedrock from the channel boundary. Consequently, quantitative descriptions of the dynamics of bedrock removal are scarce. Detailed numerical simulation of violent flows in three dimensions has been historically challenging due to technological limitations, but advances in computational fluid dynamics aided by high-performance computing have made it practical to generate approximate solutions to the governing equations of fluid dynamics. From these numerical solutions we gain detailed knowledge of the motions and forces of flowing water, which deepens our understanding of earth processes responsible for shaping landscapes. By simulating hydraulic forces generated by flowing water in bedrock channels with interconnected zones of weakness, I explore the implications of fluvial stresses, boulder impact, and rock fabric heterogeneity on landscape form. I use a Smoothed Particle Hydrodynamics (SPH) solver to simulate flow over landscapes and I use stress-strength analysis to calculate earth fabric failure using the Failure Earth Response Model (FERM). SPH modeling is used to simulate the hydraulic mobilization of a boulder in a bedrock channel and to quantify the forces associated with its subsequent rolling, sliding, and impact two-meter freefall. FERM model results reveal that strength gradients in fractured bedrock topographies exert more control on volume of eroded material and channel form than the overall strength of the surrounding bedrock. Finally, SPH model results are calibrated with three-dimensional water velocity measurements collected by an acoustic doppler current profiler in the Penobscot River. SPH modeling is used to explore the influence of in-stream logging structures on channel velocity, which has implications for the habitat of federally-protected diadromous fish species in the Penobscot River. Model results show that even at low discharges, the presence of in-stream structures changes the velocity structure at ~102 m length scales

Master of Science

thesisQUIC EnvSim (QES) is a complete building-resolving urban microclimate modeling system developed to rapidly compute mass, momentum, and heat transport for the design of sustainable cities. One of the more computationally intensive components of this type of modeling system is the transport and dispersion of scalars. In this paper, we describe and evaluate QESTransport, a Reynolds-averaged Navier-Stokes (RANS) scalar transport model. QESTransport makes use of light-weight methods and modeling techniques. It is parallelized for Graphics Processing Units (GPUs), utilizing NVIDIA's OptiX application programming interfaces (APIs). QESTransport is coupled with the well-validated QUIC Dispersion Modeling system. To couple the models, a new methodology was implemented to efficiently prescribe surface flux boundary conditions on both vertical walls and flat surfaces. In addition, a new internal boundary layer parameterization was introduced into QUIC to enable the representation of momentum advection across changing surface conditions. QESTransport is validated against the following three experimental test cases designed to evaluate the model's performance under idealized conditions: (i) flow over a step change in moisture, roughness, and temperature, (ii) flow over an isolated heated building, and (iii) flow through an array of heated buildings. For all three cases, the model is compared against published simulation results. QESTransport produces velocity, temperature, and moisture fields that are comparable to much more complex numerical models for each case. The code execution time performance is evaluated and demonstrates linear scaling on a single GPU for problem sizes up to 4.5 x 4.5 km at 5 m grid resolution, and is found to produce results at much better than real time for a 1.2 x 1.2 km section of downtown Salt Lake City, Utah

On estimating the interface normal and curvature in PLIC-VOF approach for 3D arbitrary meshes

Volume of fluid (VOF) method with its Piecewise Linear Interface Calculation (PLIC) reconstruction algorithm is one of the most popular approaches in numerical simulation of interfacial flows with a wide range of applications in different areas. In an effort to evaluate the similarity of the PLIC-generated planes in comparison with the exact interface, a point-cloud, based on the polygon centers of PLIC planes is extracted, which later is used to form a triangular grid that represents the estimated interface. The main objective of this article is to evaluate the interface geometrical properties based on the extracted triangular grid of the interface. The methods presented in this article, characterized by a higher spatially convergence ratio, are compared with the commonly used methods. The proposed methods are tested for two 3-dimensional general test cases, where an evident improvement is seen in calculation accuracy and spatial convergence of the errors of interface normal vector and curvature.This work has been financially supported by MCIN/AEI/10.13039/ 501100011033 Spain, project PID2020-115837RBI00. E. Schillaci acknowledges the financial support of the Programa Torres Quevedo (PTQ2018-010060).Peer ReviewedPostprint (author's final draft

An interactive boundary layer modelling methodology for aerodynamic flows

PURPOSE – The purpose of this paper is to introduce a unique technique to couple the two-integral boundary layer solutions to a generic inviscid solver in an iterative fashion. DESIGN/METHODOLOGY/APPROACH – The boundary layer solution is obtained using the two-integral method to solve displacement thickness point by point with a local Newton method, at a fraction of the cost of a conventional mesh-based, full viscous solution. The boundary layer solution is coupled with an existing inviscid solver. Coupling occurs by moving the wall to a streamline at the computed boundary layer thickness and treating it as a slip boundary, then solving the flow again and iterating. The Goldstein singularity present when solving boundary layer equations is overcome by solving an auxiliary velocity equation along with the displacement thickness. FINDINGS – The proposed method obtained favourable results when compared with the analytical solutions for flat and inclined plates. Further, it was applied to modelling the flow around a NACA0012 airfoil and yielded results similar to those of the widely used XFOIL code. ORIGINALITY/VALUE – A unique method is proposed for coupling of the boundary layer solution to the inviscid flow. Rather than the traditional transpiration boundary condition, mesh movement is employed to simulate the boundary layer thickness in a more physically meaningful way. Further, a new auxiliary velocity equation is presented to circumvent the Goldstein singularity.The Council for Scientific and Industrial Research (CSIR) on Thematic Type A Grant No. TA-2009-013http://www.emeraldinsight.com/journals.htm?issn=0961-5539hj201

Simulating supernova feedback in galaxy disks

In this thesis I examine supernova feedback in hydrodynamical simulations of galaxy disks. Understanding this process entails the numerical evaluation of cooling in radiative shocks, and we present a set of simulations using two widely used numerical schemes: smoothed particle hydro- dynamics and adaptive mesh refinement. We obtain a similarity solution for a shock-tube problem in the presence of radiative cooling, and test how well the solution is reproduced. We interpret our findings in terms of a resolution criterion, and apply it to realistic simulations of cosmological accretion shocks onto galaxy halos, cold accretion and thermal feedback from supernovae or active galactic nuclei. To avoid numerical overcooling of accretion shocks onto halos that should develop a hot corona requires a particle or cell mass resolution of 10^6 M⊙, which is within reach of current state-of-the-art simulations. At this mass resolution, thermal feedback in the interstellar medium of a galaxy requires temperatures of supernova or AGN driven bubbles to be in excess of 10^7 K at densities of n_H = 1.0 cm−3, in order to avoid spurious suppression of the feedback by numerical overcooling. In order to improve sub-grid models of feedback we perform a series of numerical experiments to investigate how supernova explosions shape the interstellar medium in a disk galaxy and power a galactic wind. We model a simplified ISM, including gravity, hydrodynamics, radiative cooling above 10^4 K, and star formation that reproduces the Kennicutt-Schmidt relation. By simulating a small patch of the ISM in a tall box perpendicular to the disk, we obtain sub-parsec resolution allowing us to resolve individual supernova events. We run a large grid of simulations in which we vary gas surface density, gas fraction, and star formation rate in order to investigate the dependencies of the mass loading, β ≡ dot M_wind / dot M_star. In the cases with the most effective outflows we observe a β of 4, however in other cases we find β<<1. We find that outflows are more efficient in disks with lower surface densities or gas fractions. A simple model in which the warm clouds are the barriers that limit the expansion of the blast wave reproduces the scaling of outflow properties with disk parameters at high star formation rates. We extend the scaling relations derived from an ISM patch to infer an effective mass loading for a galaxy with an exponential disk, finding that the mass loading depends on circular velocity as β ∝ V −α with α ≈ 2.5 for a model which fits the Tully-Fisher relation. Such a scaling is often assumed in phenomenological models of galactic winds in order to reproduce the flat faint end slope of the mass function. Our normalisation is in approximate agreement with observed estimates of the mass loading for the Milky Way. Finally, we extend these simulations to follow the ejecta produced by these SNe, allowing us to track the distribution of metals as they are mixed into the different phases of the ISM and swept out into a galactic wind. Such calculations are important both directly in predicting the enrichment of the intergalactic medium, but also with the sister problem of understanding the enrichment of the host galaxies and the mass-metallicity relation, owing to the unique role that supernovae are believed to play both as the sources of galactic winds and the sources of galactic metals. We study the dependence of the amount of metals released per unit of star formation, β_Z ≡ dot M_z / dot M_star, and the fraction of metals released, β_Z / y. We include thermal and momentum feedback from massive stars and find these make a less significant contribution to the galactic wind than SNe. We build up a model of galactic chemical evolution and we demonstrate that these models are compatible with the metallicity distributions of faint stars and compare to closed box models of chemical evolution. We infer metal retention fractions from the observed data, although this may be complicated by recycling in the galaxy halos. We compare these rates to the fraction of metals ejected in the simulations and demonstrate approximate agreement, although the simulation data has considerable scatter, primarily due to the stochastic nature of the feedback in the limited volumes of the simulations

Toward a rigorous derivation of a stable and consistent smoothed particle hydrodynamics method

The aim of this thesis is to provide an investigation toward a rigorous derivation of a stable and consistent numerical method based on the established Smoothed Particle Hydrodynamics method. The method should be suitable for modelling the large deformation transient response of fluids and solids, the interests of the Crashworthiness, Impact and Structural Mechanics group (CISM) at Cranfield University. A literature review of the current state of the art of the SPH method finds that the conventional SPH equations are not derived in a rigorous way, often the equations are manipulated into a mathematically equivalent form in order to preserve conservation of linear momentum, which often leads to different results; the reasons for this are unknown and it is not fully understood how each particular form of the discrete equations effects the solution in terms of stability, accuracy and convergence. This leads to specific objectives being defined which underpin the overall aim of the thesis. The first objective is to develop an understanding of the SPH method and the implementation used at Cranfield University, this is done through a capability study which demonstrates the coupled SPH-FE method and a number of relevant improvements to the MCM code including the addition of a turbulence model and the modification of the SPH contact algorithm to model lateral forces between materials. This is demonstrated through the implementation of a friction model, which suggests that the contact algorithm is suitable for resolving lateral forces based on the relative velocity between materials, with the potential for coupling with a structural FE model ... [cont.]

Fast prediction of transonic aeroelasticity using computational fluid dynamics

The exploitation of computational fluid dynamics for non linear aeroelastic simulations is mainly based on time domain simulations of the Euler and Navier-Stokes equations coupled with structural models. Current industrial practice relies heavily on linear methods which can lead to conservative design and flight envelope restrictions. The significant aeroelastic effects caused by nonlinear aerodynamics include the transonic flutter dip and limit cycle oscillations. An intensive research effort is underway to account for aerodynamic nonlinearity at a practical computational cost.To achieve this a large reduction in the numbers of degrees of freedoms is required and leads to the construction of reduced order models which provide compared with CFD simulations an accurate description of the dynamical system at much lower cost. In this thesis we consider limit cycle oscillations as local bifurcations of equilibria which are associated with degenerate behaviour of a system of linearised aeroelastic equations. This extra information can be used to formulate a method for the augmented solve of the onset point of instability - the flutter point. This method contains all the fidelity of the original aeroelastic equations at much lower cost as the stability calculation has been reduced from multiple unsteady computations to a single steady state one. Once the flutter point has been found, the centre manifold theory is used to reduce the full order system to two degrees of freedom. The thesis describes three methods for finding stability boundaries, the calculation of a reduced order models for damping and for limit cycle oscillations predictions. Results are shown for aerofoils, and the AGARD, Goland, and a supercritical transport wing. It is shown that the methods presented allow results comparable to the full order system predictions to be obtained with CPU time reductions of between one and three orders of magnitude