arXiv subjects

Andrew J. Higgins

Publications and source records attributed to Andrew J. Higgins.

At least 19 recordsLinked to original sources

arXiv2026

Detonation propagation in weakly confined gases

This study investigates the propagation of detonations along a layered configuration where a reactive gas is weakly confined by a hotter inert layer. CFD simulations are performed using a single-step, non-Arrhenius reaction model designed to suppress cellular instabilities, enabling formulation of a theoretical framework directly compared with simulation results. The simulations reach a quasi-steady state, revealing distinct flowfield regimes that depend on the acoustic-impedance ratio and relative layer thicknesses, with some detonations exhibiting velocity deficits while others propagate above the ideal Chapman-Jouguet (CJ) speed. Analytical models are developed to interpret these regimes. When a precursor shock is observed in the inert layer, the detonation is overdriven; this is modeled using shock-polar analysis and velocity estimates based on the approach of Mitrofanov (Acta Astronaut. 3:995-1004, 1976). An analytical criterion for precursor shock onset is proposed. In underdriven scenarios, the detonation front exhibits positive curvature, analyzed using a geometric construction wherein the relationship between wave speed and front curvature is evaluated a priori. A simplified characteristic-based model captures the decay of the shock wave in the inert layer, after which shock-polar analysis determines the resulting wave interaction. Predictions from these models are assembled into a phase map delineating regions of overdriven and underdriven behavior, along with corresponding shock interactions, in the space of acoustic impedance and area ratios. This map is compared directly with CFD results. The combined numerical-theoretical framework clarifies transition mechanisms governing layered detonations and provides insights into detonation dynamics relevant to rotating detonation engines in which the detonation is bounded by hotter combustion products from a previous cycle.

physics.flu-dyn↗

arXiv2025

Random-sketching Techniques to Enhance the Numerical Stability of Block Orthogonalization Algorithms for s-step GMRES

We integrate random sketching techniques into block orthogonalization schemes needed for s-step GMRES. The resulting block orthogonalization schemes generate the basis vectors whose overall orthogonality error is bounded by machine precision as long as each of the corresponding block vectors are numerically full rank. We implement these randomized block orthogonalization schemes using standard distributed-memory linear algebra kernels for s-step GMRES available in the Trilinos software packages. Our performance results on the Perlmutter supercomputer (with four NVIDIA A100 GPUs per node) demonstrate that these randomized techniques can enhance the numerical stability of the orthogonalization and overall solver, without a significant increase in the execution time.

math.NA↗

arXiv2025

A High Performance GPU CountSketch Implementation and Its Application to Multisketching and Least Squares Problems

Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some $O(1)$ distortion factor with high probability. The most popular sketches in literature are the Gaussian sketch and the subsampled randomized Hadamard transform, while the CountSketch has lower complexity. Combining two sketches, known as multisketching, offers an inexpensive means of quickly reducing the dimension of a matrix by combining a CountSketch and Gaussian sketch. However, there has been little investigation into high performance CountSketch implementations. In this work, we develop an efficient GPU implementation of the CountSketch, and demonstrate the performance of multisketching using this technique. We also demonstrate the potential for using this implementation within a multisketched least squares solver that is up to $77\%$ faster than the normal equations with significantly better numerical stability, at the cost of an $O(1)$ multiplicative factor introduced into the relative residual norm.

math.NA↗

arXiv2025

Analysis of Randomized Householder-Cholesky QR Factorization with Multisketching

CholeskyQR2 and shifted CholeskyQR3 are two state-of-the-art algorithms for computing tall-and-skinny QR factorizations since they attain high performance on current computer architectures. However, to guarantee stability, for some applications, CholeskyQR2 faces a prohibitive restriction on the condition number of the underlying matrix to factorize. Shifted CholeskyQR3 is stable but has $50\%$ more computational and communication costs than CholeskyQR2. In this paper, a randomized QR algorithm called Randomized Householder-Cholesky (\texttt{rand\_cholQR}) is proposed and analyzed. Using one or two random sketch matrices, it is proved that with high probability, its orthogonality error is bounded by a constant of the order of unit roundoff for any numerically full-rank matrix, and hence it is as stable as shifted CholeskyQR3. An evaluation of the performance of \texttt{rand\_cholQR} on a NVIDIA A100 GPU demonstrates that for tall-and-skinny matrices, \texttt{rand\_cholQR} with multiple sketch matrices is nearly as fast as, or in some cases faster than, CholeskyQR2. Hence, compared to CholeskyQR2, \texttt{rand\_cholQR} is more stable with almost no extra computational or memory cost, and therefore a superior algorithm both in theory and practice.

math.NA↗

arXiv2024

Cavitation Onset in an Impulsively Accelerated Liquid Column

This paper introduces a novel piston-driven apparatus to study the onset of cavitation in an impulsively accelerated liquid column as it compresses a closed gas volume. The experiment is monitored using high-speed videography and piezoelectric pressure transducers. Cavitation onset is observed in the liquid column as it undergoes an abrupt deceleration and is associated with a sudden drop in pressure in the liquid that leads to negative pressure (tension). A novel numerical modeling approach is introduced where the liquid column is treated as a spring-mass system. This approach can reproduce compressibility effects in the liquid column and is used to investigate the wave dynamics responsible for the onset of tension and cavitation in the liquid column. The model is formulated as a coupled set of non-linear differential equations that reproduce the dynamics of an experiment while capturing the pressure wave activity in the liquid column. A parametric study is conducted experimentally and numerically to investigate the behavior behind the onset of cavitation. The mechanism for the onset of cavitation is identified as a series of wave reflections at the boundaries of the liquid column, and this mechanism is found to be well reproduced by the model. While a traditional cavitation number criterion is shown to be unable to predict cavitation onset in our experiment, our numerical model is found to correctly predict the onset of cavitation for a wide range of experimental parameters.

physics.flu-dyn↗

arXiv2024

Asymmetry of imploding detonations in thin channels

The factors that influence the symmetry of an imploding detonation are investigated experimentally and theoretically. Detonations in sub-atmospheric acetylene-oxygen were initiated and made to converge in an apparatus that followed that of Lee and Lee (Phys Fluids 8:2148-2152, 1965). The width of the test section was controlled with a wave-shaping insert, which formed the test section against the viewing window, creating an effectively two-dimensional problem with a channel width comparable to the detonation cell size. The convergence of the detonation was observed via self-luminous open-shutter photography and high-speed videography. The resulting videos were analyzed to quantify the wave speed, degree of asymmetry, and direction and magnitude of the offset in the center of convergence. To determine the experimental parameters that influence the symmetry of the imploding wave, the wave-shaping insert was intentionally canted by 0.3°-0.6°, accentuating the asymmetry of the imploding detonation. The experiment was modeled using a Huygens construction wherein the detonation is treated as a collection of wavelets, each assumed to propagate locally at a velocity determined by the channel width. The results of the model reproduced the observed offsets in detonation convergence from the center of the apparatus, confirming that velocity deficits resulting from the narrow channel width control the observed asymmetry.

physics.flu-dyn↗

arXiv2024

Magneto-Rayleigh-Taylor instability and feedthrough in a resistive liquid-metal liner of a finite thickness

The effect of magnetic tension and diffusion on the perturbation growth of a liquid-metal liner subjected to the magneto-Rayleigh-Taylor (MRT) instability is investigated. An initially magnetic-field-free liquid-metal slab of finite thickness is surrounded by two lower-density regions. Within the lower region, a constant axial magnetic field of arbitrary magnitude is applied. The numerical examination of the MRT instability growth, initiated by a seeded perturbation parallel to the magnetic field at the liner's unstable interface, is performed for both perfectly conductive and resistive liners. To this end, a novel level set-based two-phase incompressible solver for ideal/resistive magnetohydrodynamic (MHD) flows within the finite-difference framework is introduced. Utilizing the implemented numerical toolkit, the impact of different Alfven numbers and magnetic Reynolds numbers on the MRT growth rate and feedthrough at the upper interface of the liner is studied. Accounting for the finite resistivity of the liner results in an increase in the MRT growth and feedthrough compared to the ideal MHD case. The results indicate that magnetic diffusion primarily affects the MRT growth rate for higher wavenumbers, while for smaller wavenumbers, the effect of finite resistivity is only observed over a longer duration of instability development. We further demonstrate that decreasing the Alfven number results in the faster emergence of the magnetic diffusion effect on the MRT growth rate. It is also observed that a greater electrical conductivity jump across the liner results in an increased perturbation growth. Lastly, the impact of surface tension on MRT instability growth for both ideal and resistive MHD cases is studied across different wavenumbers, specifically for Bond numbers related to fusion applications.

physics.flu-dyn↗

arXiv2024

A level set-based solver for two-phase incompressible flows: Extension to magnetic fluids

Development of a two-phase incompressible solver for magnetic flows in the magnetostatic case is presented. The proposed numerical toolkit couples the Navier-Stokes equations of hydrodynamics with Maxwell's equations of electromagnetism to model the behaviour of magnetic flows in the presence of a magnetic field. To this end, a rigorous implementation of a second-order two-phase solver for incompressible nonmagnetic flows is introduced first. This solver is implemented in the finite-difference framework, where a fifth-order conservative level set method is employed to capture the evolution of the interface, along with an incompressible solver based on the projection scheme to model the fluids. The solver demonstrates excellent performance even with high density ratios across the interface (Atwood number $\approx 1$), while effectively preserving the mass conservation property. Subsequently, the numerical discretization of Maxwell's equations under the magnetostatic assumption is described in detail, utilizing the vector potential formulation. The primary second-order solver for two-phase flows is extended to the case of magnetic flows, by incorporating the Lorentz force into the momentum equation, accounting for high magnetic permeability ratios across the interface. The implemented solver is then utilized for examining the deformation of ferrofluid droplets in both quiescent and shear flow regimes across various susceptibility values of the droplets. The results suggest that increasing the susceptibility value of the ferrofluid droplet can affect its deformation and rotation in low capillary regimes. In higher capillary flows, increasing the magnetic permeability jump across the interface can further lead to droplet breakup as well. The effect of this property is also investigated for the Rayleigh-Taylor instability growth in magnetic fluids.

physics.flu-dyn↗

arXiv2024

Two-Stage Block Orthogonalization to Improve Performance of $s$-step GMRES

On current computer architectures, GMRES' performance can be limited by its communication cost to generate orthonormal basis vectors of the Krylov subspace. To address this performance bottleneck, its $s$-step variant orthogonalizes a block of $s$ basis vectors at a time, potentially reducing the communication cost by a factor of $s$. Unfortunately, for a large step size $s$, the solver can generate extremely ill-conditioned basis vectors, and to maintain stability in practice, a conservatively small step size is used, which limits the performance of the $s$-step solver. To enhance the performance using a small step size, in this paper, we introduce a two-stage block orthogonalization scheme. Similar to the original scheme, the first stage of the proposed method operates on a block of $s$ basis vectors at a time, but its objective is to maintain the well-conditioning of the generated basis vectors with a lower cost. The orthogonalization of the basis vectors is delayed until the second stage when enough basis vectors are generated to obtain higher performance. Our analysis shows the stability of the proposed two-stage scheme. The performance is improved because while the same amount of computation as the original scheme is required, most of the communication is done at the second stage of the proposed scheme, reducing the overall communication requirements. Our performance results with up to 192 NVIDIA V100 GPUs on the Summit supercomputer demonstrate that when solving a 2D Laplace problem, the two-stage approach can reduce the orthogonalization time and the total time-to-solution by the respective factors of up to $2.6\times$ and $1.6\times$ over the original $s$-step GMRES, which had already obtained the respective speedups of $2.1\times$ and $1.8\times$ over the standard GMRES. Similar speedups were obtained for 3D problems and for matrices from the SuiteSparse Matrix Collection.

math.NA↗

arXiv2022

Dynamic Soaring as a Means to Exceed the Solar Wind Speed

A technique by which a spacecraft can interact with flows of ionized gas in space (the solar wind or interstellar medium) to be accelerated to velocities greater than the wind velocity is explored. Inspired by the dynamic soaring maneuvers performed by sea birds and gliders in which differences in wind speed are exploited to gain velocity, in the proposed technique a lift-generating spacecraft circles between regions of the heliosphere that have different wind speeds, gaining energy without the use of propellant and only modest onboard power requirements. The spacecraft motion can be modeled as a series of elastic collisions between regions of the medium moving at different speeds. Models of the trajectory are developed to predict the potential velocity gains and the maximum velocity that may be achieved in terms of the lift-to-drag ratio of the vehicle. A lift-generating mechanism is proposed in which power is extracted from the flow over the vehicle in the flight direction and then used to accelerate the surrounding medium in the transverse direction, generating lift. Large values of lift-to-drag ratio are shown to be possible in the case where a small transverse velocity is imparted over a large area of interaction. The requirement for large interaction area in the extremely low density of the heliosphere precludes the use of physical wings, but the use of plasma waves generated by compact, directional antennas to impart momentum on the surrounding medium is feasible, with R-waves, X-waves, Alfven, and magnetosonic waves appearing as promising candidates. A mission is defined in which dynamic soaring is performed on the termination shock of the heliosphere, speeds of 2% of c to be reached within 2.5 years of launch without the expenditure of propellant. The technique may comprise the first stage for a multistage mission to achieve true interstellar flight to other solar systems.

physics.space-ph↗

arXiv2022

Structural Stability of a Lightsail for Laser-Driven Interstellar Flight

The structural stability of a lightsail under the laser flux necessary for interstellar flight is studied analytically and numerically. A sinusoidal perturbation is introduced into a two-dimensional thin-film sail to determine if the sail remains stable or if the perturbations grow in amplitude. A reflective material that gives specular reflection of the laser illumination is assumed in determining the resulting loading on the sail, although other reflection models can be incorporated as well. The quasi-static solution of the critical point between shape stability and instability is found by equating the bending moments induced on the sail due to radiation pressure with the restoring moments caused by the strength of the sail and the tension applied at the edges of the sail, permitting analytical expressions for the elastic modulus and boundary tension magnitude to be found as a function of sail properties and the amplitude and wave number of the initial perturbation. These expressions are also derived from a formal variational energy approach. A numerical model of the sail dynamics is developed by discretizing the sail into finite elements. By introducing torsional and rectilinear springs between the elements into the numerical model, a hierarchy of models is produced that can incorporate the effects of bending and applied tension. The numerical models permit the transient dynamics of a perturbed sail to be compared to the analytic results of the quasi-static analysis. The analytic expressions can correctly predict the stability boundary found in the numerical simulations. The stiffness required to make a sail stable against uncontrolled perturbation growth is shown to be unfeasible for known materials. A modest tensioning of the sail (e.g., via an inflatable structure or spinning of the sail) can maintain a stable sail shape under all wavelengths and amplitudes of perturbations.

physics.space-ph↗

arXiv2022

An Explosively Driven Launcher Capable of 10 km/s Projectile Velocities

Launching large (> 1 g) well-characterized projectiles to velocities beyond 10 km/s is of interest for a number of scientific fields but is beyond the reach of current hypervelocity launcher technology. This paper reports the development of an explosively driven light-gas gun that has demonstrated the ability to launch 8 mm diameter, 0.36 g magnesium projectiles to 10.4 km/s. The implosion-driven launcher (IDL) uses the linear implosion of a pressurized tube to shock-compress helium gas to a pressure of \SI{5}{\giga\pascal}, which then expands to propel a projectile to hypervelocity. The launch cycle of the IDL is explored with the use of down-bore velocimetry experiments and a quasi-one-dimensional internal ballistics solver. A detailed overview of the design of the 8 mm launcher is presented, with an emphasis on the unique considerations which arise from the explosively driven propellant compression and the resulting extreme pressures and temperatures. The high average driving pressure results in a launcher that is compact, with a total length typically less than a meter. The possibility to scale the design to larger projectile sizes (25 mm diameter) is demonstrated. Finally, concepts for a modified launch cycle which may allow the IDL to reach significantly greater projectile velocities are explored conceptually and with preliminary experiments.

physics.app-ph↗

arXiv2022

Wind--Pellet Shear Sailing

A propulsion concept in which a spacecraft interacts with high-velocity pellets and the interstellar medium is proposed. The pellets are slower than the spacecraft and are accelerated backwards as they are overtaken, imparting a forward acceleration on the spacecraft. This maneuver is possible due to the interaction with a fixed medium (interstellar medium, ISM); as the spacecraft travels through the medium, it is able to extract power from the relative wind. This concept relies upon the relative velocities (shear) between the pellet stream and the fixed medium in order to concentrate the energy of the pellets into the spacecraft and is thus termed wind-pellet shear sailing. The equations governing the mass ratio of pellets to the spacecraft and its dependence on the final spacecraft velocity are derived; the critical role of the efficiency of the power extraction and transfer process is identified. Natural sources of energy are considered as a means to accelerate the pellets to velocities of 1000 to 6000 km/s. Techniques for onboard generation of power via electromagnetic interaction with the ISM are reviewed, with a repetitively stroked plasma magnet being identified as a promising approach. The necessity of the spacecraft to detect and track the pellets as they are overtaken dictates the desired properties of the pellets. Pellet pushers (accelerators) on board the spacecraft are also preliminarily explored in their engineering considerations, with electric field accelerators of charged nanometric particles, Lorentz-force accelerated ionized pellets, or expansion of vaporized pellets via a nozzle being highlighted as potential approaches. A preliminary mission profile is defined in which a 500-kg scientific payload is delivered to orbit about alpha-Centauri within 30 years, using wind-pellet shear sailing as the intermediate stage to bring the spacecraft from 2% to 5.5% of c.

physics.space-ph↗

arXiv2020

Effect of spatial distribution of mesoscale heterogeneities on the shock-to-detonation transition in liquid nitromethane

The sensitizing effect of cavities in the form of microbubbles on the shock initiation of a homogeneous liquid explosive is studied computationally. While the presence of voids in an explosive has long been known to induce so-called hot spots that greatly accelerate the global reaction rate, the ability to computationally resolve the details of the interaction of the shock front with heterogeneities existing on the scale of the detonation reaction zone has only recently become feasible. In this study, the influence of the spatial distribution of air-filled cavities has been examined, enabled by the use of graphic processing unit (GPU) accelerated computations that can resolve shock initiation and detonation propagation through an explosive while fully resolving features at the mesoscale. Different spatial distributions of cavities are examined in two-dimensional simulations, including regular arrays of cavities, slightly perturbed arrays, random arrays (with varying minimum spacing being imposed on the cavities), and randomly distributed clusters of cavities. The presence of the cavities is able to reduce the time required to initiate detonation---for a given input shock strength---by greater than 50%, in agreement with previous experimental results. Randomly distributing the cavities results in a 15-20% decrease in detonation initiation time in comparison to a regular array of cavities. Clustering the cavities---as would occur in the case of agglomeration---results in an additional 10% decrease in detonation initiation time in comparison to random arrays. The effect of clustering is shown not to be a result of the clusters forming an effectively larger cavity, but rather due to interactions between clusters upon shock loading occurring on the microscale.

physics.flu-dyn↗

arXiv2019

Dimensional scaling of flame propagation in discrete particulate clouds

The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate sources are not resolved and the heat release is assumed spatially uniform, is solved via conventional finite difference techniques. Second, a discrete source model, wherein the heat diffusion from individual sources is modeled via superposition of the Green's function of each source, is employed to examine the influence of the random, discrete nature of the media. Heat transfer to cold, isothermal walls and to a layer of inert gas surrounding the reactive medium are considered as the loss mechanisms. Both cylindrical and rectangular (slab) geometries of the reactive medium are considered, and the flame speed is measured as a function of the diameter and thickness of the domains, respectively. In the continuum model with inert gas confinement, a universal scaling of critical diameter to critical thickness near 2:1 is found. In the discrete source model, as the time scale of heat release of the sources is made small compared to the interparticle diffusion time, the geometric scaling between cylinders and slabs exhibits values greater than 2:1. The ability of the flame in the discrete regime to propagate in thinner slabs than predicted by continuum scaling is attributed to the flame being able to exploit local fluctuations in concentration across the slab to sustain propagation. As the heat release time of the sources is increased, the discrete source model reverts back to results consistent with the continuum model. Implications of these results for experiments are discussed.

physics.flu-dyn↗

arXiv2019

Meso-resolved simulations of shock-to-detonation transition in nitromethane with air-filled cavities

Two-dimensional, meso-resolved numerical simulations are performed to investigate the complete shock-to-detonation transition (SDT) process in a mixture of liquid nitromethane (NM) and air-filled, circular cavities. The shock-induced initiation behaviors resulting from the cases with neat NM, NM with an array of regularly spaced cavities, and NM with randomly distributed cavities are examined. For the case with randomly distributed cavities, hundreds of cavities are explicitly resolved in the simulations using a diffuse-interface approach to treat two immiscible fluids and GPU-enabled parallel computing. Without invoking any empirically calibrated, phenomenological models, the reaction rate in the simulations is governed by Arrhenius kinetics. For the cases with neat NM, the resulting SDT process features a superdetonation that evolves from a thermal explosion after a delay following the passage of the incident shock wave and eventually catches up with the leading shock front. For the cases wherein mesoscale heterogeneities are explicitly considered, a gradual SDT process is captured. These two distinct initiation behaviors for neat NM and heterogeneous NM mixtures agree with experimental findings. Via examining the global reaction rate of the mixture, a unique time scale characterizing the SDT process, i.e., the overtake time, is measured for each simulation. For an input shock pressure less than approximately $9.4~\mathrm{GPa}$, the overtake time resulting from a heterogeneous mixture is shorter than that for neat NM. This sensitizing effect is more pronounced for lower input shock pressures. A random distribution of cavities is found to be more effective in enhancing the SDT process than a regular array of cavities. Statistical analysis on the meso-resolved simulation data provides more insights into the mechanism of energy release underlying the SDT process.

physics.comp-ph↗

arXiv2017

Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable, with the local value of energy release correspondingly increased so as to maintain the same average energy density in the medium, and thus a constant Chapman Jouguet (CJ) detonation velocity. A one-step Arrhenius rate governs the rate of energy release in the reactive zones. The resulting dynamics of a detonation propagating in such systems with one-dimensional layers and two-dimensional squares are simulated using a Godunov-type finite-volume scheme. The resulting wave dynamics are analyzed by computing the average wave velocity and one-dimensional averaged wave structure. In the case of sufficiently inhomogeneous media wherein the spacing between reactive zones is greater than the inherent reaction zone length, average wave speeds significantly greater than the corresponding CJ speed of the homogenized medium are obtained. If the shock transit time between reactive zones is less than the reaction time scale, then the classical CJ detonation velocity is recovered. The spatio-temporal averaged structure of the waves in these systems is analyzed via a Favre averaging technique, with terms associated with the thermal and mechanical fluctuations being explicitly computed. The analysis of the averaged wave structure identifies the super-CJ detonations as weak detonations owing to the existence of mechanical non-equilibrium at the effective sonic point embedded within the wave structure. The correspondence of the super-CJ behavior identified in this study with real detonation phenomena that may be observed in experiments is discussed.

physics.flu-dyn↗

arXiv2017

Front Roughening of Flames in Discrete Media

The morphology of flame fronts propagating in reactive systems comprised of randomly positioned, point-like sources is studied. The solution of the temperature field and the initiation of new sources is implemented using the superposition of the Green's function for the diffusion equation, eliminating the need to use finite difference approximations. The heat released from triggered sources diffuses outward from each source, activating new sources and enabling a mechanism of flame propagation. Systems of $40000$ sources in a $200$ by $200$ two-dimensional domain were tracked using computer simulations, and statistical ensembles of $120$ realizations of each system were averaged to determine the statistical properties of the flame fronts. The reactive system of sources is parameterized by two non-dimensional values: The heat release time (normalized by interparticle diffusion time) and the ignition temperature (normalized by adiabatic flame temperature). These two parameters were systematically varied for different simulations to investigate their influence on front propagation. For sufficiently fast heat release and low ignition temperature, the front roughness (defined as the RMS deviation of the ignition temperature contour from the average flame position) grew following a power law dependence that was in excellent agreement with the KPZ universality class ($β= 1/3$). As the reaction time was increased, lower values of the roughening exponent were observed, and at a sufficiently great value of reaction time, reversion to a steady, constant-width thermal flame was observed that matched the solution from classical combustion theory. Deviation away from KPZ scaling was also observed as the ignition temperature was increased. The features of this system that permit it to exhibit both KPZ and non-KPZ scaling are discussed.

physics.flu-dyn↗