arXiv subjects

Steven J. Lind

Publications and source records attributed to Steven J. Lind.

8 recordsLinked to original sources

arXiv2026

Direct Numerical Simulation of Thermoacoustically Unstable Flames Via Non-Drifting Acoustic Delay Characteristic Boundary Conditions

Thermoacoustic instability in premixed flames results from the coupling between the flame's heat release, as determined by combustion parameters, and surrounding acoustics, as determined by combustor geometry. A primary instability results in flame flattening as intrinsic flame instability modes are stabilised. Secondary thermoacoustic instability results in a parametric flame instability and drastic growth of acoustic amplitudes. Due to their relative expense, numerical simulations of these phenomena remain scarce. In this work, Direct Numerical Simulations (DNS) of thermoacoustically unstable idealised premixed flames in a tube with acoustically closed upstream and open downstream ends are presented. Results herein demonstrate nonlinear saturation of the primary instability as the flame flattens as well as an oscillating flame fingering characteristic of the unsteady Rayleigh-Taylor effect. To reduce computational cost, we perform DNS only on the region surrounding the flame. Acoustics at in- and outflows are described using the Navier-Stokes Characteristic Boundary Condition (NSCBC) method to model their delayed reentry into the domain in a formulation referred to as the Acoustic Delay Characteristic Boundary Condition (ADCBC) method. A new Averaged Proportional and Integral Linear Relaxation (APILR) method is also introduced, which modifies the Classic Linear Relaxation (CLR) method to maintain time-averaged values of inflow velocity and outflow pressure. Here, an integral control term is used to remove non-zero equilibrium time-averaged inflow velocities which impinge control over flame position. Both new methods demonstrate their capability in inert and counterflow flames test cases. These methods enable the numerical simulation of combustion instabilities at significantly reduced computational expense.

physics.flu-dyn↗

arXiv2026

Compact LABFM: a framework for meshless methods with spectral-like resolving power

Meshless methods are often used in numerical simulations of systems of partial differential equations (PDEs), particularly those which involve complex geometries or free surfaces. Here we present a novel compact scheme based on the local anisotropic basis function method (LABFM), a meshless method which provides approximations to spatial operators to arbitrary polynomial consistency. Our approach mimics compact finite-differences by using implicit stencils to optimise the resolving power of each operator, whilst retaining diagonal dominance of the resulting global sparse linear system. The new method is demonstrated to provide improved approximations by a series of convergence tests and resolving power analysis, before solutions to canonical PDEs are computed. Significant gains in accuracy are observed, in particular for solutions containing high wavenumber components. Our compact meshfree method provides a pathway to high-order simulations of PDEs in complex geometries with spectral-like resolving power, and has the potential to lead to a step-change in the accuracy of numerical solutions to such problems.

math.NA↗

arXiv2025

A p-adaptive high-order mesh-free framework for fluid simulations in complex geometries

This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node distributions using linear combinations of anisotropic basis functions, formulated to ensure the exact reproduction of polynomial fields up to the specified p order. A dynamic p-refinement strategy is developed to refine (increase) or de-refine (decrease) the polynomial order used to approximate derivatives at each node. A new refinement indicator for mesh-free methods is proposed, based on local error estimates of the Laplacian operator, and is incorporated into the solution procedure at minimal added computational cost. Based on this error indicator, a refinement criterion is established to locally adjust the polynomial order p for the solution. The proposed adaptive mesh-free scheme is then applied to a range of canonical PDEs, and its potential is demonstrated in two-dimensional simulations of a compressible reacting flow in porous media. For the test cases studied, the proposed method exhibits potential to save up to 50% of computational costs while maintaining the specified level of accuracy. The results confirm that the developed p-adaptive high-order mesh-free method effectively captures highly non-linear regions where high-order approximation is necessary and reduces computational costs compared to the non-adaptive method, preserving high accuracy and solution stability.

math.NA↗

arXiv2025

Uncertainty in Elastic Turbulence

Elastic turbulence can lead to to increased flow resistance, mixing and heat transfer. Its control -- either suppression or promotion -- has significant potential, and there is a concerted ongoing effort by the community to improve our understanding. Here we explore the dynamics of uncertainty in elastic turbulence, inspired by an approach recently applied to inertial turbulence in Ge et al. (2023) \textit{J. Fluid Mech.} 977:A17. We derive equations for the evolution of uncertainty measures, yielding insight on uncertainty growth mechanisms. Through numerical experiments, we identify four regimes of uncertainty evolution, characterised by I) rapid transfer to large scales, with large scale growth rates of $\tau^{6}$ (where $\tau$ represents time), II) a dissipative reduction of uncertainty, III) exponential growth at all scales, and IV) saturation. These regimes are governed by the interplay between advective and polymeric contributions (which tend to increase uncertainty), viscous, relaxation and dissipation effects (which reduce uncertainty), and inertial contributions. In elastic turbulence, reducing Reynolds number increases uncertainty at short times, but does not significantly influence the growth of uncertainty at later times. At late times, the growth of uncertainty increases with Weissenberg number, with decreasing polymeric diffusivity, and with the logarithm of the maximum length scale, as large flow features adjust the balance of advective and relaxation effects. These findings provide insight into the dynamics of elastic turbulence, offering a new approach for the analysis of viscoelastic flow instabilities.

physics.flu-dyn↗

arXiv2024

A new complex fluid flow phenomenon: Bubbles-on-a-String

A liquid jet plunging into a quiescent bath of the same liquid is a fundamental fluid mechanical problem underpinning a range of processes in industry and the natural world. Significant attention has been given to the study of plunging laminar Newtonian jets and the associated air entrainment that can occur. However, there have been very few (if any) studies devoted to the equivalent case for non-Newtonian viscoelastic liquids. Here we consider the laminar plunging and associated air entrainment of a shear thinning viscoelastic jet into a still bath of the same liquid. We describe a previously unreported phenomenon, that we call ``bubbles-on-a-string'' (BUoaS), consisting of multiple stable toroidal bubbles rising co-axially around the submerged jet. In a qualitative sense, this new observation is akin to an inverse version of the well-known rheological phenomenon ``beads-on-a-string''. The BUoaS phenomenon is stable and repeatable and can be reproduced to a lesser extent in Newtonian surfactant solutions, indicating that low surface tension is key, but non-Newtonian rheology seems likely to provide the most favourable conditions for the onset of the phenomenon. A full characterisation and detailed study of this behaviour with accompanying numerical simulation is to follow in an upcoming publication.

physics.flu-dyn↗

arXiv2024

A mesh-free framework for high-order simulations of viscoelastic flows in complex geometries

The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable resolution for the solution of viscoelastic flows across a range of Weissenberg numbers. Based on the Local Anisotropic Basis Function Method (LABFM) of King et al. J. Comput. Phys. 415 (2020):109549, highly accurate viscoelastic flow solutions are found using Oldroyd B and PPT models for a range of two dimensional problems - including Kolmogorov flow, planar Poiseulle flow, and flow in a representative porous media geometry. Convergence rates up to 9th order are shown. Three treatments for the conformation tensor evolution are investigated for use in this new high-order meshless context (direct integration, Cholesky decomposition, and log-conformation), with log-conformation providing consistently stable solutions across test cases, and direct integration yielding better accuracy for simpler unidirectional flows. The final test considers symmetry breaking in the porous media flow at moderate Weissenberg number, as a precursor to a future study of fully 3D high-fidelity simulations of elastic flow instabilities in complex geometries. The results herein demonstrate the potential of a viscoelastic flow solver that is both high-order (for accuracy) and meshless (for straightforward discretisation of non-trivial geometries including variable resolution). In the near-term, extension of this approach to three dimensional solutions promises to yield important insights into a range of viscoelastic flow problems, and especially the fundamental challenge of understanding elastic instabilities in practical settings.

physics.flu-dyn↗

arXiv2023

Large Eddy Simulations of bubbly flows and breaking waves with Smoothed Particle Hydrodynamics

For turbulent bubbly flows, multi-phase simulations resolving both the liquid and bubbles are prohibitively expensive in the context of different natural phenomena. One example is breaking waves, where bubbles strongly influence wave impact loads, acoustic emissions, and atmospheric-ocean transfer, but detailed simulations in all but the simplest settings are infeasible. An alternative approach is to resolve only large scales, and model small scale bubbles adopting sub-resolution closures. Here we introduce a large eddy simulation (LES) Smoothed Particle Hydrodynamics (SPH) scheme for simulations of bubbly flows. The continuous liquid phase is resolved with a semi-implicit isothermally compressible SPH framework. This is coupled with a discrete Lagrangian bubble model. Bubbles and liquid interact via exchanges of volume and momentum, through turbulent closures, bubble breakup and entrainment, and free-surface interaction models. By representing bubbles as individual particles, they can be tracked over their lifetimes, allowing closure models for sub-resolution fluctuations, bubble deformation, breakup and free-surface interaction in integral form, accounting for the finite timescales over which these events occur. We investigate two flows: bubble plumes, and breaking waves, and find close quantitative agreement with published experimental and numerical data. In particular, for plunging breaking waves, our framework accurately predicts the Hinze scale, bubble size distribution, and growth rate of the entrained bubble population. This is the first coupling of an SPH framework with a discrete bubble model, with potential for cost effective simulations of wave-structure interactions and more accurate predictions of wave impact loads.

physics.flu-dyn↗

arXiv2020

Quantum Algorithm for Smoothed Particle Hydrodynamics

We present a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. We use a normalization procedure to encode the SPH operators and domain discretization in a quantum register. We then perform the SPH summation via an inner product of quantum registers. Using a one-dimensional function, we test the approach in a classical sense for the kernel sum and first and second derivatives of a one-dimensional function, using both the Gaussian and Wendland kernel functions, and compare various register sizes against analytical results. Error convergence is exponentially fast in the number of qubits. We extend the method to solve the one-dimensional advection and diffusion partial differential equations, which are commonly encountered in fluids simulations. This work provides a foundation for a more general SPH algorithm, eventually leading to highly efficient simulations of complex engineering problems on gate-based quantum computers.

quant-ph↗