arXiv subjects

Khang Ee Pang

Publications and source records attributed to Khang Ee Pang.

8 recordsLinked to original sources

arXiv2026

Modelling Wave Attenuation by Mangroves: Effects of Root Morphology and Sea-Level Rise

Mangroves are increasingly promoted as nature-based solutions for coastal protection, yet many existing models neglect the vertical variation of vegetation biomass, leading to oversimplified representations of root-flow interactions. In this study, we introduce a generalised parametrisation of the mangrove vegetation profile and derive a wave attenuation model that explicitly accounts for the mangrove root characteristics. The model reveals that wave attenuation is species specific and exhibits a non-monotonic dependence on wave frequency. We further quantify the sensitivity of wave attenuation efficiency to sea-level rise and show that rising sea levels do not necessarily reduce attenuation capacity. In particular, when the water depth is less than approximately 1.6 times the mean root height, wave attenuation may instead be enhanced under sea-level rise. Future changes in attenuation efficiency under different climate scenarios are also quantified. OpenFOAM simulations are further used to calibrate drag coefficients as a function of the root submergence ratio. These results highlight the critical role of vertical root structure in governing wave attenuation and provide a framework for assessing the long-term resilience of mangrove-based coastal protection under climate change.

physics.flu-dyn↗

arXiv2024

Applications and Novel Regularization of the Thin-Film Equation

The classical no-slip boundary condition of the Navier-Stokes equations fails to describe the spreading motion of a droplet on a substrate due to the missing small-scale physics near the contact line. In this thesis, we introduce a novel regularization of the thin-film equation to model droplet spreading. The solution of the regularized thin-film equation -- the Geometric Thin-Film Equation is studied and characterized. Two robust numerical solvers are discussed, notably, a fast and mesh-free numerical scheme for simulating thin-film flows in two and three spatial dimensions. Moreover, we prove the regularity and convergence of the numerical solutions. The existence and uniqueness of the solution of the Geometric Thin-Film Equation with respect to a wide range of measure-valued initial conditions are also discussed.

physics.flu-dyn↗

arXiv2023

Symmetry-Breaking in Point-Heated Droplets

We investigate theoretically the stability of thermo-capillary convection within a droplet when heated by a point source from below. To model the droplet, we use a mathematical model based on lubrication theory. We formulate a base-state droplet profile, and we examine its respect to small-amplitude perturbations in the azimuthal direction. Such linear stability analysis reveals that the base state is stable across a wide parameter space. We carry out transient simulations in three spatial dimensions: the simulations reveal that when the heating is slightly off-centered with respect to the droplet center, vortices develop within the droplet. The vortices persist when the contact line is pinned. These findings are consistent with experimental studies of point-heated sessile droplets.

physics.flu-dyn↗

arXiv2023

A new convergence analysis of the particle method for the Camassa-Holm equation

We present a new self-contained convergence analysis of the particle method that can be applied to a range of PDEs, including the Camassa-Holm equation. It is a development of the analysis of Chertock, Liu and Pendleton, which used compactness properties of spaces of functions having bounded variation. In our analysis we establish solutions by applying a metric Arzelà-Ascoli compactness result to a space of measure-valued functions equipped with the bounded Lipschitz metric. All the convergence and regularity results of the previous analysis follow as a consequence and are computationally easier to establish.

math.AP↗

arXiv2023

Convergence Analysis of the Geometric Thin-Film Equation

The Geometric Thin-Film equation is a mathematical model of droplet spreading in the long-wave limit, which includes a regularization of the contact-line singularity. We show that the weak formulation of the problem, given initial Radon data, admits solutions that are globally defined for all time and are expressible as push-forwards of Borel measurable functions whose behaviour is governed by a set of ordinary differential equations (ODEs). The existence is first demonstrated in the special case of a finite weighted sum of delta functions whose centres evolve over time -- these are known as `particle solutions'. In the general case, we construct a convergent sequence of particle solutions whose limit yields a solution of the above form. Moreover, we demonstrate that all weak solutions constructed in this way are $1/2$-Hölder continuous in time and are uniquely determined by the initial conditions.

math.AP↗

arXiv2021

A mathematical model and mesh-free numerical method for contact-line motion in lubrication theory

We introduce a mathematical model with a mesh-free numerical method to describe contact-line motion in lubrication theory. We show how the model resolves the singularity at the contact line, and generates smooth profiles for an evolving, spreading droplet. The model describes well the physics of droplet spreading -- including Tanner's Law for the evolution of the contact line. The model can be configured to describe complete wetting or partial wetting, and we explore both cases numerically. In the case of partial wetting, the model also admits analytical solutions for the droplet profile, which we present here.

physics.flu-dyn↗

arXiv2019

A mathematical framework for determining the stability of steady states of reaction-diffusion equations with periodic source terms

We develop a mathematical framework for determining the stability of steady states of generic nonlinear reaction-diffusion equations with periodic source terms, in one spatial dimension. We formulate an \textit{a priori} condition for the stability of such steady states, which relies only on the properties of the steady state itself. The mathematical framework is based on Bloch's theorem and Poincaré's inequality for mean-zero periodic functions. Our framework can be used for stability analysis to determine the regions in an appropriate parameter space for which steady-state solutions are stable.

math.AP↗

arXiv2018

cuPentBatch -- A batched pentadiagonal solver for NVIDIA GPUs

We introduce cuPentBatch -- our own pentadiagonal solver for NVIDIA GPUs. The development of cuPentBatch has been motivated by applications involving numerical solutions of parabolic partial differential equations, which we describe. Our solver is written with batch processing in mind (as necessitated by parameter studies of various physical models). In particular, our solver is directed at those problems where only the right-hand side of the matrix changes as the batch solutions are generated. As such, we demonstrate that cuPentBatch outperforms the NVIDIA standard pentadiagonal batch solver gpsvInterleavedBatch for the class of physically-relevant computational problems encountered herein.

physics.comp-ph↗