arXiv subjects

Faisal Amlani

Publications and source records attributed to Faisal Amlani.

7 recordsLinked to original sources

arXiv2026

Blend-to-zero operators for smooth transition functions

Motivated by existing blend-to-zero techniques, a formal framework is developed for defining and constructing blend-to-zero operators on closed intervals for the generation of sufficiently smooth transitions between functions. Such transitions are first formulated as a two-point Hermite-type interpolation that is not necessarily polynomial. It is shown that, in the polynomial case, the corresponding interpolant can be explicitly represented in terms of the regularized incomplete Beta-function. This representation is then used to generate linear blend-to-zero operators. Following this, additional blend-to-zero operators are constructed by considering the algebraic and geometric properties of functions with sufficiently flat ends (e.g., smooth staircase functions and smooth step functions). Finally, explicit formulas for a family of trigonometric smooth step functions are provided, and these functions are shown to be related to certain higher-order two-point boundary value problems.

math.CA↗

arXiv2025

Tsunami modeling with dynamic seafloors: a high-order solver validated with shallow water benchmarks

Recent scientific studies have suggested that, in certain physical configurations, the time-dependent behavior of earthquake rupture and seafloor (bathymetry) motion can leave observable near-field signatures in tsunami wave generation and propagation. However, dynamic ground movement is often neglected in conventional tsunami models, which commonly assume instantaneous ground displacement (sourcing). This work introduces a pseudo-spectral algorithm for the solution of the nonlinear shallow water equations with timedependent seafloor displacement and velocity. Based on a Fourier continuation (FC) methodology for the accurate trigonometric interpolation of a non-periodic function, the solver provides high-order convergence in space and time; mild (linear) Courant-Friedrichs-Lewy (CFL) constraints for explicit time integration; and results that are effectively free of numerical dispersion (or ''pollution'') errors. Such properties enable the efficient and robust resolution of the different space-time scales involved modeling tsunamis generated by dynamic earthquake ground motion (including over long distances). Numerical experiments attesting to accuracy and computational performance are presented with direct comparisons to high-order finite difference methodologies. The solver is physically validated by a number of classical and semi-classical benchmark cases based on simulated or experimental data. Additionally, a seismologically realistic, first-of-its-kind parametric study based on earthquake speed is introduced, whose results-easily facilitated by the FC-based approach proposed herein, with minimal numerical tuning-further demonstrate the potential importance of (and the motivation herein for) incorporating time-dependent seafloor behavior in quantitative tsunami hazard assessment.

math.NA↗

arXiv2024

A hybrid numerical methodology coupling Reduced Order Modeling and Graph Neural Networks for non-parametric geometries: applications to structural dynamics problems

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order modeling (ROM) framework and recently-introduced Graph Neural Networks (GNNs), where the latter is trained on highly heterogeneous databases of varying numerical discretization sizes. The proposed techniques are shown to be particularly suitable for non-parametric geometries, ultimately enabling the treatment of a diverse range of geometries and topologies. Performance studies are presented in an application context related to the design of aircraft seats and their corresponding mechanical responses to shocks, where the main motivation is to reduce the computational burden and enable the rapid design iteration for such problems that entail non-parametric geometries. The methods proposed here are straightforwardly applicable to other scientific or engineering problems requiring a large number of finite element-based numerical simulations, with the potential to significantly enhance efficiency while maintaining reasonable accuracy.

cs.LG↗

arXiv2023

A Fourier-based methodology without numerical diffusion for conducting dye simulations and particle residence time calculations

Dye experimentation is a widely used method in experimental fluid mechanics for flow analysis or for the study of the transport of particles within a fluid. This technique is particularly useful in biomedical diagnostic applications ranging from hemodynamic analysis of cardiovascular systems to ocular circulation. However, simulating dyes governed by convection-diffusion partial differential equations (PDEs) can also be a useful post-processing analysis approach for computational fluid dynamics (CFD) applications. Such simulations can be used to identify the relative significance of different spatial subregions in particular time intervals of interest in an unsteady flow field. Additionally, dye evolution is closely related to non-discrete particle residence time (PRT) calculations that are governed by similar PDEs. This contribution introduces a pseudo-spectral method based on Fourier continuation (FC) for conducting dye simulations and non-discrete particle residence time calculations without numerical diffusion errors. Convergence and error analyses are performed with both manufactured and analytical solutions. The methodology is applied to three distinct physical/physiological cases: 1) flow over a two-dimensional (2D) cavity; 2) pulsatile flow in a simplified partially-grafted aortic dissection model; and 3) non-Newtonian blood flow in a Fontan graft. Although velocity data is provided in this work by numerical simulation, the proposed approach can also be applied to velocity data collected through experimental techniques such as from particle image velocimetry.

physics.flu-dyn↗

arXiv2022

Direct 0D-3D coupling of a lattice Boltzmann methodology for fluid-structure hemodynamics simulations

This work introduces a numerical approach and implementation for the direct coupling of arbitrary complex ordinary differential equation- (ODE-)governed zero-dimensional (0D) boundary conditions to three-dimensional (3D) lattice Boltzmann-based fluid-structure systems for hemodynamics studies. In particular, a most complex configuration is treated by considering a dynamic left ventricle- (LV-)elastance heart model which is governed by (and applied as) a nonlinear, non-stationary hybrid ODE-Dirichlet system. Other ODE-based boundary conditions, such as lumped parameter Windkessel models for truncated vasculature, are also considered. Performance studies of the complete 0D-3D solver, including its treatment of the lattice Boltzmann fluid equations and elastodynamics equations as well as their interactions, is conducted through a variety of benchmark and convergence studies that demonstrate the ability of the coupled 0D-3D methodology in generating physiological pressure and flow waveforms -- ultimately enabling the exploration of various physical and physiological parameters for hemodynamics studies of the coupled LV-arterial system. The methods proposed in this paper can be easily applied to other ODE-based boundary conditions as well as to other fluid problems that are modeled by 3D lattice Boltzmann equations and that require direct coupling of dynamic 0D boundary conditions.

physics.flu-dyn↗

arXiv2022

Supershear shock front contribution to the tsunami from the 2018 $\mathbf M_{\mathbf w}$ 7.5 Palu, Indonesia earthquake

Hazardous tsunamis are known to be generated predominantly at subduction zones. However, the 2018 Mw 7.5 Sulawesi (Indonesia) earthquake on a strike-slip fault generated a tsunami that devastated the city of Palu. The mechanism by which this tsunami originated from such an earthquake has been debated. Here we present near-field ground motion (GPS) data confirming that the earthquake attained supershear speed, i.e., a rupture speed greater than the shear wave speed of the host medium. We study the effect of this supershear rupture on tsunami generation by coupling the ground motion to a one-dimensional nonlinear shallow-water wave model accounting for both time-dependent bathymetric displacement and velocity. With the local bathymetric profile of Palu bay around a tidal station, our simulations reproduce the tsunami arrival and motions observed by CCTV cameras. We conclude that Mach (shock) fronts, generated by the supershear speed, interacted with the bathymetry and contributed to the tsunami.

physics.geo-ph↗

arXiv2019

Transient Propagation and Scattering of Quasi-Rayleigh Waves in Plates: Quantitative comparison between Pulsed TV-Holography Measurements and FC(Gram) elastodynamic simulations

We study the scattering of transient, high-frequency, narrow-band quasi-Rayleigh elastic waves by through-thickness holes in aluminum plates, in the framework of ultrasonic nondestructive testing (NDT) based on full-field optical detection. Sequences of the instantaneous two-dimensional (2-D) out-of-plane displacement scattering maps are measured with a self-developed PTVH system. The corresponding simulated sequences are obtained by means of an FC(Gram) elastodynamic solver introduced recently, which implements a full three-dimensional (3D) vector formulation of the direct linear-elasticity scattering problem. A detailed quantitative comparison between these experimental and numerical sequences, which is presented here for the first time, shows very good agreement both in the amplitude and the phase of the acoustic field in the forward, lateral and backscattering areas. It is thus suggested that the combination of the PTVH system and the FC(Gram) elastodynamic solver provides an effective ultrasonic inspection tool for plate-like structures, with a significant potential for ultrasonic NDT applications.

physics.app-ph↗