arXiv subjects

Debashis Panda

Publications and source records attributed to Debashis Panda.

6 recordsLinked to original sources

arXiv2026

Numerical simulation of a two-frequency-driven superlattice Faraday-wave pattern

The formation of a superlattice pattern in two-frequency-driven Faraday waves discovered and named SSS-I by Arbell & Fineberg (1998, 2002) is investigated by means of Direct Numerical Simulations (DNS) of the full three-dimensional Navier--Stokes equations with a free surface. Two simulations with distinct quasi-hexagonal initial conditions run at a forcing amplitude $25\%$ above the Faraday-wave onset followed quite different routes, but both led eventually to the same superlattice pattern after around 250 forcing periods. This regime is inaccessible to the approximations of weak nonlinearity or viscosity. The standing-wave pattern contain rows of patches, alternating in time between hills and lakes that are connected by a long skeleton resembing the backbone of DNA strands. The patches and skeleton of the pattern can be related to its spatial Fourier decomposition, which combines hexagonal modes with a spatially and temporally subharmonic mode. One of the transition routes passes through several fairly long-lived transients including different hexagonal patterns and another superlattice pattern; the other passes only through erratic and disordered states. After another 100 periods, the pattern became unstable and was succeeded by a dynamic version of SSS-I in which the superlattice is modulated and drifts in the direction of the backbone, while preserving its basic shape. Convergence to SSS-I states both experimentally in a large geometry and numerically from two different initial conditions and in a minimal geometry demonstrates the robustness of the SSS-I pattern.

physics.flu-dyn↗

arXiv2026

Interfacial standing wave-patterns disentangle dilatational and shear surface viscous effects

Dilatational and shear surface viscosities are highly correlated parameters, making their individual contributions difficult to disentangle in Stokes flow, linearised flow models, or two-dimensional flows. We therefore investigate the three-dimensional interfacial standing waves as a means to decouple the influence of dilatational and shear surface viscosities. Two dimensionless controlling parameters are introduced: $Bq$, the total Boussinesq number, which quantifies the the relative importance of surface viscous stresses compared with bulk viscous stresses, and $\tan \chi$, which quantifies the ratio of surface dilatational viscosity to surface shear viscosity. The growth rates and threshold accelerations are independent of $\chi$, consistent with previous theoretical predictions. Nonlinear analyses of square and hexagonal patterns reveal that Fourier decomposition of wave-patterns can effectively decouple the intricate dynamics into axial modes, where the waves are weakly dependent on $\chi$, and oblique modes, where additional damping occurs in the shear surface viscous dominant interface. These results demonstrate that Faraday wave-patterns provide a route for identifying and quantifying the distinct roles of dilatational and shear surface viscosities.

physics.flu-dyn↗

arXiv2025

Direct numerical simulation of two-phase flows with surfactant-induced surface viscous effects

Direct numerical simulations of interfacial flows with surfactant-induced complexities involving surface viscous stresses are performed within the framework of the Level Contour Reconstruction Method (LCRM); this hybrid front-tracking/level-set approach leverages the advantages of both methods. In addition to interface-confined surfactant transport that results in surface diffusion and Marangoni stresses, the interface, endowed with shear and dilatational viscosities; these act to resist deformation arising from velocity gradients in the plane of the two-dimensional manifold of the interface, and interfacial compressibility effects, respectively. By adopting the Boussinesq-Scriven constitutive model, We provide a mathematical formulation of these effects that accurately captures the interfacial mechanics, which is then implemented within the LCRM-based code by exploiting the benefits inherent to the underlying front-tracking/level-sets hybrid approach. We validate our numerical predictions against a number of benchmark cases that involve drops undergoing deformation when subjected to a flow field or when rising under the action of buoyancy. The results of these validation studies highlight the importance of adopting a rigorous approach in modelling the interfacial dynamics. We also present results that demonstrate the effects of surface viscous stresses on interfacial deformation in unsteady parametric surface waves and atomisation events.

physics.flu-dyn↗

arXiv2024

Marangoni-driven patterns, ridges, and hills in surfactant-covered parametric surface waves

Parametric oscillations of an interface separating two fluid phases create nonlinear surface waves, called Faraday waves, which organise into simple patterns, like squares and hexagons, as well as complex structures, such as double hexagonal and superlattice patterns. In this work, we study the influence of surfactant-induced Marangoni stresses on the formation and transition of Faraday wave patterns. We use a quantity $B$, that assesses the relative importance of Marangoni stresses as compared to the the surface wave dynamics. Our results show that the threshold acceleration required to destabilise a surfactant-covered interface through vibration increases with increasing $B$. For a surfactant-free interface, a square wave pattern is observed. As $B$ is incremented, we report transitions from squares to asymmetric squares, weakly wavy stripes, and ultimately to ridges and hills. These hills are a consequence of the bi-directional Marangoni stresses at the neck of the ridges. The mechanisms underlying the pattern transitions and the formation of exotic ridges and hills are discussed.

physics.flu-dyn↗

arXiv2023

Direct Numerical Simulation for Parametric Vertical Vibration and Atomization of Sessile Drops

Sessile drop vertical vibrations and atomization is commonly analyzed by simpler unconstrained instabilities like Faraday waves and hence, detailed studies of the phenomenon are still an open question to the fluid dynamics community. We address two critical gaps using direct numerical simulation, i.e., (i) the cause of subharmonic response of azimuthal waves, and (ii) the dependence of vertical vibrations to the universal pinchoff regime in the atomization. First, a high mode excitation of a large drop of 100 microliters is implemented. It is found that the subharmonic response is not via Faraday waves, rather it is the harmonics of the interfacial waves that induce azimuthal waves near the contact line. An analogous self-inducing dynamical system is formalized between the tip and near the contact line to elucidate the mechanism. Second, a low mode excitation of small drop of 30 microliter is used to critically explain the cause of primary pinch-off via crater formation and secondary pinch-off via ligament retraction. The pinch-off test in both cases revealed that the primary pinch-off is in visco-capillary scaling regime, while the secondary pinch-off is affected by the inertial forces via oscillatory body forces of vibration.

physics.flu-dyn↗

arXiv2022

Fast hardware-aware matrix-free algorithm for higher-order finite-element discretized matrix multivector products on distributed systems

Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work proposes efficient matrix-free algorithms for evaluating FE discretized matrix-multivector products on both multi-node CPU and GPU architectures. We address a critical gap in existing matrix-free implementations, which are well suited only for the action of FE discretized matrices on a single vector. We employ batched evaluation strategies, with the batchsize tailored to underlying hardware architectures, leading to better data locality and enabling further parallelization. On CPUs, we utilize even-odd decomposition, SIMD vectorization, and overlapping computation and communication strategies. On GPUs, we employ strategies to overlap compute and data movement in conjunction with GPU shared memory, constant memory, and kernel fusion to reduce data accesses. Our implementation outperforms the baselines for Helmholtz operator action, achieving up to 1.4x improvement on one CPU node and up to 2.8x on one GPU node, while reaching up to 4.4x and 1.5x improvement on multiple nodes for CPUs ($\sim 3000$ cores) and GPUs ($\sim$ 25 GPUs), respectively. We further benchmark the performance of the proposed implementation for solving a model eigenvalue problem for 1024 smallest eigenvalue-eigenvector pairs by employing the Chebyshev Filtered Subspace Iteration method, achieving up to 1.5x improvement on one CPU node and up to 2.2x on one GPU node while reaching up to 3.0x and 1.4x improvement on multinode CPUs ($\sim 3000$ cores) and GPUs ($\sim$ 25 GPUs), respectively.

physics.comp-ph↗