arXiv subjects

Khemraj Gautam Kshetri

Publications and source records attributed to Khemraj Gautam Kshetri.

3 recordsLinked to original sources

arXiv2026

Fully resolved particle dynamics over long time scales in acoustofluidic flows: Theory and numerical simulations

We present a perturbation-based theoretical framework, together with its immersed boundary/volume penalization implementation, for long-time simulations of fully resolved rigid-particle dynamics in acoustically actuated flows. A perturbation formulation separates the fast acoustic time scale from the slow mean dynamics, avoiding long-time direct integration of the fully compressible Navier-Stokes equations. The immersed rigid body is represented through a Brinkman penalization term in equations posed over a unified fluid-solid domain. The coupled fluid-particle system is decomposed into a time-harmonic first-order problem governing the acoustic response and a time-averaged second-order problem. A central challenge in this decomposition is the treatment of the moving fluid-solid interface. We derive order-consistent expressions for the structural velocities, comprising rigid-body and Stokes-drift contributions, and formulate the corresponding first- and second-order rigid-body equations of motion. For a circular particle in two dimensions, the simulations reveal substantial differences in the magnitude and structure of acoustic streaming around fixed and freely moving particles, highlighting the importance of two-way fluid-structure coupling. The results also show that particle-density effects are more complex than suggested by simplified descriptions based solely on the acoustic contrast factor. The framework captures the mean particle dynamics using time steps associated with the slow particle-motion scale rather than the much smaller acoustic time scale. Finally, simulations of an elliptical particle demonstrate the ability of the method to capture coupled translational and rotational motion. The proposed approach therefore provides an efficient route to fully resolved, long-time simulations of acoustically driven rigid-particle motion while retaining two-way fluid-structure coupling.

physics.flu-dyn↗

arXiv2026

Simulating acoustically-actuated flows in complex microchannels using the volume penalization technique

We present a volume penalization technique for simulating acoustically-actuated flows in geometrically complex microchannels. Using a perturbation approach, the nonlinear response of an acoustically-actuated compressible Newtonian fluid moving over obstacles or flowing in a geometrically complex domain is segregated into two sub-problems: a harmonic first-order problem and a time-averaged second-order problem, where the latter utilizes forcing terms and boundary conditions arising from the first-order solution. This segregation results in two distinct volume penalized systems of equations. The no-slip boundary condition at the fluid-solid interface is enforced by prescribing a zero structure velocity for the first-order problem, while spatially varying Stokes drift -- which depends on the gradient of the first-order solution -- is prescribed as the structure velocity for the second-order problem. The harmonic first-order system is solved via MUMPS direct solver, whereas the steady state second-order system is solved iteratively using a novel projection method-based preconditioner. The preconditioned iterative solver for the second-order system is demonstrated to be highly effective and scalable with respect to increasing penalty force and grid resolution, respectively. A novel contour integration technique to evaluate the acoustic radiation force on an immersed object is also proposed. Through test cases featuring representative microfluidic geometries, we demonstrate excellent agreement between the volume penalized and body-fitted grid. We also identify suitable penalty factors and interfacial smearing widths to accurately capture the first- and second-order solutions. These results provide first-of-its-kind empirical evidence of the efficacy of the volume penalization method for simulating acoustic streaming problems that have so far been analyzed using body-fitted methods in literature.

physics.flu-dyn↗

arXiv2025

Consistent continuum equations and numerical benchmarks for a perturbation-based, variable-coefficient acoustofluidic solver

We present a consistent continuum framework and a variable-coefficient acoustofluidic solver to analyze acoustic streaming. A perturbation approach is used to split the compressible Navier-Stokes equations into two sub-systems: a first-order harmonic system and a time-averaged second-order mean system. Prior acoustofluidic numerical studies have typically employed simplifying assumptions regarding the second-order mass balance equation and boundary conditions. These assumptions -- frequently left unjustified -- result in an incongruent problem statement where the boundary conditions are not consistent with the governing equations. To clarify these assumptions and mitigate the associated confusion, we systematically formulate the second-order mass balance equation into two analytically equivalent but numerically distinct forms by introducing the fluid's Lagrangian and mass transport velocity. We clarify the relation between these quantities to illustrate that a zero mass transport velocity does not necessarily imply a zero Lagrangian velocity. A second-order accurate finite difference/volume scheme is used to discretize the governing equations and boundary conditions expressed in Eulerian form. We solve the first-order coupled Helmholtz system via a sparse direct solver while the second-order system is solved via a Krylov (FGMRES) solver with a projection method-based preconditioner. To ascertain the spatial accuracy and consistency of numerical implementation of the split system of equations and boundary conditions, we demonstrate verification results and convergence rates using manufactured solutions. We provide benchmark test cases to demonstrate the impact of the choice of boundary conditions on second-order flow field. Lastly, we examine a system with spatially varying density to illustrate the difference in flow fields between constant and variable density systems.

physics.flu-dyn↗