Suneet Singh | Searcharxiv

arXiv2025

Phototactic Bioconvection in a Rotating Isotropic Porous Medium: Linear Stability Analysis

This study investigates the linear stability of phototactic bioconvection in a rotating porous medium under collimated light, incorporating the effects of critical intensity, Darcy number, and Taylor number. Using a mathematical model and the MATLAB Bvp4c solver, the critical Rayleigh number and wavenumber for instability onset are identified. The results reveal that higher Darcy numbers enhance instability, increasing the wavelength of bioconvection patterns, while rotation exerts a stabilizing effect by limiting vertical motion and confining fluid dynamics to the horizontal plane. Additionally, an increase in critical intensity amplifies instability. Furthermore, the study explores the transition between oscillatory and stationary solutions, highlighting the role of rotational dynamics in altering instability modes. These findings provide novel insights into the interplay of phototaxis, rotation, and porous media, advancing the understanding of bioconvective systems with potential applications in environmental engineering, biophysics, and geophysical fluid dynamics.

physics.flu-dyn↗

arXiv2024

Efficient cell-centered nodal integral method for multi-dimensional Burgers equations

An efficient coarse-mesh nodal integral method (NIM), based on cell-centered variables and termed the cell-centered NIM (CCNIM), is developed and applied to solve multi-dimensional, time-dependent, nonlinear Burgers equations, extending the applicability of CCNIM to nonlinear problems. To overcome the existing limitation of CCNIM to linear problems, the convective velocity in the nonlinear convection term is approximated using two different approaches, both demonstrating accuracy comparable to or better than traditional NIM for nonlinear Burgers problems. Unlike traditional NIM, which utilizes surface-averaged variables as discrete unknowns, this innovative approach formulates the final expression of the numerical scheme using discrete unknowns represented by cell-centered (or node-averaged) variables. Using these cell centroids, the proposed CCNIM approach presents several advantages compared to traditional NIM. These include a simplified implementation process in terms of local coordinate systems, enhanced flexibility regarding the higher order of accuracy in time, straightforward formulation for higher-degree temporal derivatives, and offering a viable option for coupling with other physics. The multi-dimensional time-dependent Burgers problems (propagating shock, propagation, and diffusion of an initial sinusoidal wave, shock-like formation) with known analytical solutions are solved in order to validate the developed scheme. Furthermore, a detailed comparison between the proposed CCNIM approach and other traditional NIM schemes is conducted to demonstrate its effectiveness. The proposed approach has shown quadratic convergence in both space and time, i.e., O[$(\Delta x)^2, (\Delta t)^2$], for the considered test problems. The simplicity and robustness of the approach provide a strong foundation for its seamless extension to more complex fluid flow problems.

math.NA↗