Electro-osmotic creeping physiological propulsion between uniform and non-uniform microtubes with transversely deflecting walls Muhammad Roshan, Pramod Kumar Yadav, Ritesh Kumar Dubey Physics of Fluids, 2025 This work focuses on the mathematical modeling of a flow situation that arises from the interaction of two flow mechanisms, such as peristalsis and electro-osmosis, through an annular space between a non-uniform microtube (a physiological vessel) with non-zero wall surface roughness and a microtube (an artificially designed peristaltic endoscope) with uniform cross section and zero wall surface roughness. The authors have modeled the roughness of the outer microtube's wall as a sinusoidal structure to represent the roughness found in a physiological microtube. The flow setup is mathematically modeled using conservation laws like the continuity equation, Cauchy equations of motion, and the Poisson equation. To explore the kinematics of the present flow model, the governing equations are simplified by taking certain approximations, such as the Debye–Hückel approximations and lubrication approach, and obtained the axial velocity profile of the fluid flow and electric potential function. To ensure the correctness and reliability of the present model, the authors also provided a graphical validation. Furthermore, authors have plotted the illustrative figures to describe the effect of control parameters, including the Debye–Hückel parameter and Helmholtz–Smoluchowski velocity, non-uniformity and wall surface roughness of the outer microtube, radius ratio and peristalsis generating factor (occlusion), and fluid rheology (Jeffrey fluid parameter) on the hydrodynamic quantities. The findings reveal that a higher surface roughness parameter increases wall shear stress at the outer non-uniform microtube, reducing flow velocity, whereas electro-osmotic forces enhance fluid propulsion by overcoming flow resistance. Furthermore, increasing the non-uniformity of the outer microtube restricts both electric potential and wall shear stress at its wall, while simultaneously enhancing the profile of instantaneous flow rate and axial velocity. The results and insights of this research work may be beneficial in exploring the physiological propulsion of physiological fluids, such as urine, blood, cervical mucus, and embryos, as well as in designing and manufacturing microfluidic tools, advanced endoscopes, and bio-microfluidic devices.
On the learning of high order polynomial reconstructions for essentially non-oscillatory schemes Vikas Kumar Jayswal, Ritesh Kumar Dubey Physica Scripta, 2024 Approximation accuracy and convergence behavior are essential required properties for the computed numerical solution of differential equations. These requirements restrict the application of deep learning networks in the domain of scientific computing. Moreover, the recipe to create suitable synthetic data which can be used to train a good model is also not very clear. This study focuses on learning of third order essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstructions using classification neural networks with small data sets. In particular, this work (i) proposes a novel way to obtain a third order WENO reconstruction which can be posed as classification problem, (ii) gives simple and novel approach to sample data sets which are small but rich enough to inherit the latent feature of inter-spatial regularity information in the constructed data, (iii) it is established that sampling of train data sets impacts quantitatively as well as qualitatively the required accuracy and non-oscillatory properties of resulting ENO3 and WENO3 schemes, (iv) proposes to use a limiter based multi model to retain desired accuracy as well as non-oscillatory properties of the resulting numerical schemes. Computational results are given which established that learned networks perform well and retain the features of the reconstruction methods.
WENO schemes using optimized third order fuzzy weight limiter functions Prabhat Mishra, Ritesh Kumar Dubey Physica Scripta, 2024 This work presents an improved version of non-linear weight limiters to obtain third order non-oscillatory WENO scheme. The construction of this modified weight limiter is based on fuzzy inference system, which is a knowledge based rule system. The linear combination of overlapped basis functions is used to achieve the optimized weight limiters by exploring the linguistics hedges operator on the basis functions. The WENO scheme using optimized weight limiter achieves third order of accuracy and gives higher resolution to discontinuities compared to other established third order WENO schemes.
Entropy stable non-oscillatory fluxes: An optimized wedding of entropy conservative flux with non-oscillatory flux Ritesh Kumar Dubey Journal of Numerical Mathematics, 2024 This work frames the problem of constructing non-oscillatory entropy stable fluxes as a least square optimization problem. A flux sign stability condition is defined for a pair of entropy conservative flux (F∗ ) and a non-oscillatory flux (Fs ). This novel approach paves a way to construct non-oscillatory entropy stable flux (F̂) as a simple combination of (F∗ and Fs ) which inherently optimize the numerical diffusion in the entropy stable flux (F̂) such that it reduces to the underlying non-oscillatory flux (Fs ) in the flux sign stable region. This robust approach is (i) agnostic to the choice of flux pair (F∗, Fs ), (ii) does not require the computation of costly dissipation operator and high order reconstruction of scaled entropy variable to construct the diffusion term. Various non-oscillatory entropy stable fluxes are constructed and exhaustive computational results for standard test problems are given which show that fully discrete schemes using these entropy stable fluxes do not exhibit nonphysical spurious oscillations in approximating the discontinuities compared to the non-oscillatory schemes using underlying fluxes (Fs ) only. Moreover, these entropy stable schemes maintain the formal order of accuracy of the lower order flux in the pair.
Data dependent stability of forward in time and centred in space (FTCS) scheme for scalar hyperbolic equations International Journal of Numerical Analysis and Modeling, 2016
