arXiv subjects

Santosh Ansumali

Publications and source records attributed to Santosh Ansumali.

At least 19 recordsLinked to original sources

arXiv2026

A Scalable OpenLB LAMMPS Framework for Fully Resolved Simulations of Hindered Settling of Arbitrary Non-Spherical Particles

Hindered settling of non spherical particles remains significantly less understood than spherical particles due to the computational challenges in resolving the complex contact mechanics and hydrodynamic interactions. In this paper, we present a scaleable fluid structure interaction (FSI) framework coupling the open-source LBM software in OpenLB with the Discrete Element Method (DEM) implemented in LAMMPS to simulate arbitrary shaped rigid bodies in a fluid. Particle contacts are captured using a multi-sphere "clump" representation in DEM, while particle geometries are resolved on the fluid grid via voxelization. We validate our model against single and multi-particle benchmarks, and proceed to study the hindered setttling of cubes in systems containing upto 100,000 cubes. Our simulations show distinct differences between the settling of cubes and sphere, as cubes form pronounced coordination shells without face-parallel contact, in contrast to the contact-dominated clustering observed in spheres. Our results find that correlation length in velocity fluctuations scale with system size even for the largest system studied. These findings highlight the role of particle morphology in suspension dynamics and demonstrate a robust framework for simulating large-scale geotechnical and particulate flows.

physics.flu-dyn↗

arXiv2026

Magnetohydrodynamic equilibrium and neutronics study on MAST-U using Jenga framework

Tokamak design is inherently challenging due to several cross-competing effects which require a careful and calibrated treatment to obtain an optimal operational envelope. Incorporating physics across varied fidelities is crucial in this exercise. Jenga is developed as a unified design and modeling framework for tokamaks, seamlessly coupling systems-level studies to high-fidelity models based on first principles. In this work, static Grad-Shafranov (GS) equilibrium for an entire pulse and the neutronics study of the Mega Ampere Spherical Tokamak Upgrade (MAST-U) tokamak are carried out in Jenga. Coil currents and plasma profiles from the EFIT++ reconstruction of MAST-U shots are used to reproduce the plasma poloidal flux and shape targets at different time slices. The results from Jenga are also in good agreement with FreeGSNKE and Fiesta codes. Neutronics analysis is performed for a hypothetical 50-50 mixture of deuterium-tritium (DT) fuel, using the same data structure as the systems and equilibrium studies. A distributed neutron source is initialized within the last closed flux surface (LCFS) of the plasma, with their strength being functions of the density and temperature of the ions. The distribution of the neutron flux across the energy spectrum is computed for the active coils and the first wall (limiter) independently over multiple scenarios. We demonstrate the capabilities of Jenga with a comprehensive analysis that takes inputs about the plasma geometry, tokamak design and plasma profiles and performs 0D, 2D and 3D numerics for the systems study, equilibrium and neutron transport respectively.

physics.plasm-ph↗

arXiv2026

Design and mechanical analysis of the PRAGYA tokamak vacuum vessel

PRAGYA is India's first privately developed low aspect ratio tokamak designed by Pranos Fusion Energy. The device is designed for a plasma major radius (R0) of about 0.4 m, a plasma minor radius (a) greater than 0.18 m, a plasma current (Ip) of up to 25 kA, and a toroidal magnetic field (B_T) of 0.1 T. The PRAGYA vacuum vessel incorporates several distinctive features, including a toroidal electrical break to minimize induced eddy currents and a double O-ring arrangement to reduce vacuum leakage. This paper presents the final design of the PRAGYA vacuum vessel and a comprehensive three-dimensional (3D) finite element model (FEM) assessment of its structural performance. The analysis evaluates the effects of self-weight, atmospheric pressure loading, and thermal stress arising from in-situ baking. The results confirm that the design satisfies the required safety margins under these combined loading conditions, providing a robust foundation for subsequent plasma operations in this compact tokamak.

physics.plasm-ph↗

arXiv2026

Kinetic-based regularization: Learning spatial derivatives and PDE applications

Accurate estimation of spatial derivatives from discrete and noisy data is central to scientific machine learning and numerical solutions of PDEs. We extend kinetic-based regularization (KBR), a localized multidimensional kernel regression method with a single trainable parameter, to learn spatial derivatives with provable second-order accuracy in 1D. Two derivative-learning schemes are proposed: an explicit scheme based on the closed-form prediction expressions, and an implicit scheme that solves a perturbed linear system at the points of interest. The fully localized formulation enables efficient, noise-adaptive derivative estimation without requiring global system solving or heuristic smoothing. Both approaches exhibit quadratic convergence, matching second-order finite difference for clean data, along with a possible high-dimensional formulation. Preliminary results show that coupling KBR with conservative solvers enables stable shock capture in 1D hyperbolic PDEs, acting as a step towards solving PDEs on irregular point clouds in higher dimensions while preserving conservation laws.

math.NA↗

arXiv2026

Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning

We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between the numerical/exact solutions of the Burgers' and Eikonal equations, and the same obtained via PINNs is presented. We show that PINN learning provides a different computational pathway compared to standard numerical discretization in approximating essentially the same underlying dynamics of the system. Within this framework, DNNs can be interpreted as discrete dynamical systems whose layer-wise evolution approaches attractors, and multiple parameter configurations may yield comparable solutions, reflecting the degeneracy of the inverse mapping. In contrast to the structured operators associated with finite-difference (FD) procedures, PINNs learn dense parameter representations that are not directly associated with classical discretization stencils. This distributed representation generally involves a larger number of parameters, leading to reduced interpretability and increased computational cost. However, the additional flexibility of such representations may offer advantages in high-dimensional settings where classical grid-based methods become impractical.

cs.LG↗

arXiv2025

Fluid-kinetic multiscale solver for wall-bounded turbulence

We present a two-level (fluid-kinetic) coupling procedure for the simulation of wall-bounded flows at Reynolds numbers up to thousands. The method combines a kinetic Direct Simulation Monte Carlo (DSMC) treatment of the near-wall layer, with a high-order Lattice-Boltzmann (HOLB) scheme as a fluid solver in the bulk flow. Given the kinetic nature of HOLB, this coupling is expected to provide a physically accurate treatment of the near-wall instabilities which trigger the transition to turbulence above a critical threshold around $Re_c \sim 750$. The coupled DSMC-HOLB solver is validated by simulating plane Poiseuille and Couette flows far from equilibrium, i.e at finite Knudsen number regimes. Based on this validation, we provide the first preliminary evidence that the combination of HOLB and DSMC permits to observe the regeneration cycles of coherent structures which arise above a critical value of the Reynolds number. This task would be hardly attainable by either of the two solvers separately; while DSMC can capture strong near-wall non-equilibrium effects, it lacks the compute power to deal with both near-wall and bulk flow at the same time. We look to HOLB to make it computationally feasible to perform such a simulation. The present two-level coupling procedure may pave the way to a new generation of fluid-kinetic simulations of wall-bounded turbulent flows, thus helping to gain deeper insights into the role of wall micro-corrugations in triggering the dynamic instabilities that drive the transition to turbulent regimes.

physics.flu-dyn↗

arXiv2025

Randomness and signal propagation in physics-informed neural networks (PINNs): A neural PDE perspective

Physics-informed neural networks (PINNs) often exhibit weight matrices that appear statistically random after training, yet their implications for signal propagation and stability remain unsatisfactorily understood, let alone the interpretability. In this work, we analyze the spectral and statistical properties of trained PINN weights using viscous and inviscid variants of the one-dimensional Burgers' equation, and show that the learned weights reside in a high-entropy regime consistent with predictions from random matrix theory. To investigate the dynamical consequences of such weight structures, we study the evolution of signal features inside a network through the lens of neural partial differential equations (neural PDEs). We show that random and structured weight matrices can be associated with specific discretizations of neural PDEs, and that the numerical stability of these discretizations governs the stability of signal propagation through the network. In particular, explicit unstable schemes lead to degraded signal evolution, whereas stable implicit and higher-order schemes yield well-behaved dynamics for the same underlying neural PDE. Our results offer an explicit example of how numerical stability and network architecture shape signal propagation in deep networks, in relation to random matrix and neural PDE descriptions in PINNs.

cs.LG↗

arXiv2025

A kinetic-based regularization method for data science applications

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce corrections that impose constraints on the lower-order moments of the data distribution. This minimizes the discrepancy between the discrete and continuum representations of the data, in turn allowing to access more favorable energy landscapes, thus improving the accuracy of the interpolator. Our approach improves performance in both interpolation and regression tasks, even in high-dimensional spaces. Unlike traditional methods, it does not require empirical parameter tuning, making it particularly effective for handling noisy data. We also show that thanks to its local nature, the method offers computational and memory efficiency advantages over Radial Basis Function interpolators, especially for large datasets.

cs.LG↗

arXiv2025

A simplified digital twin of a pressure swing adsorption plant for air separation

The pressure swing adsorption (PSA) process is one of the widely utilized techniques for air separation. Operating on the Skarstrom cycle, the porous adsorbent columns of a PSA system alternate between adsorption and desorption phases to selectively enrich the desired component in a gas mixture. The current work presents a robust and generalizable digital twin CFD model of a PSA system that can significantly help in design and device characterization. Using an axisymmetric representation, the digital twin accurately mimics all the key components of an air separation plant, including the air reservoir, adsorbent columns, product buffer tank, pressure regulator, solenoidal valves, and mesh filters. The model simulates the flow and adsorption processes in the system by solving the conservation equations for mass, momentum, energy, and species, along with the equation for adsorption kinetics. The cyclic operation of the PSA plants, typically controlled by solenoid valves, is emulated by dynamically modifying the boundary conditions of different subdomains. Such an integrated approach is shown here to closely replicate the performance of an in-house PSA pilot setup producing oxygen in terms of purity and pressure transience. Also, both the numerical and the experimental results yield an optimum performance for the same process parameters, such as pressurization time (26 s), purge time (2 s), and equalization time (4 s). The proposed numerical model is versatile and can be adapted to various industrial applications of PSA technology, such as hydrogen purification and carbon capture. Thus, it offers a cost-effective tool for designing and optimizing PSA systems.

physics.flu-dyn↗

arXiv2022

Flow force calculation in Lattice Boltzmann Method

We revisit force evaluation methodologies on rigid solid particles suspended in a viscous fluid and simulated via lattice Boltzmann method (LBM). We point out the non-commutativity of streaming and collision operators in the force evaluation procedure and provide a theoretical explanation for this observation. Based on this analysis, we propose a discrete force calculation scheme with enhanced accuracy. The proposed scheme is essentially a lattice version of the Reynolds Transport Theorem (RTT) in the context of the lattice Boltzmann formulation. Besides maintaining satisfactory levels of reliability and accuracy, the method also handles force evaluation on complex geometries in a simple and transparent way. We run simulations for NACA0012 airfoil for a range of Reynolds numbers ranging from 100 to 0.5x10^6 and show that the current approach significantly reduces the grid size requirement for accurate force evaluation.

physics.flu-dyn↗

arXiv2022

LES/DNS of flow past T106 LPT cascade using a higher-order LB model

The main objective of the present work is to assess higher-order Entropic Lattice Boltzmann Method (ELBM) for separated and transitional flows without the use of any explicit turbulence model. For this, we chose to simulate two cases of T106 Low-Pressure Turbine (LPT) cascade -- T106A and T106C -- representing incompressible and compressible flow regimes respectively. These results are obtained using our company's in-house higher-order ELBM transonic solver. We have carried out two sets of simulations for both the test cases. One with a clean inlet and the other with an inlet disturbance given by white Gaussian noise superimposed on the inlet velocity. For the clean inlet case, the flow remains laminar on the entire blade surface for both the test cases. It undergoes transition on the suction side for the inlet disturbance case. The pressure coefficient for the T106A and the isentropic Mach number on the blade surface for the T106C matches well with the experimental results. Also, the qualitative comparison of flow features in terms of the Q-criterion is in good agreement with the earlier computational results reported in literature.

physics.flu-dyn↗

arXiv2022

Essentially entropic lattice Boltzmann model: Theory and simulations

We present a detailed description of the essentially entropic lattice Boltzmann model. The entropic lattice Boltzmann model guarantees unconditional numerical stability by iteratively solving the nonlinear entropy evolution equation. In this paper we explain the construction of closed-form analytic solutions to this equation. We demonstrate that near equilibrium this exact solution reduces to the standard lattice Boltzmann model. We consider a few test cases to show that the exact solution does not exhibit any significant deviation from the iterative solution. We also extend the analytical solution for the ES-BGK model to remove the limitation on the Prandtl number for heat transfer problems. The simplicity of the exact solution removes the computational overhead and algorithmic complexity associated with the entropic lattice Boltzmann models.

cond-mat.stat-mech↗

arXiv2022

Two-fluid kinetic theory for dilute polymer solutions

We provide a Boltzmann-type kinetic description for dilute polymer solutions based on two-fluid theory. This Boltzmann-type description uses a quasi-equilibrium based relaxation mechanism to model collisions between a polymer dumbbell and a solvent molecule. The model reproduces the desired macroscopic equations for the polymer-solvent mixture. The proposed kinetic scheme leads to a numerical algorithm which is along the lines of the lattice Boltzmann method. Finally, the algorithm is applied to describe the evolution of a perturbed Kolmogorov flow profile, whereby we recover the major elastic effect exhibited by a polymer solution, specifically, the suppression of the original inertial instability.

physics.comp-ph↗

arXiv2022

Reduced kinetic model of polyatomic gases

Kinetic models of polyatomic gas typically account for the internal degrees of freedom at the level of the two-particle distribution function. However, close to the hydrodynamic limit, the internal (rotational) degrees of freedom tend to be well represented just by rotational kinetic energy density. We account for the rotational energy by augmenting the Ellipsoidal-statistical BGK (ES-BGK) model, an extension of the Bhatnagar-Gross- Krook (BGK) model, at the level of the single-particle distribution function with an advection-diffusion-relaxation equation for the rotational energy. This reduced model respects the H theorem and recovers the compressible hydrodynamics for polyatomic gases as its macroscopic limit. As required for a polyatomic gas model, this extension of the ES-BGK model has not only correct specific heat ratio but also allows for three independent tunable transport coefficients: thermal conductivity, shear viscosity, and bulk viscosity. We illustrate the effectiveness of the model via a lattice Boltzmann method implementation.

physics.flu-dyn↗

arXiv2020

Estimating Hidden Asymptomatics, Herd Immunity Threshold and Lockdown Effects using a COVID-19 Specific Model

A quantitative COVID-19 model that incorporates hidden asymptomatic patients is developed, and an analytic solution in parametric form is given. The model incorporates the impact of lockdown and resulting spatial migration of population due to announcement of lockdown. A method is presented for estimating the model parameters from real-world data. It is shown that increase of infections slows down and herd immunity is achieved when symptomatic patients are 4-6\% of the population for the European countries we studied, when the total infected fraction is between 50-56 \%. Finally, a method for estimating the number of asymptomatic patients, who have been the key hidden link in the spread of the infections, is presented.

q-bio.PE↗

arXiv2019

Fokker-Planck model for binary mixtures

In dilute gas kinetic theory, model collision dynamics such as Bhatnagar-Gross-Krook (BGK) model is often used to get a better insight and numerical modelling. BGK model and its variants assume that highly nonlinear collision term can be replaced by a simple relaxation dynamics towards Maxwell-Boltzmann distribution. Lebowitz et al., proposed an alternative framework for the collision model, known as Fokker-Planck model, where the relaxation of an arbitrary distribution towards Maxwell-Boltzmann distribution is modelled as a drift-diffusion process in velocity space. In the present manuscript, we extend the single component Fokker-Planck model to a binary gas mixture model over a large range of Schmidt numbers. We prove that these mixture models satisfy the necessary conservation laws and the H-theorem.

cond-mat.stat-mech↗

arXiv2019

Lattice Boltzmann model for weakly compressible flows

We present an energy conserving lattice Boltzmann model based on a crystallographic lattice for simulation of weakly compressible flows. The theoretical requirements and the methodology to construct such a model are discussed. We demonstrate that the model recovers the isentropic sound speed in addition to the effects of viscous heating and heat flux dynamics. Several test cases for acoustics, thermal and thermoacoustic flows are simulated to show the accuracy of the proposed model.

physics.comp-ph↗

arXiv2017

Isotropic finite-difference discretization of stochastic conservation laws preserving detailed balance

The dynamics of thermally fluctuating conserved order parameters are described by stochastic conservation laws. Thermal equilibrium in such systems requires the dissipative and stochastic components of the flux to be related by detailed balance. Preserving this relation in spatial and temporal discretization is necessary to obtain solutions that have fidelity to the continuum. Here, we propose a finite-difference discretization that preserves detailed balance on the lattice, has spatial error that is isotropic to leading order in lattice spacing, and can be integrated accurately in time using a delayed difference method. We benchmark the method for model B dynamics with a $ϕ^{4}$ Landau free energy and obtain excellent agreement with analytical results.

cond-mat.stat-mech↗