arXiv subjects

Anil Lal S

Publications and source records attributed to Anil Lal S.

4 recordsLinked to original sources

arXiv2025

A Computational Approach for Multi-Body Potential-Flow Interaction Effects Using Matrix-Free FEM and Body-Conforming Grids

This paper presents a unified and computationally efficient framework for predicting incompressible, irrotational (potential) flow around multiple immersed bodies in two-dimensional domains, with particular emphasis on quantifying irrotational interaction effects in multi-body configurations. The methodology integrates three components: a fast body-conforming mesh-generation strategy, a matrix-free finite-element solution of the Laplace equation, and a systematic procedure for determining the stream-function values associated with each immersed solid. Body-fitted grids are generated by imposing boundary displacements on a Cartesian background mesh followed by Laplacian smoothing, yielding simple, robust, and accurate meshes for domains containing multiple immersed bodies. The potential-flow field is obtained by solving the Laplace equation using a matrix-free Conjugate Gradient method, wherein element-level operators are evaluated without assembling global stiffness matrices. Immersed bodies are treated as constant-\,$ψ$ streamlines, and their unknown stream-function values are determined through multi-point constraints that naturally capture inter-body flow connectivity. The results highlight the ability of the proposed approach to resolve subtle multi-body interaction phenomena with minimal case-setup effort and very low memory requirements, while providing a quantitative measure of potential-flow interference in complex immersed-body systems.

physics.flu-dyn↗

arXiv2023

Physics-informed Neural Networks approach to solve the Blasius function

Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to solve the Blasius function. This method eliminates the process of changing the non-linear differential equation to an initial value problem. Also, it tackles the convergence issue arising in the conventional series solution. It is seen that this method produces results that are at par with the numerical and conventional methods. The solution is extended to the negative axis to show that PINNs capture the singularity of the function at $η=-5.69$

cs.LG↗

arXiv2022

Accurate benchmark results of Blasius boundary layer problem using a leaping Taylors series that converges for all real values

Blasius boundary layer solution is a Maclaurin series expansion of the function $f(η)$, which has convergence problems when evaluating for higher values of $η$ due to a singularity present at $η\approx-5.69$. In this paper we are introducing an accurate solution to $f(η)$ using Taylor's series expansions with progressively shifted centers of expansion(Leaping centers). Each series is solved as an IVP with the three initial values computed from solution of the previous series, so the gap between the centers of two consecutive expansions is selected from within the convergence disc of the first series. The last series is formed such that it is convergent for a reasonable high $η$ value needed for implementing the boundary condition at infinity. The present methodology uses Newton-Raphson method to compute the value of the unknown initial condition viz. $f''(0)$ in an iterative manner. Benchmark accurate results of different parameters of flat plate boundary layer with no slip and slip boundary conditions have been reported in this paper.

math.GM↗

arXiv2021

Assessing the practicability of the condition used for dynamic equilibrium in Pasinetti theory of distribution

In this note an assessment of the condition $K_w/K=S_w/S$ is made to interpret its meaning to the Passineti's theory of distribution\cite{pasinetti1962rate}. This condition leads the theory to enforce the result $s_w\rightarrow0$ as $P_w\rightarrow 0$, which is the Pasinetti's description about behavior of the workers. We find that the Pasinetti's claim, of long run worker's propensity to save as not influencing the distribution of income between profits and the wage can not be generalized. This claim is found to be valid only when $W>>P_w$ or $P_w=0$ with $W\ne0$. In practice, the Pasinetti's condition imposes a restriction on the actual savings by one of the agents to a lower level compared to its full saving capacity. An implied relationship between the propensities to save by workers and capitalists shows that the Passineti's condition can be practiced only through a contract for a constant value of $R=s_w/s_c$, to be agreed upon between the workers and the capitalists. It is showed that the Passineti's condition can not be described as a dynamic equilibrium of economic growth. Implementation of this condition (a) may lead to accumulation of unsaved income, (b) reduces growth of capital, (c)is not practicable and (d) is not warranted. We have also presented simple mathematical steps for the derivation of the Pasinetti's final equation compared to those presented in \cite{pasinetti1962rate}

econ.GN↗