Chennakesava Kadapa

The use of computational fluid dynamics (CFD) to simulate the spread of COVID19 and many other airborne diseases, especially in an indoor environment needs accurate understanding of dispersion models. Modelling the transport/dispersion of vapour droplets within the atmosphere is a complex problem, as it involves the motion of more than one phase, as well as the interphase interactions between the phases. This paper reviews the current canon of research on dispersion modelling of vapour droplets by looking at three specific aspects: (i) physical definition/specification of the initial droplet size distribution; (ii) physics of evaporation/condensation models and (iii) transport equations (with molecular/turbulent dispersion models) to describe the movement of the vapour droplets as they propagate through the air. This review found that the state of modelling implements a wide range of models which shows variances in results thus leading to a state where it is difficult to know which model is most accurate. The authors suggest that further studies in this direction should focus on developing a principle set of equations by benchmarking the previously developed models to establish model uncertainty of the previously developed models with reference to a fixed theoretical model and be compared under identical conditions. However, it must be noted that due to the complex nature of microdroplet evaporation and dispersion coupled with the unpredictable way droplet size distributions are produced, current experimental methodologies that are available to validate such simulations, such as particle image velocimetry, are still not robust enough to provide detailed data to verify minute aspects of the simulations.

This paper presents a simplified implementation of the arc-length method for computing the equilibrium paths of nonlinear structural mechanics problems using the finite element method. In the proposed technique, the predictor is computed by extrapolating the solutions from two previously converged load steps. The extrapolation is a linear combination of the previous solutions; therefore, it is simple and inexpensive. Additionally, the proposed extrapolated predictor also serves as a means for identifying the forward movement along the equilibrium path without the need for any sophisticated techniques commonly employed for explicit tracking.
The ability of the proposed technique to successfully compute complex equilibrium paths in static structural mechanics problems is demonstrated using seven numerical examples involving truss, beam-column and shell models. The computed numerical results are in excellent agreement with the reference solutions. The present approach does not require prohibitively small increments for its success.

In this paper, we present a mixed displacement-pressure finite element formulation that can successively model compressible as well as truly incompressible behaviour in growth-induced deformations significantly observed in soft materials. Inf-sup stable elements of various shapes based on quadratic Bezier elements are employed ´ for spatial discretisation. At first, the capability of the proposed framework to accurately model finite-strain growth-induced deformations is illustrated using several examples of plate models in which numerical results are directly compared with analytical solutions. The framework is also compared with the classical Q1/P0 finite element that has been used extensively for simulating the deformation behaviour of soft materials using the quasi-incompressibility assumption. The comparisons clearly demonstrate the superior capabilities of the proposed framework. Later, the effect of hyperelastic constitute models and compressibility on the growthinduced deformation is also studied using the example of a bilayered strip in three dimensions. Finally, the potential of the proposed finite element framework to simulate growth-induced deformations in complex threedimensional problems is illustrated using the models of flower petals, morphoelastic rods, and thin cylindrical tubes