A short review of vapour droplet dispersion models used in CFD to study the airborne spread of COVID19.

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. [Abstract copyright: Copyright © 2022 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the Innovative Technologies in Mechanical Engineering-2021.

A fictitious domain/distributed Lagrange multiplier based fluid–structure interaction scheme with hierarchical B-Spline grids

We present a numerical scheme for fluid–structure interaction based on hierarchical B-Spline grids and fictitious domain/distributed Lagrange multipliers. The incompressible Navier–Stokes equations are solved over a Cartesian grid discretised with B-Splines. The fluid grid near the immersed solids is refined locally using hierarchical B-Splines. The immersed solid is modelled as geometrically-exact beam discretised with standard linear Lagrange shape functions. The kinematic constraint at the fluid–solid interface is enforced with distributed Lagrange multipliers. The unconditionally-stable and second-order accurate generalised- method is used for integration in time for both the fluid and solid domains. A fully-implicit and fully-coupled solution scheme is developed by using the Newton–Raphson method to solve the non-linear system of equations obtained with Galerkin weak formulation. First, the spatial and temporal convergence of the proposed scheme is assessed by studying steady and unsteady flow past a fixed cylinder. Then, the scheme is applied to several benchmark problems to demonstrate the efficiency and robustness of the proposed scheme. The results obtained with the present scheme are compared with the reference values

On the advantages of using the first-order generalised-alpha scheme for structural dynamic problems

The advantages of using the generalised-alpha scheme for first-order systems for computing the numerical solutions of second-order equations encountered in structural dynamics are presented. The governing equations are rewritten so that the second-order equations can be solved directly without having to convert them into state-space. The stability, accuracy, dissipation and dispersion characteristics of the scheme are discussed. It is proved through spectral analysis that the proposed scheme has improved dissipation properties when compared with the standard generalised-alpha scheme for second-order equations. It is also proved that the proposed scheme does not suffer from overshoot. Towards demonstrating the application to practical problems, proposed scheme is applied to the benchmark example of three degrees of freedom stiff-flexible spring-mass system, two-dimensional Howe truss model, and elastic pendulum problem discretised with non-linear truss finite elements

Subdivision based mixed methods for isogeometric analysis of linear and nonlinear nearly incompressible materials

This paper addresses the use of isogeometric analysis to solve solid mechanics problems involving nearly incompressible materials. The present work is focused on extension of two-field mixed variational formulations in both small and large strains to isogeometric analysis. Inf–sup stable displacement–pressure combinations for mixed formulations are developed based on the subdivision property of NURBS. Stability and convergence properties of the proposed displacement–pressure combinations are illustrated by computing numerical inf–sup constants and error norms. The performance of the proposed formulations is assessed by studying several benchmark examples involving nearly incompressible and incompressible elastic and elasto-plastic materials in both small and large strain regime

A stabilised immersed framework on hierarchical b-spline grids for fluid-flexible structure interaction with solid–solid contact

We present a robust and efficient stabilised immersed framework for fluid–structure interaction involving incompressible fluid flow and flexible structures undergoing large deformations and also involving solid–solid contact. The efficiency of the formulation stems from the use of second-order accurate sequential staggered solution scheme for resolving fluid–solid coupling. Mixed Galerkin formulation, along with SUPG/PSPG stabilisation, is employed to obtain the numerical solutions of the incompressible Navier–Stokes equations. The immersed formulation is based on hierarchical b-spline grids, with unsymmetric Nitsche method employed to impose boundary as well as interface conditions on the fluid domain, while ghost-penalty operators are applied to alleviate the numerical instabilities arising due to small cut cells. The solid is modelled using linear continuum elements with finite strain formulation to facilitate the modelling of large structural deformations, and the contact between solids is modelled using the normal frictionless node-to-segment contact elements with Lagrange multipliers. In order to deal with the issue of uncovering for cut-cell based numerical schemes, a simple mapping technique is also introduced. Spatial and temporal convergence studies of the proposed scheme are performed by studying a simple example of flow over a deformable beam in cross flow. The robustness and accuracy of the proposed scheme are demonstrated by studying the benchmark examples of an oscillating beam in two-dimensions and flutter of a flexible simplified bridge deck in three-dimensions. In order to demonstrate the applicability of the proposed framework to complex fluid–structure interaction problems, the proposed methodology is used to simulate the fluid–structure interaction of a check valve with flexible valve plate

A stabilised immersed boundary method on hierarchical b-spline grids

In this work, an immersed boundary finite element method is proposed which is based on a hierarchically refined cartesian b-spline grid and employs the non-symmetric and penalty-free version of Nitsche’s method to enforce the boundary conditions. The strategy allows for - and -refinement and employs a so-called ghost penalty term to stabilise the cut cells. An effective procedure based on hierarchical subdivision and sub-cell merging, which avoids excessive numbers of quadrature points, is used for the integration of the cut cells. A basic Laplace problem is used to demonstrate the effectiveness of the cut cell stabilisation and of the penalty-free Nitsche method as well as their impact on accuracy. The methodology is also applied to the incompressible Navier–Stokes equations, where the SUPG/PSPG stabilisation is employed. Simulations of the lid-driven cavity flow and the flow around a cylinder at low Reynolds number show the good performance of the methodology. Excessive ill-conditioning of the system matrix is robustly avoided without jeopardising the accuracy at the immersed boundaries or in the field

A stabilised immersed boundary method on hierarchical b-spline grids for fluid–rigid body interaction with solid–solid contact

An accurate, efficient and robust numerical scheme is presented for the simulation of the interaction between flexibly-supported rigid bodies and incompressible fluid flow with topology changes and solid–solid contact. The solution of the incompressible Navier–Stokes equations is approximated by employing a stabilised formulation on Cartesian grids discretised with hierarchical b-splines. The solid is modelled as a rigid body and represented by linear segments along its boundary. Kinematic conditions along the fluid–rigid body interface are enforced weakly using Nitsche’s method, while ghost penalty operators are employed to avoid excessive ill-conditioning of the system matrix arising from small cut cells. A staggered scheme is used for resolving the coupled fluid–rigid body interaction. The contact between moving or moving and fixed solid bodies is modelled with Lagrange multipliers. The excellent performance and wide range of applicability of the proposed scheme are demonstrated in a number of benchmark tests as well as industrially relevant model problems. The examples cover the galloping phenomena, particulate flow, hydraulic check valves and a model turbine

Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Extension to nearly incompressible implicit and explicit elastodynamics in finite strains

We present a novel unified finite element framework for performing computationally efficient large strain implicit and explicit elastodynamic simulations using triangular and tetrahedral meshes that can be generated using the existing mesh generators. For the development of a unified framework, we use Bézier triangular and tetrahedral elements that are directly amenable for explicit schemes using lumped mass matrices and employ a mixed displacement-pressure formulation for dealing with the numerical issues arising due to volumetric and shear locking. We demonstrate the accuracy of the proposed scheme by studying several challenging benchmark problems in finite strain elastostatics and nonlinear elastodynamics modelled with nearly incompressible hyperelastic and von Mises elastoplastic material models. We show that Bézier elements, in combination with the mixed formulation, help in developing a simple unified finite element formulation that is accurate, robust, and computationally very efficient for performing a wide variety of challenging nonlinear elastostatic and implicit and explicit elastodynamic simulations