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The present study aims to develop a vortex method capable for solving the complex vortical flows past the moving/deforming bodies.

To achieve such a goal, some innovative work is conducted on the basis of vortex-in-cell (VIC) method that uses the improved semi-Lagrangian scheme. The penalization technique is incorporated with the VIC, which makes the complex boundaries of moving/deforming bodies readily treated. Iterative algorithm is further proposed for the penalization and used to solve the Poisson equation, which enhances the vorticity solution accuracy at the body boundary.

The developed method is used to simulate some distinct flows of different boundaries and features: the impulsively started circular cylinder flow represents the one-way coupling; the falling circular cylinder flow and ellipse leaf flow both represent the two-way coupling of moving boundary; the fish-like body flow represents the two-way fluid-structure interaction of deforming boundary. The vortical physics of the above flows are well revealed, and the developed method is proven capable in dealing with the complex fluid-structure interaction problems.

The penalization technique is incorporated with the semi-Lagrangian VIC method, which makes the complex boundaries of moving/deforming bodies readily treated. An iterative algorithm is further proposed for the penalization and used to solve the Poisson equation, which enhances the vorticity solution accuracy at the body boundary. The complex vortical physics of the moving/deforming body flows are well revealed, and the propulsive mechanism of fish-like swimmer is well illustrated with the present method.

A calculation procedure is proposed for heat and fluid flows in geometries with a time‐dependent boundary. The procedure incorporates a moving mesh arrangement with multi‐block iteration and has been developed to assist future simulations of heat and mass transfer with phase change. The solver for the basic equations is the SIMPLE algorithm with a non‐staggered grid arrangement. The space conservation law is invoked and applied for the explicit tracking of a moving boundary with a moving mesh. For mapping complex geometries a multi‐block iteration strategy is employed. A cubic spline interpolation allows the “uniqueness of zonal boundary” requirement to be met. An interpolation method is also developed for variables near the zone boundaries.The calculation procedure using multi‐block iteration and a moving mesh is applied to three benchmark‐testing problems. The numerical results are in very good general agreement with available experimental data.

The purpose of this paper is to investigate two-dimensional viscous incompressible magnetohydrodynamic boundary layer flow and heat transfer of an electrically conducting fluid over a continuous moving flat surface considering the viscous dissipation and Joule heating.

Suitable similarity variables are introduced to reduce the governing nonlinear boundary layer partial differential equations to ordinary differential equations. A numerical solution of the resulting two-point boundary value problem is carried out by using the finite element method with the help of Gauss elimination technique.

A comparison of obtained results is made with the previous work under the limiting cases. Behavior of flow and thermal fields against various governing parameters like mass transfer parameter, moving flat surface parameter, magnetic parameter, Prandtl number and Eckert number are analyzed and demonstrated graphically. Moreover, shear stress and heat flux at the moving surface for various values of the physical parameters are presented numerically in tabular form and discussed in detail.

The work is relatively original, as very little work has been reported on magnetohydrodynamic flow and heat transfer over a continuous moving flat surface. Viscous dissipation and Joule heating are neglected in most of the previous studies. The numerical method applied to solve governing equations is finite element method which is new and efficient.

Boundary setting is identified as an important and highly useful factor, both in management practice and in dealing with phenomena in management research. It has significant implications for how circumstances and phenomena will be analysed and interpreted. Change – moving or change in nature – is a key factor in all attempts to strategise and economise. The authors argue that boundary setting is critical in analysing and interpreting business problems, both in the practice of management and in business research. The nature and function of boundaries vary. It can be exemplified with two archetypes of organisation – the integrated hierarchy and the connected company. In the first, the basic principle for boundary setting is buffering to protect the company from external variations. In the second type, it is bridging – connecting the company with specific changing factors. One important consequence is that when analysing and handling boundaries, both location and permeability become the central aspects to consider.

The oxygen diffusion problem is usually formulated in two stages: first, the steady state and second, the moving boundary stage. In this paper, we will consider the solution of the second stage in which a new semi‐analytical method for solving such a problem was developed. The present method starts by assuming a polynomial representing the profile of oxygen concentration, and then by some mathematical manipulation a system of linear equations is obtained. Numerical solution for the system with a simple scheme relating the moving boundary and its velocity leads to the unknown functions in the assumed polynomial.

The purpose of this paper is to improve the accuracy and stability of the existing solutions to 1D Stefan problem with time-dependent Dirichlet boundary conditions. The accuracy improvement should come with respect to both temperature distribution and moving boundary location.

The variable space grid method based on mixed finite element/finite difference approach is applied on 1D Stefan problem with time-dependent Dirichlet boundary conditions describing melting process. The authors obtain the position of the moving boundary between two phases using finite differences, whereas finite element method is used to determine temperature distribution. In each time step, the positions of finite element nodes are updated according to the moving boundary, whereas the authors map the nodal temperatures with respect to the new mesh using interpolation techniques.

The authors found that computational results obtained by proposed approach exhibit good agreement with the exact solution. Moreover, the results for temperature distribution, moving boundary location and moving boundary speed are more accurate than those obtained by variable space grid method based on pure finite differences.

The authors’ approach clearly differs from the previous solutions in terms of methodology. While pure finite difference variable space grid method produces stable solution, the mixed finite element/finite difference variable space grid scheme is significantly more accurate, especially in case of high alpha. Slightly modified scheme has a potential to be applied to 2D and 3D Stefan problems.

The purpose of this paper is to describe the micro fluid flow analysis in a micro thruster of micro‐/nano‐ satellite propulsion system and to propose the algorithm for the fluid flow simulations with the open boundary based on moving boundary method.

The analysis is based on a finite volume moving boundary method. Underlying mathematical model is the system of Navier‐Stokes‐Fourier partial differential equation describing compressible gas model. Propellant under the study is pure nitrogen gas. First, the static geometry velocity vector field is calculated and the information of the velocity at the outflow boundary is obtained; then, with the moving boundary method the outlet boundary is evolved. Evolution of the boundary is stopped when the continuum model ceases to hold. The criteria of the continuum model failure are based on the local Knudsen number.

The validations of the flow with respect to the Knudsen number showed that the continuum model is valid in the nozzle interior part (from the pressure value to the nozzle throat). The exterior nozzle part (diverging side) showed immediate raising of the Knudsen number above the continuum threshold (0.01). For the overall accurate computations of thruster flow, the continuum model must be coupled with molecular model (i.e. Boltzmann BGK).

In this paper, the authors propose a method for the computation of an open boundary flow with the application of the moving boundary method.

We present in this paper a finite element analysis of Navier‐Stokes equations in a time‐varying domain. The method of weighted residuals is used together with the semi‐discretization approach to obtain the discrete equations. In this approach, where the physical domain is allowed to vary, care is taken to retain the space conservation law property. We describe in detail the transformation of equations between fixed and moving grids. The validity of this method has been tested against two problems which are amenable to analytic solutions. Time accurate results show favorable agreement with analytic solutions. Having verified the applicability of the Galerkin finite element code to problems involving moving grids, we consider the fluid flow in a vessel, where a portion of its boundary moves in time. Results are presented with emphasis on the depiction of vortical flow details.

Understanding the factors that contribute to the growth of sediment delta lobes in river systems has significant benefit towards protecting civil and social infrastructure from severe weather events. To develop this understanding, this paper aims to construct a three‐dimensional numerical model of a sediment delta depositing on to a two‐dimensional bedrock basement entering an ocean at a constant sea‐level.

The approach used adapts and applies techniques and schemes previously used in building numerical heat transfer models of melting systems. Particular emphasis is placed on modifying fixed grid enthalpy like schemes.

The resulting model provides important insight on the features that control the partition of sediment delta deposition between the land and ocean domains. The model also illustrates how tectonic subsidence may control the rate of delta growth.

This is the first numerical heat transfer inspired model of a three‐dimensional sediment delta deposit over both land and ocean domains. The problem has scientific merit in that it represents a melting‐like moving boundary problem with two distinct moving boundaries and a space/time dependent latent heat. Further, this work is a necessary first step towards building a comprehensive understanding of how to restore delta systems to protect civil and social infrastructure.

In engineering applications, gas-solid two-phase reaction flow with multi-moving boundaries is a common phenomenon. The launch process of multiple projectiles is a typical example. The flow of adjacent powder chambers is coupled by projectile’s motion. The purpose of this paper is to study this flow by numerical simulation.

A one-dimensional two-phase reaction flow model and MacCormack difference scheme are implemented in a computational code, and the code is used to simulate the launch process of a system of multiple projectiles. For different launching rates and loading conditions, the simulated results of the launch process of three projectiles are obtained and discussed.

At low launching rates, projectiles fired earlier in the series have little effect on the launch processes of projectiles fired later. However, at higher launching rates, the projectiles fired first have a great influence on the launch processes of projectiles fired later. As the launching rate increases, the maximum breech pressure for the later projectiles increases. Although the muzzle velocities increase initially, they reach a maximum at some launching rate, and then decrease rapidly. The muzzle velocities and maximum breech pressures of the three projectiles have an approximate linear relationship with the charge weight, propellant web size and chamber volume.

This paper presents a prediction tool to understand the physical phenomenon of the gas-solid two-phase reaction flow with multi-moving boundaries, and can be used as a research tool for future interior ballistics studies of launch system of multiple projectiles.