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The purpose of this paper is to develop a simple and efficient conservative semi-Lagrangian scheme (SL) for solving advection equation in fast fluid dynamics (FFD), so FFD can provide fast indoor airflow simulations while preserving conservation for energy and species transport.

This study thus proposed a mass-fixing type conservative SL that redistributes global surplus/deficit on the advected field after performing the standard semi-Lagrangian advection. The redistribution weights were designed to preserve the properties of conservatives and monotonicity.

The effectiveness of the conservative SL was validated with several test cases, and the results show that the proposed scheme is indeed conservative with negligible impact on the accuracy of the standard solutions. The numerical tests show that the proposed scheme was indeed conservative with negligible impact on the accuracy of the flow prediction.

The FFD with conservative SL can effectively enforce the energy and species conservation for indoor airflow and predict airflow distributions with reasonable accuracy.

The purpose of this paper is to suggest a new approach to the numerical simulation of shallow‐water flows both in plane domains and on the sphere.

The approach involves the technique of splitting of the model operator by geometric coordinates and by physical processes. Specially chosen temporal and spatial approximations result in one‐dimensional finite difference schemes that conserve the mass and the total energy. Therefore, the mass and the total energy of the whole two‐dimensional split scheme are kept constant too.

Explicit expressions for the schemes of arbitrary approximation orders in space are given. The schemes are shown to be mass‐ and energy‐conserving, and hence absolutely stable because the square root of the total energy is the norm of the solution. The schemes of the first four approximation orders are then tested by simulating nonlinear solitary waves generated by a model topography. In the analysis, the primary attention is given to the study of the time‐space structure of the numerical solutions.

The approach can be used for the numerical simulation of shallow‐water flows in domains of both Cartesian and spherical geometries, providing the solution adequate from the physical and mathematical standpoints in the sense of keeping its mass and total energy constant even when fully discrete shallow‐water models are applied.

The NIRVANA project is concerned with the development of a nonoscillatory, integrally reconstructed, volume‐averaged numerical advection scheme. The conservative, flux‐based finite‐volume algorithm is built on an explicit, single‐step, forward‐in‐time update of the cell‐average variable, without restrictions on the size of the time‐step. There are similarities with semi‐Lagrangian schemes; a major difference is the introduction of a discrete integral variable, guaranteeing conservation. The crucial step is the interpolation of this variable, which is used in the calculation of the fluxes; the (analytic) derivative of the interpolant then gives sub‐cell behaviour of the advected variable. In this paper, basic principles are described, using the simplest possible conditions: pure one‐dimensional advection at constant velocity on a uniform grid. Piecewise Nth‐degree polynomial interpolation of the discrete integral variable leads to an Nth‐order advection scheme, in both space and time. Nonoscillatory results correspond to convexity preservation in the integrated variable, leading naturally to a large‐Δt generalisation of the universal limited. More restrictive TVD constraints are also extended to large Δt. Automatic compressive enhancement of step‐like profiles can be achieved without exciting “stair‐casing”. One‐dimensional simulations are shown for a number of different interpolations. In particular, convexity‐limited cubic‐spline and higher‐order polynomial schemes give very sharp, nonoscillatory results at any Courant number, without clipping of extrema. Some practical generalisations are briefly discussed.

This paper aims to investigate post-buckling responses of shell-like structures using an implicit conservative-decaying time integration dynamic scheme.

In this work, the authors have proposed the use of a four-node quadrilateral flat shell finite element with drilling rotational degree of freedom within the framework of an updated Lagrangian formulation mutually with an implicit conservative-dissipative time integration dynamic scheme.

Several numerical simulations were considered to evaluate the accuracy, robustness, stability and the capacity of the considered time integration scheme to dissipate numerical noise in the presence of high frequencies. The obtained results illustrate a very satisfying performance of the implicit conservative-dissipative direct time integration scheme conjointly with the quadrilateral flat shell finite element with drilling rotation.

The authors have investigated the potential of the implicit dynamic scheme to deal with unstable branches after limit points in the non-linear post-buckling response of shell structures with no need for structural damping. The capability of the studied algorithm to study buckling and post-buckling behaviour of thin shell structures is illustrated through several numerical examples.

While still arguing whether a quasi‐linear equation has a “stability” problem in integration, comparative analyses are made by numerical experimentations using conservation with smoothing and non‐conservation schemes as well as a time‐moving treatment scheme proposed by the first author respectively. The results show that the solution seeking method of the quasi‐linear model should not be considered as a “stability” problem. The traditional well‐posed computational model needs to be improved. The Lorenz’s “butterfly effect” should be in nature a Richardson’s explosive increase in time evolution of moving fluid.

The simulation of magnetic fields with geometric discretization schemes using magnetic vector potentials involves the solution of very large discrete consistently singular curl‐curl systems of equations. Geometric and algebraic multigrid schemes for their solution require intergrid transfer operators of restriction and prolongation that achieve the discrete conservation of integral quantities serving as state‐variables of geometric discretization methods. For non‐conservative restriction operations, a consistency error correction operator related to an algebraic filtering is proposed. Numerical results show the effects of the consistency correction for a non‐nested geometric multigrid method.

A finite difference scheme for convection term discretization, called BSOU (stands for Bounded Second Order Upwind), is developed and its performance is assessed against exact or benchmark solutions in linear and non‐linear cases. It employs a flux blending technique between first order upwind and second order upwind schemes only in those regions of the flow field where spurious oscillations are likely to occur. The blending factors are calculated with the aid of the convection boundedness criterion. In all cases the scheme performed very well, minimizing the numerical diffusion errors. The scheme is transportive, conservative, bounded, stable and accurate enough so as to be suitable for inclusion into a general purpose solution algorithm.

In the original effective heat capacity method the latent heat effect is approximated by a large effective heat capacity over a small temperature range. This method is simple in concept and easy to implement. However, it is so sensitive to the choice of the phase change temperature interval and the chosen time integration scheme that non‐convergence always occurs when it is implemented with implicit time integration schemes. Presents the cause and cure of non‐convergence in effective heat capacity methods and discusses sample results.

Based on the concept of blown‐ups of evolution, introduced by OuYang in 1995, for nonlinear models, the logistic model and its modification of population evolutions are analyzed analytically and numerically. Presents results that imply: (1) There does not exist successive whole evolution of time in both the logistic model and its modifications. (2) The increase or decrease of the population size, caused by unsuccessive evolution, is limited. (3) The discontinuity characteristic realizes the philosophy that “things will develop in the opposite direction when they have reached extremes”. (4) The exponential increase of the population size is a special case, where it is shown that the modified logistic model agrees more with the reality than the original model. At the end, it points out that it is necessary to reconsider the method of reducing the original model into an algebraic equation by changing Δt to a non‐dimensional nonvariable by using difference scheme.

A finite volume, semi‐implicit scheme, is proposed and discussed, which solves the two‐dimensional Euler equations for the hypersonic flow of a mixture of chemically reactive specie. The present scheme can be applied on a general, unstructured grid. The first order version guarantees non negativity of the densities and of the vibrational energies for arbitrarily large time steps. The semi‐implicit time discretization of advective terms and the fully implicit discretization of the highly nonlinear terms yield a simple and efficient computer algorithm. Numerical tests show that shocks are well captured and the correct profiles for the chemical specie are reproduced at low computational cost.