定时间步长变坐标步长差分求解单相Stefan问题

对单相Stefan问题提出了一种定时间步长、变坐标步长的差分求解方法.在固定时间步长内,以计算得到的移动界面位置作为网格节点的坐标,前后界面位置之差为空间步长,逐步地自动形成网格的划分,计算这些节点处的温度,从而获得下一时刻的移动界面的位置.

Analysis and modeling of alumina dissolution based on heat and mass transfer

A comprehensive heat and mass transfer model of dissolution process of non-agglomerated and agglomerated alumina particles was established in an aluminum reduction cell. An appropriate finite difference method was used to calculate the size dissolution rate, dissolution time and mass of alumina dissolved employing commercial software and custom algorithm based on the shrinking sphere assumption. The effects of some convection and thermal condition parameters on the dissolution process were studied. The calculated results show that the decrease of alumina content or the increase of alumina diffusion coefficient is beneficial for the increase of size dissolution rate and the decrease of dissolution time of non-agglomerated particles. The increase of bath superheat or alumina preheating temperature results in the increase of size dissolution rate and the decrease of dissolution time of agglomerated particles. The calculated dissolution curve of alumina（mass fraction of alumina dissolved） for a 300 k A aluminum reduction cell is in well accordance with the experimental results. The analysis shows that the dissolution process of alumina can be divided into two distinct stages： the fast dissolution stage of non-agglomerated particles and the slow dissolution stage of agglomerated particles, with the dissolution time in the order of 10 and 100 s, respectively. The agglomerated particles were identified to be the most important factor limiting the dissolution process.

LARGE-EDDY SIMULATION OF TWO-PHASE REACTING FLOW IN MODEL COMBUSTOR

The gas-droplet two-phase reacting flow in a model combustor with the V-gutter flame holder is studied by an Eulerian-Lagrangian large-eddy simulation (LES) approach. The k-equation subgrid-scale model is used to simulate the subgrid eddy viscosity, and the eddy-break-up (EBU) combustion subgrid-scale model is used to determine the chemical reaction rate. A two-step turbulent combustion subgrid-scale model is employed for calculating carbon monoxide CO concentration, and the NO subgrid-scale pollutant formation model for the evaluation of the rate of NO formation. The heat flux model is applied to the prediction of radiant heat transfer. The gas phase is solved with the SIMPLE algorithm and a hybrid scheme in the staggered grid system. The liquid phase equations are solved in a Lagrangian frame in reference of the particle-source-in-cell (PSIC) algorithm. From simulation results, the exchange of mass, moment and energy between gas and particle fields for the reacting flow in the afterburner with a V-gutter flame holder can be obtained. By the comparison of experimental and simulation results, profile temperature and pollutant of the outlet are quite in agreement with experimental data. Results show that the LES approach for predicting the two-phase instantaneous reacting flow and pollutant emissions in the afterburner is feasible.

Use of Spreadsheets as an Introductory Tool for Solving Fluid-Structure Interaction Problem

A simple and intuitive manner for solving fluid-structure interaction problem has been developed using Microsoft Excel spreadsheets. By eliminating the need of previous knowledge of any programming language, the method appears as an interesting introduction to numerical solutions of partial differential equations, due to the direct and didactic way that it is developed. Proposed procedure enables the analysis of tridimensional geometries using the finite difference method and can be extended to other differential equations or boundary conditions. The author＇s objective in this paper is to develop a simple and reliable preliminary method for solving acoustic fluid-structure interaction problems with application to dam-reservoir interaction phenomena and also contribute in the educational growth for undergraduate students that are beginning research in such matter.

A second order finite difference-spectral method for space fractional diffusion equations

A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis.

An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.