A parallel cell‐based DSMC method on unstructured adaptive meshes

A parallel DSMC method based on a cell‐based data structure is developed for the efficient simulation of rarefied gas flows on PC‐clusters. Parallel computation is made by decomposing the computational domain into several subdomains. Dynamic load balancing between processors is achieved based on the number of simulation particles and the number of cells allocated in each subdomain. Adjustment of cell size is also made through mesh adaptation for the improvement of solution accuracy and the efficient usage of meshes. Applications were made for a two‐dimensional supersonic leading‐edge flow, the axi‐symmetric Rothe's nozzle, and the open hollow cylinder flare flow for validation. It was found that the present method is an efficient tool for the simulation of rarefied gas flows on PC‐based parallel machines. Copyright © 2004 John Wiley & Sons, Ltd.     

A time‐accurate pseudo‐compressibility approach based on an unstructured hybrid finite volume technique applied to unsteady turbulent premixed flame propagation

A preconditioning approach based on the artificial compressibility formulation is extended to solve the governing equations for unsteady turbulent reactive flows with heat release, at low Mach numbers, on an unstructured hybrid grid context. Premixed reactants are considered and a flamelet approach for combustion modelling is adopted using a continuous quenched mean reaction rate. An overlapped cell‐vertex finite volume method is adopted as a discretisation scheme. Artificial dissipation terms for hybrid grids are explicitly added to ensure a stable, discretised set of equations. A second‐order, explicit, hybrid Runge–Kutta scheme is applied for the time marching in pseudo‐time. A time derivative of the dependent variable is added to recover the time accuracy of the preconditioned set of equations. This derivative is discretised by an implicit, second‐order scheme. The resulting scheme is applied to the calculation of an infinite planar (one‐dimensional) turbulent premixed flame propagating freely in reactants whose turbulence is supposed to be frozen, homogeneous and isotropic. The accuracy of the results obtained with the proposed method proves to be excellent when compared to the data available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.     

A virtual boundary method with improved computational efficiency using a multi‐grid method

The flow around spherical, solid objects is considered. The boundary conditions on the solid boundaries have been applied by replacing the boundary with a surface force distribution on the surface, such that the required boundary conditions are satisfied. The velocity on the boundary is determined by extrapolation from the flow field. The source terms are determined iteratively, as part of the solution. They are then averaged and are smoothed out to nearby computational grid points. A multi‐grid scheme has been used to enhance the computational efficiency of the solution of the force equations. The method has been evaluated for flow around both moving and stationary spherical objects at very low and intermediate Reynolds numbers. The results shows a second order accuracy of the method both at creeping flow and at Re=100. The multi‐grid scheme is shown to enhance the convergence rate up to a factor 10 as compared to single grid approach. Copyright © 2004 John Wiley & Sons, Ltd.     

High‐order accurate numerical solutions of incompressible flows with the artificial compressibility method

A high‐order accurate, finite‐difference method for the numerical solution of incompressible flows is presented. This method is based on the artificial compressibility formulation of the incompressible Navier–Stokes equations. Fourth‐ or sixth‐order accurate discretizations of the metric terms and the convective fluxes are obtained using compact, centred schemes. The viscous terms are also discretized using fourth‐order accurate, centred finite differences. Implicit time marching is performed for both steady‐state and time‐accurate numerical solutions. High‐order, spectral‐type, low‐pass, compact filters are used to regularize the numerical solution and remove spurious modes arising from unresolved scales, non‐linearities, and inaccuracies in the application of boundary conditions. The accuracy and efficiency of the proposed method is demonstrated for test problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

Least‐squares meshfree method for incompressible Navier–Stokes problems

A least‐squares meshfree method based on the first‐order velocity–pressure–vorticity formulation for two‐dimensional incompressible Navier–Stokes problem is presented. The convective term is linearized by successive substitution or Newton's method. The discretization of all governing equations is implemented by the least‐squares method. Equal‐order moving least‐squares approximation is employed with Gauss quadrature in the background cells. The boundary conditions are enforced by the penalty method. The matrix‐free element‐by‐element Jacobi preconditioned conjugate method is applied to solve the discretized linear systems. Cavity flow for steady Navier–Stokes problem and the flow over a square obstacle for time‐dependent Navier–Stokes problem are investigated for the presented least‐squares meshfree method. The effects of inaccurate integration on the accuracy of the solution are investigated. Copyright © 2004 John Wiley & Sons, Ltd.     

A subdomain boundary element method for high‐Reynolds laminar flow using stream function‐vorticity formulation

The paper presents a new formulation of the integral boundary element method (BEM) using subdomain technique. A continuous approximation of the function and the function derivative in the direction normal to the boundary element (further ‘normal flux’) is introduced for solving the general form of a parabolic diffusion‐convective equation. Double nodes for normal flux approximation are used. The gradient continuity is required at the interior subdomain corners where compatibility and equilibrium interface conditions are prescribed. The obtained system matrix with more equations than unknowns is solved using the fast iterative linear least squares based solver. The robustness and stability of the developed formulation is shown on the cases of a backward‐facing step flow and a square‐driven cavity flow up to the Reynolds number value 50 000. Copyright © 2004 John Wiley & Sons, Ltd.     

One step synthesis of 2-substituted 3-tri-(or di-)fluoromethyl-2-propenals in an ionic liquid

Investigation of one step synthesis of 2-substituted 3-tri-(or di-)fluoromethyl-2-propenals has been carried out using versatile aldehydes, tri- or di-fluoroacetaldehyde ethyl hemiacetal in the presence of diethylaminotrimethylsilane (DEATMS) in an ionic liquid, and it was demonstrated that this route enabled us to successfully construct 2-substituted 3-tri-(or di-)fluoromethyl-2-propenals with the high level selectivity of geometric isomers.     

Synthesis and association of poly(N,N‐dimethylacrylamide) copolymers with perfluorocarbon pendent groups connected through polyethylene‐glycol tethers

The synthesis is reported of copolymers of N,N‐dimethylacrylamide (DMA) and methacrylates containing 2,2′‐dihydroperfluorodecanoyl (RF) groups separated from the methacrylate by long polyethylene glycol (PEG) tether groups (between 1000 and 14,000 Da). At concentrations of between 1 and 8 wt % the copolymers with macromonomer contents of 1 mol % or less give gels in organic solvents such as dioxane, THF, or methanol, as well as in water. Given the low molecular weights, this indicates very efficient association of very low numbers of RF groups. Association and gel formation is enormously enhanced in the presence of longer PEG tethers. This is consistent with smaller poly(N,N,‐dimethylacrylamide) (PDMA) intermolecular excluded volume effects that are mediated by the longer PEG tethers and possibly by the incompatibility of PEG and PDMA that may lead to the formation of PEG microdomains. This increases the local concentrations of the RF groups in the PEO domains that are not diluted by the PDMA chains, as would be the case in the absence of PEG tethers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 360–373, 2004     

Sulfonated poly(aryl ether ketone)s containing naphthalene moieties obtained by direct copolymerization as novel polymers for proton exchange membranes

A series of sulfonated poly(aryl ether ketone)s (SPAEKs) were prepared by aromatic nucleophilic polycondensation of 2,6‐dihydroxynaphthalene with 5,5′‐carbonyl‐bis(2‐fluorobenzenesulfonate) and 4,4′‐difluorobenzophenone. The structure and degree of sulfonation (DS) of the SPAEKs were characterized using ¹H NMR spectroscopy. The experimentally observed DS values were close to the expected values derived from the starting material ratios. The thermal stabilities of the SPAEKs were characterized by thermogravimetric analysis, which showed that in acid and sodium salt forms they were thermally stable in air up to about 240 and 380 °C, respectively. Transparent membranes cast from the directly polymerized SPAEKs exhibited good mechanical properties in both dry and hydrated states. The dependence of water uptake and of membrane swelling on the DS at different temperatures was studied. SPAEK membranes with a DS from 0.72 to 1.60 maintained adequate mechanical properties after immersion in water at 80 °C for 24 h. The proton conductivity of SPAEK membranes with different degrees of sulfonation was measured as a function of temperature. The proton conductivity of the SPAEK films increased with increased DS, and the highest room temperature conductivity (4.2 × 10^?2 S/cm) was recorded for a SPAEK membrane with a DS of 1.60, which further increased to 1.1 × 10^?1 S/cm at 80 °C. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2866–2876, 2004