Finite element solution of an enclosed turbulent diffusion flame

A finite element formulation of enclosed turbulent diffusion flames is presented. A primitive variables approach is preferred in the analysis. A mixed interpolation is employed for the velocity and pressure. In the solution of the Navier-Stokes equations, a segregated formulation is adopted, where the pressure discretization equation is obtained directly from the discretized continuity equation, considering the velocity-pressure relationships in the discretized momentum equations. The state of turbulence is defined by a κ–? model. Near solid boundaries, a wall function approach is employed. The combustion rates are estimated using the eddy dissipation concept. The expensive direct treatment of the integrodifferential equations of radiation is avoided by employing the moment method, which allows the derivation of an approximate local field equation for the radiation intensity. The proposed finite element model is verified by investigating a technical turbulent diffusion flame of semi-industrial size, and comparing the results with experiments and finite difference predictions.     

Anionic groups on cellulosic fiber surfaces investigated by XPS, FTIR-ATR, and different sorption methods

Anionic groups (AGs) on different cellulosic fiber surfaces were investigated by methylene blue (MB) and polyelectrolyte (PE) sorption, X-ray photoelectron spectroscopy (XPS), and total attenuated reflectance infrared spectrometry (FTIR-ATR). The MB sorption isotherms fitted well the Langmuir equation that gave consistent estimations of sorption capacities. FTIR-ATR showed that MB molecules had extensive accessibility to the fiber wall pores. Estimation of surface AGs by PE sorption gave much higher values than a new method combining MB sorption and XPS measurements (MB-XPS). The surface AGs in different cellulosic fibers accounted for 1-3% of the total AG content as revealed by MB-XPS. It was suggested that PE molecules can penetrate the fiber wall and form loops or unattached segments at external fiber surfaces that disrupt the PE sorption stoichiometry. The competition of MB and PE for the anionic sites in papermaking was assessed and it was shown that MB ions have a much stronger affinity to AGs than PE molecules.     

Direct numerical simulation of the interaction of isotropic turbulence with a shock wave using shock-fitting

The interaction of three-dimensional isotropic turbulence with a plane shock at Mach numbers of $M=2.0$ and $M=3.0$ is investigated via direct numerical simulation. The numerical scheme is based on a characteristic-type formulation of the Navier–Stokes equations and uses fifth-order upwind schemes in space, a fourth order Runge Kutta scheme in time and a shock-fitting as inlet condition. The isotropic turbulence was generated in a separate computation based on a prescribed energy spectrum. This turbulent flow is considered as frozen, and is convected through the shock with a prescribed average shock speed. An FFT interpolation is used to obtain the upstream values at the instantaneous shock location. Turbulence enhancement is observed, and the evolution of velocity fluctuations as well as turbulence microscales are in good agreement with the behaviour observed using shock-capturing. To cite this article: J. Sesterhenn et al., C. R. Mecanique 333 (2005).     

Quasilinear first-order PDEs with hysteresis

This paper deals with the Cauchy problem for a quasilinear first-order equation that includes a possibly discontinuous hysteresis operatorF:

     

A C0-WEAK GALERKIN FINITE ELEMENT METHOD FOR THE TWO-DIMENSIONAL NAVIER-STOKES EQUATIONS IN STREAM-FUNCTION FORMULATION

We propose and analyze a $C^0$-weak Galerkin (WG) finite element method for the numerical solution of the Navier-Stokes equations governing 2D stationary incompressible flows. Using a stream-function formulation, the system of Navier-Stokes equations is reduced to a single fourth-order nonlinear partial differential equation and the incompressibility constraint is automatically satisfied. The proposed method uses continuous piecewise-polynomial approximations of degree $k+2$ for the stream-function $\psi$ and discontinuous piecewise-polynomial approximations of degree $k+1$ for the trace of $\nabla\psi$ on the interelement boundaries. The existence of a discrete solution is proved by means of a topological degree argument, while the uniqueness is obtained under a data smallness condition. An optimal error estimate is obtained in $L^2$-norm, $H^1$-norm and broken $H^2$-norm. Numerical tests are presented to demonstrate the theoretical results.     

Optimal error estimates for the pseudostress formulation of the Navier–Stokes equations

In this paper, we prove optimal a priori error estimates for the pseudostress-velocity mixed finite element formulation of the incompressible Navier–Stokes equations, thus improve the result of Cai et al. (SINUM 2010). This is achieved by applying Petrov–Galerkin type Brezzi–Rappaz–Raviart theory.     

Improved lower bounds for the Split Delivery Vehicle Routing Problem

This paper presents an algorithm to obtain lower bounds for the Split Delivery Vehicle Routing Problem. An extended formulation over a large set of variables is provided and valid inequalities are identified. The algorithm combined column and cut generation and improved the best known lower bounds for all instances from the literature. Some reasonably sized instances are solved to optimality for the first time.     

Innovative solution of a 2D elastic transmission problem¶

This article is concerned with a boundary-field equation approach to a class of boundary value problems exterior to a thin domain. A prototype of this kind of problems is the interaction problem with a thin elastic structure. We are interested in the asymptotic behavior of the solution when the thickness of the elastic structure approaches to zero. In particular, formal asymptotic expansions will be developed, and their rigorous justification will be considered. As will be seen, the construction of these formal expansions hinges on the solutions of a sequence of exterior Dirichlet problems, which can be treated by employing boundary element methods. On the other hand, the justification of the corresponding formal procedure requires an independence on the thickness of the thin domain for the constant in the Korn inequality. It is shown that in spite of the reduction of the dimensionality of the domain under consideration, this class of problems are, in general, not singular perturbation problems, because of appropriate interface conditions.     

Mean–semivariance portfolio selection under probability distortion

We formulate and study a mean–semivariance portfolio selection problem in continuous time when the probability is distorted by a nonlinear transformation. We give necessary and sufficient conditions for the feasibility and the existence of optimal strategies, respectively, and present the general form of optimal solutions when they exist. In sharp contrast with the previously established result that the infimum of the problem is not attainable when there is no probability distortion, we show that the infimum can be achieved with proper probability distortions. Finally, for a number of interesting cases we derive the optimal solutions in closed forms whenever they exist.     

Weak convergence of approximate solutions of random equations

Approximations of random operator equations are considered where the stochastic inputs and the underlying deterministic equation are approximated simultaneously. The main convergence result asserts that, under reasonable and verifiable assumptions, a sequence of weak solutions of approximate random equations converges weakly to a weak solution of the original equation. It is shown that this theorem extends and unifies results already known. We apply our theory to approximations of random differential equations involving stochastic processes with discontinuous paths and to projection methods for nonlinear random Hammerstein integral equations in spaces of integrable functions.