Norberto M. Nigro

A Petrov-Galerkin formulation for advection-reaction-diffusion problems

Abstract In this work we present a new method called (SU + C)PG to solve advection-reaction-diffusion scalar equations by the Finite Element Method (FEM). The SUPG (for Streamline Upwind Petrov-Galerkin ) method is currently one of the most popular methods for advection-diffusion problems due to its inherent consistency and efficiency in avoiding the spurious oscillations obtained from the plain Galerkin method when there are discontinuities in the solution. Following this ideas, Tezduyar and Park treated the more general advection-reaction-diffusion problem and they developed a stabilizing term for advection-reaction problems without significant diffusive boundary layers. In this work an SUPG extension for all situations is performed, covering the whole plane represented by the Peclet number and the dimensionless reaction number. The scheme is based on the extension of the super-convergence feature through the inclusion of an additional perturbation function and a corresponding proportionality constant. Both proportionality constants (that one corresponding to the standard perturbation function from SUPG, and the new one introduced here) are selected in order to verify the ‘super-convergence’ feature, i.e. exact nodal values are obtained for a restricted class of problems (uniform mesh, no source term, constant physical properties). It is also shown that the (SU + C)PG scheme verifies the Discrete Maximum Principle (DMP), that guarantees uniform convergence of the finite element solution. Moreover, it is shown that super-convergence is closely related to the DMP, motivating the interest in developing numerical schemes that extend the super-convergence feature to a broader class of problems.

A parallel finite element program on a Beowulf cluster

Some experiences on writing a parallel finite element code on a Beowulf cluster are shown. This cluster is made up of seven Pentium III processors connected by Fast Ethernet. The code was written in C++ making use of MPI as message passing library and parallel extensible toolkit for scientific computations. The code presented here is a general framework where specific applications may be written. In particular CFD applications regarding Laplace equations, Navier-Stokes and shallow water flows have been implemented. The parallel performance of this application code is assessed and several numerical results are presented.

A fast and accurate method to solve the incompressible Navier‐Stokes equations

Purpose – The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution of the incompressible Navier‐Stokes equations with very large time steps.Design/methodology/approach – The design of the paper is based on introducing the origin of this novel numerical method, originally inspired on the Particle Finite Element Method (PFEM), summarizing the previously published theory in its moving mesh version. Afterwards its extension to fixed mesh version is introduced, showing some details about the implementation.Findings – The authors have found that even though this method was originally designed to deal with heterogeneous or free‐surface flows, it can be competitive with Eulerian alternatives, even in their range of optimal application in terms of accuracy, with an interesting robustness allowing to use large time steps in a stable way.Originality/value – With this objective in mind, the authors have chosen a number of benchmark examples and have pr...

Phasewise numerical integration of finite element method applied to solidification processes

Abstract Phase change is a very complex physical phenomenon that governs a lot of industrial situations. Due to the inherent difficulties that arise in manufacturing activities they need a numerical treatment using models to predict the behavior of the different phases involved in the process. Historically, solidification problems were solved considering only the solution of an energy balance with isothermal phase change including conduction and or convection in the material. Nowadays computational fluid dynamics is becoming a well-suited numerical technique to investigate all kind of transport phenomena, especially when coupled fields are involved. This trend has addressed the research in solidification problems towards the solution of models combining incompressible Navier–Stokes equations coupled with heat and mass transfer including phase change. In this paper we present a phasewise discontinuous numerical integration method to solve thermal phase change problems in a fast and accurate way. Moreover, this methodology was extended to coupled fluid flow and energy balance equations with success and in a future work we will apply to binary alloy solidification with macrosegregation.

Visco-plastic constitutive models of steel at high temperature

Abstract Two constitutive elasto-visco-plastic models are adopted to simulate the behavior of plain carbon steel at high temperature, specifically at the austenitic range (950–1300°C), being particularly appropriate for the numerical simulation of casting and hot-working processes. The response in hardening, creep and non-uniform loading conditions is analyzed and compared with experimental data. An efficient numerical integration scheme is proposed and its accuracy is evaluated using iso-error maps. The consistent isothermal tangent matrix is computed and the final models are implemented into an FEM code. Several tests are performed to evaluate the accuracy and robustness of the integration scheme. Finally an application concerning the analysis of the thermal stresses produced at the early stage of a steel continuous casting process is shown.

Steady state incompressible flows using explicit schemes with an optimal local preconditioning

Abstract Solving large systems of equations from CFD problems by the explicit pseudo-temporal scheme requires a very low amount of memory and is highly parallelizable, but the CPU time largely depends on the conditioning of the system. For advective systems it is shown that the rate of convergence depends on a condition number defined as the ratio of the maximum and the minimum group velocities of the continuum system. If the objective is to reach the steady state, the temporal term can be modified in order to reduce this condition number. Another possibility consists in the addition of a local preconditioning mass matrix. In this paper an optimal preconditioning for incompressible flow is presented, also applicable to compressible ones with locally incompressible zones, like stagnation points, in contrast with the artificial compressibility method. The preconditioned system has a rate of convergence independent from Mach number. Moreover, the discrete solution is highly improved, eliminating spurious oscillations frequently encountered in incompressible flows.

Assessment of a zero‐dimensional model of tumble in four‐valve high performance engine

Purpose – The purpose of this paper is to assess a phenomenological zero‐dimensional model (0‐D model) in order to evaluate both the in‐cylinder tumble motion and turbulence in high‐performance engine, focusing on the capability and sensitivity of the model.Design/methodology/approach – The study was performed using a four‐valve pentroof engine, testing two different intake ports. The first one was a conventional port and the second one was design in such a way to promote tumble. CFD simulations for admission and compression strokes under different engine conditions were carried out. Then, the in‐cylinder entrance mass and mean velocities from CFD were imposed as boundary conditions in the 0‐D model.Findings – Marked discrepancies between 0‐D model and CFD results were found. As expected, for the original port, CFD results displayed a poor tumble generation during the admission period. It was followed by a fast degradation of the tumble momentum along the compression stroke due to it was not dominant over...

Hot-pressing process modeling for medium density fiberboard (MDF)

We present a numerical solution for the mathematical modeling of the hot- pressing process applied to medium density fiberboard. The model is based on the work of Humphrey (1982), Humphrey and Bolton (1989), and Carvalho and Costa (1998) with some modifications and extensions in order to take into account mainly the convective effects on the phase change term and also a conservative numerical treatment of the resulting system of partial differential equations.

Residence Time Distribution Determination of a Continuous Stirred Tank Reactor using Computational Fluid Dynamics and its Application on the Mathematical Modeling of Styrene Polymerization

Abstract The continuous operation of a stirred tank reactor for styrene polymerization was modeled. The proposed approach consists of an iterative procedure between two modules that considers the fluid-dynamics and kinetics respectively. The kinetic module considers a complex kinetic mechanism and is used to predict the time evolution of global variables, such as conversion and species concentrations, physicochemical properties and molecular structure characteristics of the final product. In order to obtain a 3D representation of the flow field, the simulation of the hydrodynamics of the reactor was carried out with the aid of a commercial computational fluid dynamics (CFD) software package. Because CFD is capable to predict the complete velocity distribution in a tank, it provided a good alternative to carry out residence time distribution (RTD) studies. It was found that the stimulus-response tracer method is reasonably accurate to obtain a complete RTD compared to the particle tracking method. The obtained RTD results showed a good agreement when validated with experimental data and literature information.From the estimates of the kinetic module and the RTD predictions, a statistical calculus allows the determination of the average properties at the reactor outlet. The convergence of the iterative procedure was tested and reasonable predictions were achieved for an industrial reactor.

In-cylinder flow control in a four-valve spark ignition engine: numerical and experimental steady rig tests

Computational fluid dynamic (CFD) simulations and experimental steady flow tests (flow discharge, swirl, and tumble) were carried out to study the in-cylinder flow in a commercial four-valve spark ignition engine. The present investigation was aimed at analysing and controlling the generation of macro-vortex structures (swirl and tumble) during the inlet process. A comparative study of the most commonly employed tumble benches along with in-house design was performed, the last showing some advantages with respect to the others. The outcomes from the simulations were in agreement with experimental results. Mainly, the tumble generation rate was in general proportional to the valve lift. However, tumble was reduced drastically at medium valve lift due to a change in the vortex pattern. A stagnation zone was observed between inlet valves. CFD calculations successfully captured this tumble-fall effect, which was related to characteristic changes in the vortex pattern downstream of the inlet valves at medium valve lift. This affects tumble production without affecting the mass flowrate efficiency. Finally, at high valve lifts the tumble production and the vortex pattern were recovered. The capability of the cylinder head to induce swirl, tumble, or combined swirl–tumble by modifying the valve timing or by introducing adjustable flow deflectors was evaluated using CFD. Several valve timing strategies were analysed: some of them produced significant swirl, but introduced high mass flowrate losses. On the other hand, adjustable flow deflectors were shown to be an interesting alternative to induce swirl–tumble at low load and to improve tumble at high load.