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

In this paper we present a numerical solution for the mathematical modeling of the hot-pressing process applied to medium density fiberboard. The model is based in the work of Humphrey[82], Humphrey and Bolton[89] and Carvalho and Costa[98], 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.Comment: LaTeX, 11 figures. Added references. Fixed some errors. To appear in International Journal of Mathematics and Mathematical Sciences, http://jam.hindawi.co

Modelización numérica de un motor de combustión interna monocilíndrico encendido por chispa

El objetivo de este trabajo fue el desarrollo de un código computacional para la resolución de problemas de dinámica de gases en su escurrimiento a través de ductos y toberas y su posterior inserción dentro de un código que simule el ciclo de potencia y el de bombeo en un motor de combustión interna encendido por chispa. Es sabido que los motores de combustión interna son altamente influenciados por el diseño de los múltiples de admisión y escape. Factores como el ruido, la emisión y el rendimiento volumétrico son algunos de los principales temas de actualidad en el área de motores térmicos. Es por esto que en pos de poder modelar un motor y sus partes pensamos que será muy provechoso contar con un desarrollo previo en el flujo en tubos de sección arbitraria, siendo los ductos y las toberas sólo una aplicación particular del código generado. Se utilizó una discretización espacial unidimensional en elementos _nitos con una discretización temporal según un esquema de Lax-Wendro de dos pasos. La física del problema es gobernada por las ecuaciones de Euler, flujo invíscido, con el agregado de términos fuentes para incluir los efectos de la fricción en las paredes del tubo, la variabilidad de la sección de paso del fluido y la transferencia de calor a través de las paredes del ducto. Las primeras secciones introducen acerca de la dinámica de gases en sus aspectos teóricos básicos incluyendo el análisis de discontinuidades tipo ondas de choque. Posteriormente se analizan aspectos numéricos como la formulación empleada, el tratamiento de las condiciones de contorno y las técnicas de resolución numérica del sistema resultante. A continuación se presentan una gran variedad de resultados y su comparación con sus contrapartes analíticas. Finalmente se presentan algunos aspectos computacionales acerca del modelo completo de simulación de un motor de combustión interna encendido por chispa y las curvas características obtenidas para un caso test.Peer Reviewe

Modelización numérica de un motor de combustión interna monocilíndrico encendido por chispa

El objetivo de este trabajo fue el desarrollo de un código computacional para la resolución de problemas de dinámica de gases en su escurrimiento a través de ductos y toberas y su posterior inserción dentro de un código que simule el ciclo de potencia y el de bombeo en un motor de combustión interna encendido por chispa. Es sabido que los motores de combustión interna son altamente influenciados por el diseño de los múltiples de admisión y escape. Factores como el ruido, la emisión y el rendimiento volumétrico son algunos de los principales temas de actualidad en el área de motores térmicos. Es por esto que en pos de poder modelar un motor y sus partes pensamos que será muy provechoso contar con un desarrollo previo en el flujo en tubos de sección arbitraria, siendo los ductos y las toberas sólo una aplicación particular del código generado. Se utilizó una discretización espacial unidimensional en elementos _nitos con una discretización temporal según un esquema de Lax-Wendro de dos pasos. La física del problema es gobernada por las ecuaciones de Euler, flujo invíscido, con el agregado de términos fuentes para incluir los efectos de la fricción en las paredes del tubo, la variabilidad de la sección de paso del fluido y la transferencia de calor a través de las paredes del ducto. Las primeras secciones introducen acerca de la dinámica de gases en sus aspectos teóricos básicos incluyendo el análisis de discontinuidades tipo ondas de choque. Posteriormente se analizan aspectos numéricos como la formulación empleada, el tratamiento de las condiciones de contorno y las técnicas de resolución numérica del sistema resultante. A continuación se presentan una gran variedad de resultados y su comparación con sus contrapartes analíticas. Finalmente se presentan algunos aspectos computacionales acerca del modelo completo de simulación de un motor de combustión interna encendido por chispa y las curvas características obtenidas para un caso test.Peer Reviewe

CFD presenta compresible + incompresible un matrimonio por conveniencia

Este trabajo presenta por un lado una breve síntesis de algunas importantes contribuciones dirigida a la unificación de códigos computacionales para flujos tanto compresible como incompresible y por otro un eficiente precondicionador local para todo el rango de números de Mach y Reynolds implementado sobre un esquema iterativo tipo GMRES con una estrategia que evita el ensamblaje de matrices llamada matriz-free usando como discretización espacial una formulación en elementos finitos. El principal objetivo de esta investigación es lograr un tratamiento unificado de flujo de fluidos tanto compresible como incompresible, viscoso o inviscido apto para simulaciones a gran escala y capaz de ser utilizado sobre plataformas de hardware paralelas.This paper presents a brief review of important contributions towards the unification of compressible and incompressible flow solvers and an efficient local preconditioner for al1 Mach and Reynolds numbers implemented with a matrix-free GMRES iterative scheme and a finite element method. The main goal of this research is the unified treatment of fluid flow at al1 speeds for large scale simulation capable of being implemented over parallel platforms.Peer Reviewe

Two‐phase flow modelling in gas‐stirred liquid vessels with SUPG‐stabilized equal‐order interpolations

The modelling of liquid flow in gas‐stirred vessels is described. A simple two‐phase model accounts for the buoyancy effect of bubbles. Friction between liquid and gas is modelled with the hypothesis of independent bubbles. The resulting PDE system is discretized with an original version of the SUPG‐FEM technique which stabilizes both the convection term and equal‐order interpolations for velocity and pressure, which are known to be unstable for incompressible flows. The resulting steady state discrete system is solved via pseudotemporal explicit iteration with a local time step and a preconditioning to homogenize the temporal scales for liquid and gas

GMRES physics‐based preconditioner for all Reynolds and Mach numbers: numerical examples

This paper presents several numerical results using a vectorized version of a 3D finite element compressible and nearly incompressible Euler and Navier–Stokes code. The assumptions were set on laminar flows and Newtonian fluids. The goal of this research is to show the capabilities of the present code to treat a wide range of problems appearing in laminar fluid dynamics towards the unification from incompressible to compressible and from inviscid to viscous flow codes. Several authors with different approaches have tried to attain this target in CFD with relative success. At the beginning the methods based on operator splitting and perturbation were preferred, but lately, with the wide usage of time‐marching algorithms, the preconditioning mass matrix (PMM) has become very popular. With this kind of relaxation scheme it is possible to accelerate the rate of convergence to steady state solutions with the modification of the mass matrix under certain restrictions. The selection of the mass matrix is not an easy task, but we have certain freedom to define it in order to improve the condition number of the system. In this paper we have used a physics‐based preconditioner for the GMRES implicit solver developed previously by us and an SUPG formulation for the semidiscretization of the spatial operator. In sections 2 and 3 we present some theoretical aspects related to the physical problem and the mathematical model, showing the inviscid and viscous flow equations to be solved and the variational formulation involved in the finite element analysis. Section 4 deals with the numerical solution of non‐linear systems of equations, with some emphasis on the preconditioned matrix‐free GMRES solver. Section 5 shows how boundary conditions were treated for both Euler and Navier–Stokes problems. Section 6 contains some aspects about vectorization on the Cray C90. The performance reached by this implementation is close to 1 Gflop using multitasking. Section 7 presents several numerical examples for both models covering a wide range of interesting problems, such as inviscid low subsonic, transonic and supersonic regimes and viscous problems with interaction between boundary layers and shock waves in either attached or separated flows

Equal-order interpolations: a unified approach to stabilize the incompressible and advective effects

In this paper we present a new SUPG formulation for compressible and near incompressible Navier-Stokes equations [5]. It introduces an extension of the exact solution for one-dimensional systems to the multidimensional case, in a similar way to that arising in the scalar problem. It is important to note that this formulation satisfies both the one-dimensional advective-diffusive system limit case and the advection-dominated multidimensional system case presented by Mallet et al. Another interesting feature of this formulation is that it introduces naturally a stabilizing term for the incompressibility condition, in a similar way to that found by other authors [1–4]. However, in our formulation the stabilization is introduced to the whole system of equations, while other authors introduce a term to stabilize the incompressibility condition and another one for the advective term. In Section 1 we present Navier-Stokes equations for compressible flow and, then, we pass to detail several topics related to the numerical discretization of such advective-diffusive multidimensional systems of PDEs, in the Petrov-Galerkin context. The method is applicable and described for the general Re > 0 laminar flow, but the nature of the stabilizing effect of the artificial diffusion matrix introduced is discussed in depth for the simpler Stokes (Re = 0) flow. Several numerical results are shown in Section 5, taking the well-known test problem of the square-cavity and a variant of this, namely a multiply connected square-cavity, as a validation for this cod

A general algorithm for compressible and incompressible flow. Stability analysis and explicit time integration

Addresses two difficulties which arise when using a compressible code with equal order interpolation (non‐staggered grids in the finite‐difference nomenclature) to capture a steady‐state solution in the incompressible limit, i.e. at low Mach numbers. Explains that, first, numerical instabilities in the form of spurious oscillations in pressure pollute the solution and, second, the convergence to the steady state becomes extremely slow owing to bad conditioning of the different speeds of propagation. By using a stabilized method, allows the use of equal‐order interpolations in a consistent (weighted‐residual) formulation which stabilizes both the convection and the continuity terms at the same time. On the other hand, by using specially devised preconditioning, assures a rate of convergence independent of Mach number

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

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

Adaptive refinement criterion for elliptic problems discretized by FEM

In a recent paper we presented a data structure to be used with multigrid techniques on non‐homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance)