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• Shock capturing viscosities for the general fluid mechanics algorithm

  P. Nithiarasu, O. Zienkiewicz, B. Sai, K. Morgan, R. Codina, M. Vázquez

  Int. J. Numer. Meth. Fluids (1998). Vol. 28 (9), pp. 1325-1353

  
  

  Abstract

  The performance of different shock capturing viscosities has been examined using our general fluid mechanics algorithm. Four different schemes have been tested, both for viscous and inviscid compressible flow problems. Results show that the methods based on the second gradient of pressure give better performance in all situations. For instance, the method constructed from the nodal pressure values and consistent and lumped mass matrices is an excellent choice for inviscid problems. The method based on L2 projection is better than any other method in viscous flow computations. The residual based anisotropic method gives excellent performance in the supersonic range and gives better results in the hypersonic regime if a small amount of residual smoothing is used

  Abstract
  The performance of different shock capturing viscosities has been examined using our general fluid mechanics algorithm. Four different schemes have been tested, both for viscous [...]

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• A fractional-step method for the incompressible navier-stokes equations related to a predictor-multicorrector algorithm

  J. Blasco, R. Codina, A. Huerta

  Int. J. Numer. Meth. Fluids (1998). Vol. 28 (10), pp. 1391-1419

  
  

  Abstract

  An implicit fractional-step method for the numerical solution of the time-dependent incompressible Naiver-Stokes equations in primitive variables is developed and studied in this paper. The method, which is first order accurate in the time-step, is shown to convergence to an exact solution of the equations. By adequately splitting the viscous term, it allows to enforce full Dirichlet boundary conditions on the velocity in all substeps of the scheme, while needing no boundary condition at all for the pressure. It is also shown to be related to an iterative predictor-multicorrector algorithm for evolution equations, when this is applied to the incompressible Naiver-Stokes system. A new derivation of the algorithm in a general setting is provided. Two different finite element interpolations are considered for the implementation of the algorithm; numerical results obtained with them for standard benchmark cases are presented.

  Abstract
  An implicit fractional-step method for the numerical solution of the time-dependent incompressible Naiver-Stokes equations in primitive variables is developed and studied [...]

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• A numerical model for temporal variations during explosive central vent eruptions

  A. Folch, J. Marti, R. Codina, M. Vázquez

  Journal of Geophysical Research: Solid Earth (1998). Vol. 103, 20883-20899

  
  

  Abstract

  An axisymmetrical numerical model has been developed in order to find the temporal evolution of pressure, the position of the exsolution level, the velocity field, the eruption rate, and the amount of erupted material of a shallow, volatile‐rich, felsic magma chamber during a Plinian central vent eruption. The overpressure necessary to trigger the eruption is assumed to result from crystallization‐driven volatile oversaturation. We solve the resulting set of equations using a finite element method. The results obtained show that the pressure at the conduit entrance decreases exponentially as the eruption proceeds. This produces a shifting of the exsolution level, so that deeper parts of the chamber become progressively volatile oversaturated during the eruption. We assess the influence of chamber geometry and the physical properties of the magma on the computed parameters using several numerical examples. The results are also compared with those predicted by previous models from the literature and are found to be in good agreement with documented eruptions. The model constitutes a first attempt to numerically model the dynamics and the temporal evolution of the most relevant physical parameters during withdrawal from a closed magma chamber.

  Abstract
  An axisymmetrical numerical model has been developed in order to find the temporal evolution of pressure, the position of the exsolution level, the velocity field, the eruption [...]

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• Comparison of some finite element methods for solving the diffusion-convection-reaction equation

  R. Codina

  Comput. Methods Appl. Mech. Engrg., (1998). Vol. 156, (1-4), pp. 185-210

  
  

  Abstract

  In this paper we describe several finite element methods for solving the diffusion-convection-reaction equation. None of them is new, although the presentation is non-standard in an effort to emphasize the similarities and differences between them. In particular, it is shown that the classical SUPG method is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerkin method has a stabilization effect similar to a sub-grid scale model, which is un turn related to the introduction of bubbles functions.

  Abstract
  In this paper we describe several finite element methods for solving the diffusion-convection-reaction equation. None of them is new, although the presentation is non-standard [...]

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• A general algorithm for compressible and incompressible flows. Part III: The semi‐implicit form

  R. Codina, M. Vázquez, O. Zienkiewicz

  Int. J. Numer. Meth. Fluids (1998). Vol. 27 (1-4), 13-32

  
  

  Abstract

  In this paper we consider some particular aspects related to the semi‐implicit version of a fractional step finite element method for compressible flows that we have developed recently. The first is the imposition of boundary conditions. We show that no boundary conditions at all need to be imposed in the first step where an intermediate momentum is computed. This allows us to impose the real boundary conditions for the pressure, a point that turns out to be very important for compressible flows. The main difficulty of the semi‐implicit form of the scheme arises in the solution of the continuity equation, since it involves both the density and the pressure. These two variables can be related through the equation of state, which in turn introduces the temperature as a variable in many cases. We discuss here the choice of variables (pressure or density) and some strategies to solve the continuity equation. The final point that we study is the behaviour of the scheme in the incompressible limit. It is shown that the method has an inherent pressure dissipation that allows us to reach this limit without having to satisfy the classical compatibility conditions for the interpolation of the velocity and the pressure

  Abstract
  In this paper we consider some particular aspects related to the semi‐implicit version of a fractional step finite element method for compressible flows that we have developed [...]

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• A finite element formulation for Stokes proble allowing equal velocity-pressure interpolation

  R. Codina, J. Blasco

  Comput. Methods Appl. Mech. Engrg., (1997). Vol. 143 (3–4), pp. 373-391

  
  

  Abstract

  In this paper we study a variational formulation of the Stokes problem that accommodates the use of equal velocity-pressure finite element interpolations. The motivation of this method relies on the analysis of a class of fractional-step methods for the Navier-Stokes equations for which it is known that equal interpolations yield good numerical results. The reason for this turns out to be the difference between two discrete Laplacian operators computed in a different manner. The formulation of the Stokes problem considered here aims to reproduce this effect. From the analysis of the finite element approximation of the problem we obtain stability and optimal error estimates using velocity-pressure interpolations satisfying of the standard formulation. In particular, this condition is fulfilled by the most common equal order interpolations.

  Abstract
  In this paper we study a variational formulation of the Stokes problem that accommodates the use of equal velocity-pressure finite element interpolations. The motivation of [...]

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• Finite element solution of the Stokes problem with dominating Coriolis force

  R. Codina, O. Soto

  Comput. Methods Appl. Mech. Engrg., (1997). Vol. 142 (3-4), pp. 215-234

  
  

  Abstract

  The objective of this paper is to present a finite element formulation to solve the Stokes problem with Coriolis force. This force results in a skew-symmetric term in the weak formulation of the problem that deteriorates the stability of the standard Galerkin finite element method when the viscosity is small. We show that the stability is worsened due to the presence of the pressure gradient to enforce the incompressibility of the flow. The relevance of this effect depends on the relative importance of the viscous force and the Coriolis force, which is measured by the Ekman number. When it is small, oscillations occur using the Galerkin approach. To overcome them, we propose two different methods based on a consistent modification of the basic Galerkin formulation. Both methods eliminate the oscillations, keeping the accuracy of the formulation and enhancing its numerical stability.

  Abstract
  The objective of this paper is to present a finite element formulation to solve the Stokes problem with Coriolis force. This force results in a skew-symmetric term in the [...]

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• Split, characteristic based semi‐implicit algorithm for laminar/turbulent incompressible flows

  O. Zienkiewicz, B. Sai, K. Morgan, R. Codina

  Int. J. Numer. Meth. Fluids (1996). Vol. 23, 787-809

  
  

  Abstract

  In an earlier paper, Zienkiewicz and Codina (Int. j. numer. methods fluids, 20, 869–885 (1995)) presented a general algorithm for the solution of both compressible and incompressible Navier–Stokes equations. The algorithm, based on operator splitting, permits arbitrary interpolation functions to be used while avoiding the Babŭska–Brezzi restriction. In addition, its characteristic based approach introduces a form of rational dissipation. Zienkiewicz et al. (Int. j. numer. methods fluids, 20, 887–913 (1995)) presented the application of this algorithm in its fully explicit form to various inviscid compressible flow problems. They also presented two incompressible flow problems solved by the fully explicit form, employing a pseudo compressibility. The present work deals with the application of the above algorithm it its semi‐implicit form to some incompressible flow benchmark problems. Further, it extends the methodology to turbulent flows by employing both one, and two equation turbulence models. A comparison of results with earlier investigations is presented. Other issues addressed in this study include the effect of additional diffusion terms present in the scheme for both laminar and turbulent flow problems and some practical difficulties associated with local time stepping.

  Abstract
  In an earlier paper, Zienkiewicz and Codina (Int. j. numer. methods fluids, 20, 869–885 (1995)) presented a general algorithm for the solution of both compressible [...]

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• A general algorithm for compressible and incompressible flow—Part I. the split, characteristic‐based scheme

  O. Zienkiewicz, R. Codina

  Int. J. Numer. Meth. Fluids (1995). Vol. 20, 869-885

  
  

  Abstract

  The paper outlines the formulation of a novel algorithm which can be used for the solution of both compressible and incompressible Navier‐Stokes or Euler equations. Full incompressibility can be dealt with if the algorithm is used in its semi‐explicit form and its structure permits arbitrary interpolation functions to be used avoiding the Babuška‐Brezzi restriction. In a fully explicit version it introduces a rational form of balancing dissipation avoiding the use of arbitrary parameters and forms for this.

  Abstract
  The paper outlines the formulation of a novel algorithm which can be used for the solution of both compressible and incompressible Navier‐Stokes or Euler equations. Full [...]

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• An investigation on thermal performance of wollastonite and bentonite reinforced intumescent fire-retardant coating for steel structures

  F. Ahmad, S. Ullah, N. Merican, E. Oñate, A. Al-Sehemi, G. Yeoh

  Construction and Building Material (2019). Vol. 228, 116734

  
  

  Abstract

  This research emphases on the synthesis of new formulations of intumescent coating with improved thermal performance for steel structures. The coating formulations were based on the expandable graphite reinforced with wollastonite and bentonite. Ten samples of five formulations were synthesized by varying grinding time duration between 1 and 2 min. To analyse the substrate temperature of coated steel, fire test was performed according to ASTM-E119. The char morphology was observed by Field Emission Scanning Electron (FESEM) and Transmission Electron Microscopy (TEM). FTIR and X-ray Diffraction (XRD) test is conducted to analyse the composition of the residual char. The residual char mass was perceived by Thermogravimetric analysis (TGA) of the coating. X-ray Photo Electron Spectroscopy (XPS) was utilized for binding energy and elemental composition of the char. One-hour fire protection test showed 166 _C, the lowest substrate temperature of IFRC5-2 and 40.46% residual mass was obtained by TGA analysis. XRD analysis showed that residual char has aluminum borate and borophosphate and confirmed by functional group analysis using and FTIR. FESEM and TEM illustrated that char relates to hexagonal particles of wollastonite. XPS analysis of IFRC5-2 showed the carbon and oxygen contents were 41.40% and 51.20%. Pyrolysis-Gas Chromatography–Mass Spectrometry (Pyrolysis GC–MS) results showed IFRC-5 produced less concentration of the gaseous products compared to IFRC-C. The formulations developed by grinding solid ingredients for 2 min showed improved thermal performance compared with the formulation produced by grinding solid ingredients for 1 min. Longer grinding time and higher amount of filler improved the thermal properties of the intumescent coating.

  Abstract
  This research emphases on the synthesis of new formulations of intumescent coating with improved thermal performance for steel structures. The coating formulations were based [...]

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