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• A Numerical Model for the Prediction of Microstructure Distribution across the Thickness of Quenched Steel Plates

  J. Gawad, I. Iaconeta, S. Bhogireddy, B. Cooman, P. Hernaut, A. Lebedev, G. Wierink

  Materials Science Forum (2019). Vol. 949, pp. 32-39

  
  

  Abstract

  In this work we apply a numerical inverse analysis procedure based on the ICME framework to ensure a required microstructure and combination of properties in the quenched plate. The microstructure is decided first, and the cooling profile needed to obtain such microstructure is then calculated using the CALPHAD approach. Subsequently, an inverse analysis of the heat transfer problem provides the description of the convection mechanism in quenching that results in the demanded cooling profile. An additional constraint is set on the through-thickness thermal gradient to achieve a homogeneous microstructure. Finally, the resultant microstructure is computed. By means of the proposed model we are able to retrieve the necessary quenching process parameters and to quantify the influence of these parameters on the temperature and microstructure distribution within the plate after the quenching.

  Abstract
  In this work we apply a numerical inverse analysis procedure based on the ICME framework to ensure a required microstructure and combination of properties in the quenched [...]

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• The solution of non‐linear hyperbolic equation systems by the finite element method

  R. Lohner, K. Morgan, O. Zienkiewicz

  International Journal for Numerical Methods in Fluids (1984). Vol. 4 (11), pp. 116-120

  
  

  Abstract

  The difficulties experienced in the treatment of hyperbolic systems of equations by the finite element method (or other) spatial discretization procedures are well known. In this paper a temporal discretization precedes the spatial one which in principle is considered along the characteristics to achieve a self adjoint form. By a suitable expansion, the original co‐ordinates are preserved and combined with the use of a standard Galerkin process to achieve an accurate discretization. It is shown that the process is equivalent to the Taylor‐Galerkin methods of Donea.17 Several examples illustrate the accuracy and efficiency attainable in such problems as transport, shallow water equations, transonic flow etc.

  Abstract
  The difficulties experienced in the treatment of hyperbolic systems of equations by the finite element method (or other) spatial discretization procedures are well known. [...]

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• Accelerated ‘relaxation’ or direct solution? Future prospects for fem

  R. Lohner, O. Zienkiewicz

  International Journal for Numerical Methods in Engineering (1985). Vol. 21 (1), pp. 1-11

  
  

  Abstract

  ‘Dynamic’ or ‘viscous’ relaxation procedures have not gained much popularity in finite element analysis in which the direct (Gaussian elimination) solution dominates. Reasons for this are various—the most important being the rather slow convergence generally achieved for such procedures. However, it is possible to accelerate this quite dramatically and a method of doing so is shown in this paper. With the use of such acceleration and the inherent advantages of greatly reduced storage requirements and simplicity of programming, relaxation procedures promise an exciting possibility for the solution of large two‐ and three‐dimensional problems in both linear and nonlinear ranges.

  Abstract
  ‘Dynamic’ or ‘viscous’ relaxation procedures have not gained much popularity in finite element analysis in which the direct (Gaussian elimination) [...]

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• Recent developments in FEM-CFD

  R. Lohner, K. Morgan, J. Peraire, O. Zienkiewicz

  (1985). The Free-Lagrange Method. Lecture Notes in Physics, vol 238. Springer, Berlin, Heidelberg

  
  

  Abstract

  The current status of CFD with regard to unstructured grids employing finite element methods and Eulerian frames is reviewed. Algorithms suitable for the computation of large three-dimensional problems involving flow past arbitrary geometries are developed. Adaptive mesh refinement strategy is reviewed, and domain splitting or local time-stepping are briefly addressed. The development of search algorithms of optimal order, variable time-stepping Jacobi smoothers for elliptic problems, and transport concepts for hyperbolics to help achieve good performance for unstructured multigrid processes is discussed. As examples, transient supersonic flow in a channel, regular shock reflection of a wall, viscous flow past a protruberance, potential flow past a cylinder, and Burgers equation are considered.

  Abstract
  The current status of CFD with regard to unstructured grids employing finite element methods and Eulerian frames is reviewed. Algorithms suitable for the computation of large [...]

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• A simple extension to multidimensional problems of the artificial viscosity due to Lapidus

  R. Lohner, K. Morgan, J. Peraire

  Communications in numerical methods in engineering (1985). Vol. 1 (4), pp. 141-147

  
  

  Abstract

  An artificial viscosity suitable for use in the simulation of multidimensional high-speed compressible flows by the finite element method is proposed. The form adopted is a consistent extension of the method due to Lapidus.

  Abstract
  An artificial viscosity suitable for use in the simulation of multidimensional high-speed compressible flows by the finite element method is proposed. The form adopted is [...]

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• An adaptive finite element procedure for compressible high speed flows

  R. Lohner, K. Morgan, O. Zienkiewicz

  Computer Methods in Applied Mechanics and Engineering (1985). Vol. 51 (1-3), pp. 441-465

  
  

  Abstract

  A two-step explicit finite element procedure for obtaining time-accurate solutions to the compressible Euler equations is described. The method is coupled with an adaptive mesh refinement process which enables steady state solutions of improved quality to be obtained.

  Abstract
  A two-step explicit finite element procedure for obtaining time-accurate solutions to the compressible Euler equations is described. The method is coupled with an adaptive [...]

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• Effective Programming of Finte Element Methods for Computational Fluid Dynamics on Supercomputers

  R. Lohner, K. Morgan, O. Zienkiewicz

  (1986). The Efficient Use of Vector Computers with Emphasis on Computational Fluid Dynamics. Notes on Numerical Fluid Mechanics, vol 12. Vieweg+Teubner Verlag, Wiesbaden

  
  

  Abstract

  The effective programming of Finite Element Methods for CFD on vector-machines is discussed. It is shown, that for unstructured grids the performance observed on this class of machine depends heavily of the availability of hardware Gather/Scatter. Timings obtained for a 3-D Euler code are presented for the CYBER-205, CRAY-XMP11 and CRAY-XMP48.

  Abstract
  The effective programming of Finite Element Methods for CFD on vector-machines is discussed. It is shown, that for unstructured grids the performance observed on this class [...]

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• Unstructured multigrid methods for elliptic problems

  R. Lohner, K. Morgan

  International Journal for Numerical Methods in Engineering (1987). Vol. 24 (1), pp. 3323-3331

  
  

  Abstract

  A multigrid algorithm for implementation on unstructured meshes is proposed. The algorithm uses a sequence of unnested grids and requires the development of efficient inter-grid interpolation procedures. It is demonstrated how elliptic problems can be solved in this fashion by using Jacobi smoothers

  Abstract
  A multigrid algorithm for implementation on unstructured meshes is proposed. The algorithm uses a sequence of unnested grids and requires the development of efficient inter-grid [...]

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• An adaptive finite element scheme for transient problems in CFD

  R. Lohner

  Computer Methods in Applied Mechanics and Engineering (1987). Vol. 61 (6), pp. 323-338

  
  

  Abstract

  An adaptive finite element scheme for transient problems is presented. The classic h-enrichment / coarsening is employed in conjunction with a triangular finite element discretization in two dimensions. A mesh change is performed every n timesteps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/ coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved on the CRAY XMP 12 at NRL. Several examples involving shock-shock interactions and the impact of shocks on structures demonstrate the performance of the method, indicating that considerable savings in CPU time and storage can be realized even for strongly unsteady flows.

  Abstract
  An adaptive finite element scheme for transient problems is presented. The classic h-enrichment / coarsening is employed in conjunction with a triangular finite element [...]

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• Finite elements in CFD: What lies ahead

  R. Lohner

  International Journal for Numerical Methods in Engineering (1987). Vol. 24 (9), pp. 1741-1756

  
  

  Abstract

  The current state of the art of Finite Element Methods in Computational Fluid Dynamics is reviewed. The aim of this review is to point out what appear currently as the main shortcomings of Finite Element Methods, so as to concentrate the efforts to remove them. The analysis of flows using Finite Elements will only be successful if all steps involved in it are optimized. Therefore, I deem it necessary to describe explicit and implicit flow solvers, unstructured multigrid methods, adaptive refinement schemes, grid generation and graphics in 3‐D, the effective use of supercomputer hardware and memory, as well as the combination of structured and unstructured grids.

  Abstract
  The current state of the art of Finite Element Methods in Computational Fluid Dynamics is reviewed. The aim of this review is to point out what appear currently as the [...]

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