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• Eulerian-Eulerian and Eulerian-Lagrangian methods in two phase flow

  S. Siver, E. Loth, J. Baum, R. Lohner

  (1993). Thirteenth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 414. Springer, Berlin, Heidelberg

  
  

  Abstract

  This paper describes a Finite Element Method - Flux Corrected Transport (FEM-FCT) approach with an unstructured adaptive grid scheme to the simulation of two-phase flow. The gas equations are computed using an Eulerian frame of reference, while the particle transport is computed using both Eulerian and Lagrangian frames of reference. One dimensional shock wave attenuation was investigated to evaluate the performance of these methodologies and the gas-solid interphase transport models

  Abstract
  This paper describes a Finite Element Method - Flux Corrected Transport (FEM-FCT) approach with an unstructured adaptive grid scheme to the simulation of two-phase flow. The [...]

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• An implicit three-dimensional finite element solver for unstructured meshes

  H. Luo, J. Baum, R. Lohner, J. Cabello

  AIAA Journal (1993). Vol. 11 (2), pp. 1027-1028

  
  

  Abstract

  The development of an implicit 3D finite element algorithm for the solution of the compressible Euler and Navier-Stokes equations on unstructured meshes is reported. Numerical results for both inviscid and viscous flows are presented to demonstrate the proposed scheme's performance. The treatment of boundary conditions is found to be vital to the success of an implicit scheme

  Abstract
  The development of an implicit 3D finite element algorithm for the solution of the compressible Euler and Navier-Stokes equations on unstructured meshes is reported. [...]

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• Some useful renumbering strategies for unstructured grids

  R. Lohner

  International Journal for Numerical Methods in Engineering (1993). Vol. 36 (19), pp. 3259-3270

  
  

  Abstract

  Several renumbering strategies for unstructured grids are discussed. They lead to a minimization of eache-misses and an optimal grouping of elements for different computer platforms, from superscalar workstations to multiprocessor register-to-register vector machines. Timings for a typical computational fluid dynamics (CFD) code that employs these renumbering strategies indicate that CPU requirements may be halved by applying them. The renumbering strategies discussed are all of linear time complexity, making them ideally suited for applications requiring frequent mesh changes. Furthermore, these renumbering strategies are not only valid for element-based codes but carry over to edge-based or face-based field solvers

  Abstract
  Several renumbering strategies for unstructured grids are discussed. They lead to a minimization of eache-misses and an optimal grouping of elements for different computer [...]

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• Three‐dimensional parallel unstructured grid generation

  A. Shostko, R. Lohner

  International Journal for Numerical Methods in Engineering (1994). Vol. 38 (6), pp. 905-925

  
  

  Abstract

  An algorithm for the parallel generation of 3-D unstructured grids is presented. The technique is an extension of the algorithm presented in Reference 21 for the 2-D case. The method uses a background grid as the means to separate spatially different regions, enabling the concurrent, parallel generation of elements in different domains and interdomain regions. The parallel 3-D grid generator was implemented and tested on the INTEL hypercube and Touchstone Delta parallel computers. The results obtained demonstrate the effectiveness of the algorithm developed. The methodology is applicable to the parallel implementation of a wide range of problems that are, in principle, scalar by nature, and do not lend themselves to SIMD parallelization.

  Abstract
  An algorithm for the parallel generation of 3-D unstructured grids is presented. The technique is an extension of the algorithm presented in Reference 21 for the 2-D case. [...]

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• Electromagnetics via the Taylor-Galerkin Finite Element Method on Unstructured Grids

  J. Ambrosiano, S. Brandon, R. Lohner, R. DeVore

  Journal of Computational Physics (1994). Vol. 110 (2), pp. 310-319

  
  

  Abstract

  Traditional techniques for computing electromagnetic solutions in the time domain rely on finite differences. These so-called finite-difference time-domain (FDTD) methods are usually defined only on regular lattices of points and can be too restrictive for geometrically demanding problems. Great geometric flexibility can be achieved by abandoning the regular latticework of sample points and adopting an unstructured grid. An unstructured grid allows one to place the grid points anywhere one chooses, so that curved boundaries can be fit with ease and local regions in which the field gradients are steep can be selectively resolved with a fine mesh. In this paper we present a technique for solving Maxwell's equations on an unstructured grid based on the Taylor-Galerkin finite-element method. We present several numerical examples which reveal the fundamental accuracy and adaptability of the method. Although our examples are in two dimensions, the techniques and results generalize readily to 3D.

  Abstract
  Traditional techniques for computing electromagnetic solutions in the time domain rely on finite differences. These so-called finite-difference time-domain (FDTD) methods [...]

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• Numerical simulation of shock-box interaction using an adaptive finite element scheme

  J. Baum, R. Lohner

  AIAA Journal (1994). Vol. 32 (4), pp. 682-692

  
  

  Abstract

  A transient two-dimensional, finite elemnt shock capturing scheme on unstructured grids was applied to the study of a shock interacting with a box suspended above a rigid elevated surface. The area between the box and the surface was partially blocked by the box support beams, resulting in complex shock diffraction processes. The results demonstrate the capability of the developed adaptive refinement/corsening algorithm to properly adapt to weak shocks, expansions, and contact discontinuities, and highlight the resulting excellent resolution of the captured flow features. In addition to interesting shock diffraction and propagation phenomena, the results demonstrate the capability of the new code to capture, and define in great detail, vortex sheets shed from sharp corners. We show that the baroclinic effect, an inviscid process, controls the shedding phenomenon during the diffraction phase. Hence, the Eulerian model is able to correctly predict the process.

  Abstract
  A transient two-dimensional, finite elemnt shock capturing scheme on unstructured grids was applied to the study of a shock interacting with a box suspended above a rigid [...]

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• Edge-based element scheme for the Euler equations

  H. Luo, J. Baum, R. Lohner

  AIAA Journal (1994). Vol. 32 (6), pp. 1182-1190

  
  

  Abstract

  This paper describes the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of the upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm.

  Abstract
  This paper describes the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. [...]

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• Unstructured Adaptive Remeshing Finite Element Method for Dusty Shock Flows

  S. Siver, E. Loth, J. Baum, R. Lohner

  Shock Waves (1994). Vol. 4 (1), pp. 15-23

  
  

  Abstract

  The passage of planar shocks in a dusty gas was investigated to note effects due to particle loading and initial shock Mach number. Two-phase flow equations have been added to a conservative, monotonic flow solver to allow study of compressible particle and droplet flows, which are of importance for shock propagation in two-phase flows and spray propulsion systems. The formulation developed herein employed a conservative Eulerian treatment for the gas and particle phases. The computations were performed using the finite element method-flux corrected transport (FEM-FCT) scheme, which has shown excellent predictive capability of various compressible flows which include both strong and weak shocks. The flux limiting technique was modified to provide monotonic particle velocity fields to increase the scheme's computational stability. Adaptive unstructured methodology based on adapting to high gradients of both the fluid and particle densities was used in conjunction with the conservative shock-capturing scheme to adequately resolve strong flowfield gradients. The shock attenuation of this scheme was then compared with previous experimental and numerical results and was found to yield robust predictions. Various interphase coupling terms were also considered to note their effect on the shock attenuation.

  Abstract
  The passage of planar shocks in a dusty gas was investigated to note effects due to particle loading and initial shock Mach number. Two-phase flow equations have been added [...]

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• Ray tracing with a space‐filling finite element mesh

  J. Fave, R. Lohner

  International Journal for Numerical Methods in Engineering (1994). Vol. 37 (20), pp. 3571-3580

  
  

  Abstract

  A new ray‐tracing technique is presented which does not work with ray–object intersections per se , but is based on the traversal of an unstructured tetrahedral mesh providing a convex enclosure of a scene of polyhedral objects. The tetrahedral mesh provides tight bounding and an adaptive subdivision of space. This non‐hierarchical data structure is traversed adaptively until one is led directly and unconditionally to the first object intersected. Rendering times are directly related to the average thickness of the enclosing mesh since all tetrahedra are traversed in constant time. Since the proposed algorithm operates directly with volume elements, it allows for volumetric rendering effects. Volume rendering or anisotropic media can be implemented without any further effort. This is an important advantage as compared to usual techniques, which only operate on surface data. Timings for several examples show that the use of this type of ray‐tracing technique, which is more suitable for general purpose visualization codes than traditional techniques, results in CPU times that are comparable with the best ray‐tracing techniques presently used. This is an unexpected and important result, as the vectorization and parallclization of the proposed technique are straightforward, in contrast with traditional ray‐tracing techniques

  Abstract
  A new ray‐tracing technique is presented which does not work with ray–object intersections per se , but is based on the traversal of an unstructured tetrahedral [...]

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• Edges, stars, superedges and chains

  R. Lohner

  Computer Methods in Applied Mechanics and Engineering (1994). Vol. 111 (3-4), pp. 255-263

  
  

  Abstract

  Several possibilities for the reduction of indirect addressing operations within edge-based solvers are discussed. It is shown that indirect addressing operations may be reduced by a factor in excess of 1 : 4 if edges are grouped and linked together. Tests of benchmark loops on two common engineering computer platforms reveal that CPU saving factors ranging from 1.3 to 3.5 may be realized when switching from edge-based to superedge or chain-based loops.

  Abstract
  Several possibilities for the reduction of indirect addressing operations within edge-based solvers are discussed. It is shown that indirect addressing operations may be reduced [...]

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