Rainald Loehner

IMPLEMENTATION OF UNSTRUCTURED GRID GMRES+LU-SGS METHOD ON SHARED-MEMORY, CACHE-BASED PARALLEL COMPUTERS

The implementation of an unstructured grid matrix-free GMRES+LU-SGS scheme on shared-memory, cache-based parallel machines is described. A special grid renumbering technique is used for the parallelization rather than the traditional method of partitioning the computational domain. The renumbering technique helps to avoid inter-processor data dependencies, cache-misses, and cache-line overwrite while allowing pipelining. The resulting source code can be used with maximum efficiency and without modifications on traditional (scalar) computers, vector supercomputers, and shared-memory parallel systems. Special attention has been paid to develop an optimally parallelized preconditioner for the GMRES scheme.

A parallelizable load balancing algorithm

We present a parallelizable load balancing algorithm for grid-based problems that employs a give and take concept among neighboring subdomains. The algorithm is found to converge very quickly to almost perfect load balance while minimizing the surface-to-volume ratio of the domains. The algorithm can be used for problems whose volume cost grows nonlinearly with the number of elements, because it measures continuously the computational cost to be incurred for each subdomain. This is an advantage over most algorithms currently in use (e.g., recursive subdivision), which assume a linear relationship between the computational cost and the number of elements. 10 refs.

Fluid-structure coupling - Extensions and improvements

The requirement to deal with arbitrarily complex fluid and structural models, geometries and discretization techniques, introduces a number of problems associated to the transfer of information between the coupled programs. We study the transfer of loads from the fluid to the solid, the transfer of deformations from the solid to the fluid and the synchronization of the solutions. For the time integration, explicit and implicit loose coupling schemes are considered. Although the discussions are centered on fluid-structure interaction problems, the techniques presented are of a general character. Therefore, they can also be applied in other multidisciplinary fields.

New methods for computational fluid dynamics modeling of carotid artery from magnetic resonance angiography

Computational fluid dynamics (CFD) models of the carotid artery are constructed from contrast-enhanced magnetic resonance angiography (MRA) using a deformable model and a surface-merging algorithm. Physiologic flow conditions are obtained from cine phase-contrast MRA at two slice locations below and above the carotid bifurcation. The methodology was tested on image data from a rigid flow-through phantom of a carotid artery with 65% degree stenosis. Predicted flow patterns are in good agreement with MR flow measurements at intermediate slice locations. Our results show that flow in a rigid flow-through phantom of the carotid bifurcation with stenosis can be simulated accurately with CFD. The methodology was then tested on flow and anatomical data from a normal human subject. The sum of the instantaneous flows measured at the internal and external carotids differs from that at the common carotid, indicating that wall compliance must be modeled. Coupled fluid-structure calculations were able to reproduce the significant dampening of the velocity waveform observed between different slices along the common carotid artery. Visualizations of the blood flow in a compliant model of the carotid bifurcation were produced. A comparison between compliant and rigid models shows significant differences in the time-dependent wall shear stress at selected locations. Our results confirm that image-based CFD techniques can be applied to the modeling of hemodynamics in compliant carotid arteries. These capabilities may eventually allow physicians to enhance current image-based diagnosis, and to predict and evaluate the outcome of interventional procedures non- invasively.

Vorticity confinement on unstructured grids

A general vorticity connnement term has been derived using dimensional analysis. The resulting vorticity connnement is a function of the local vorticity-based Reynolds-number, the local element size, the vorticity and the gradient of the absolute value of the vorticity. The vorticity connnement term disappears for vanishing mesh size, and is applicable to unstructured grids with large element size disparity. The new term has been found to be successful for a number of testcases, allowing better deenition of vortices without any deleterious eects on the owweld. 1. INTRODUCTION The requirement to accurately track vortices over large distances is common to many areas of engineering , e.g. rotating helicopter blades Car00, Str00, Wen01] and vortices shed by submarines. Due to the inherent dissipation built into numerical ux functions in order to avoid numerical instabilities and un-physical solutions, any current Euler or RANS eld solver will tend to dissipate these vortices too fast. In order to obtain a rough estimate for the grid sizes required to capture accurately typical trailing edges vortices, consider a helicopter blade with radius

Flow visualization on unstructured grids using geometrical cuts, vortex detection and shock surfaces

In order to overcome the limitation of cutting planes for curved, branching geometries, new visualization techniques are presented. The basic idea is to compute surface cuts that “follow” the geometry of the computational domain. Procedures for the detection of vortex centerlines and shock surfaces operating on unstructured grids are also presented. Both schemes yield satisfactory results as illustrated in various examples.

AN OVERLAPPING UNSTRUCTURED GRID METHOD FOR VISCOUS FLOWS

An overlapping unstructured grid method has been developed to solve compressible turbulent flow problems using one equation turbulence model. The idea behind this is to combine the advantages of both overlapping and unstructured grids in an effort to develop a more efficient, robust, and user-friendly method for solving high Reynolds number viscous flow problems around complex geometries. In this method, an anisotropic unstructured grid is independently generated for each component of a given configuration, and an isotropic unstructured grid is then generated to cover the whole computational domain. The developed method is applied to compute a variety of high Reynolds number flow problems. The numerical results obtained indicate that the present method provides an accurate, viable, robust, and user-friendly approach for computing viscous flows.

Measurement of stenosis from magnetic resonance angiography using vessel skeletons

Measurement of stenosis due to atherosclerosis is essential for interventional planning. Currently, measurement of stenosis from magnetic resonance angiography (MRA) is made based on 2D maximum intensity projection (MIP) images. This methodology, however, is subjective and does not take full advantage of the 3D nature of MRA. To address these limitations we present a deformable model for reconstructing the vessel surface with particular application to the carotid artery. The deformable model is based on a cylindrical coordinate system of a curvilinear axes. In this coordinate system, the location of each point on the surface of the deformable model is described by its axial, circumferential and radial position. The points on the surface deform in the radial direction so as to minimize discontinuity in radial position between adjacent points while maximizing the proximity of the surface to local edges in the image. The algorithm has no bias towards either narrower or wider cross- sectional shapes and is thus appropriate for the measurement of stenosis. Axes of the vessels are indicated manually or determined by axes detection methods. Once completed, the surface reconstruction lends itself directly to 3D methods for measuring cross-sectional diameter and area.

A Mixed Adjoint Formulation for Incompressible Turbulent Problems

A design methodology based on a mixed adjoint approach for flow problems governed by the Incompressible Turbulent Navier Stokes equations is deduced and tested. The main feature of the algorithm is that instead of solving an exact discrete adjoint equation, it solves a fastconverging low-order adjoint formulation, saving an important amount of CPU time, and giving a smoothed approximation to the real gradient. It has been shown that this type of smoothed gradients is very convenient to avoid possible diverging cycles in the whole design process, and to reduce the total optimization cost. The boundary conditions for the discrete adjoint formulation are inferred at the continuous level. In this way, the formulation is mixed. Furthermore, the methodology is general in the sense that it does not depend on the geometry representation, and all the gridpoints on the surface to be optimized can be chosen as design parameters. The partial derivatives of the flow equations with respect to the mesh movements are computed by finite differences. Hence, this computation is independent of the numerical scheme employed to obtain the flow solution and of the mesh type. Once the sensitivities and the direction of movement have been computed, the new solid surface is obtained with an improved pseudo-shell approach in such a way that local singularities, which can degrade or inhibit the convergence to the optimal solution, are avoided. Moreover, this surface parametrization allows to impose geometrical restrictions in a very easy manner. The volume mesh is updated to fix the new boundary using an innovative level approach for the highly stretched elements close to the solid boundary (boundary layer mesh), and a quasi-incompressible elastic movement scheme for the rest of them. Such type of combined mesh movement algorithm allows to compute the sensitivity contribution of the interior mesh points by using finite differences in a very fast manner, and avoids expensive remeshing procedures during the whole design process. The methodologies can deal with multi-objective function problems. Some numerical examples are presented to demonstrate the methodology behaviour.

Interactive On-Line Visualization and Collaboration for Parallel Unstructured Multidisciplinary Applications

In this paper we describe a visualization software being developed for parallel unstructured multidisciplinary applications. One of its most attractive features is the possibility of connecting to a remotely running parallel solver for on-line display. This loose coupling of viewer-solver allows full interactivity and makes the solution and the visualization processes completely independent. Other capabilities include parallel visualization of distributed data, multidisciplinary data, collaboration sessions and automatic movie making with scripts and navigation cameras.