Some useful renumbering strategies for unstructured grids

Abstract

SUMMARYSeveral renumbering strategies for unstructured grids are discussed. They lead to a minimization of cache-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 he 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.

Comparison between element, edge and compressed storage schemes for iterative solutions in finite element analyses

“…To achieve data locality, first the bandwidth should be optimized, that is, the largest length should be minimum and almost constant for all elements (see Figure 1). Second, the equations should be accessed in ascending (or descending) order [23]. …”

Development and Application of New Algorithms for the Simulation of Viscous Compressible Flows with Moving Bodies in Three Dimensions

“…The same applies to turbulent flows simulated using the Reynolds-Averaged Navier-Stokes (RANS) equations with suitable turbulence models. The reliable generation of high quality grids for RANS simulations has been attempted with varying degrees of success by several authors during the last decade (Nakahashi, 1987;Kallinderis, 1992;Löhner, 1993;Pirzadeh, 1994;Marcum, 1995;Pirzadeh, 1996;Morgan, 1996-1998). Given that the generation of highly stretched grids is not trivial, and that computing power is increasing steadily, the immediate question that comes to mind is when RANS simulations will be replaced by Large-Eddy Simulations (LES) or even Direct Navier-Stokes (DNS) simulations.…”

“…However, they fail when attempting to generate highly stretched elements, a key requirement for Reynolds-Averaged Navier Stokes (RANS) calculations with turbulence models that reach into the sublayer. A number of specialized schemes have been proposed to remedy this situation (Nakahashi, 1987;Kallinderis, 1992;Löhner, 1993;Pirzadeh, 1994;Marcum, 1995;Pirzadeh, 1996;Peraire and Morgan, 1996). The domain to be gridded was divided into isotropic and stretched element regions.…”

“…In addition, a blending procedure to transition smoothly between these zones was provided. Typically, the stretched mesh region was generated first (Kallinderis, 1992;Löhner, 1993; Pirzadeh, 1994;Marcum, 1995;Pirzadeh, 1996). Although we have used such a scheme (Löhner, 1993) for a number of years, we have found several situations in which the requirement of a semi-structured element or point placement close to wetted surfaces is impossible, prompting us to search for a more general technique.…”

Simulation of flows with violent free surface motion and moving objects using unstructured grids

“…Most of the work is spent in loops over the edges (upwind solvers, limiters, gradients, etc.). Given that edges have to be grouped in order to avoid memory contention/allow vectorization when forming right-hand sides [50,51], this opens a natural way of avoiding unnecessary work: form relatively small edge-groups that still allow for efficient vectorization, and deactivate groups instead of individual edges [35]. In this way, the basic loops over edges do not require any changes.…”