Full Approximation Storage Scheme Research Articles

Multi-level adaptive solution of anisotropic porous media flow with strong discontinuous jumps in permeability

A fast and robust multi-grid algorithm for the efficient solution of diffusion-like, elliptic problems which exhibit strong discontinuous jumps in diffusivity is presented. Although generally applicable to this class of problem, the focus for illustrative purposes is that of porous media flow; in particular, such flows for which accurate solutions can only be achieved if the full permeability tensor is taken into consideration. The merits of adopting one or the other of two different approaches to deriving a discrete analogue to the steady-state Darcy equation, namely a novel weighted average of permeability formulation and a continuity of flux preservation method, are explored. In addition, automatic mesh refinement is incorporated seamlessly via a multi-level adaptive technique, making full use of the local truncation error estimates available from the inclusive full approximation storage scheme. Adaptive cell- and patch-wise mesh refinement strategies are developed and investigated for this purpose and used to solve a sequence of benchmark problems of increasing complexity. The results obtained reveal: (a) the ease with which the overall approach deals with generating accurate solutions for flows involving both distributed anisotropy and strong discontinuous jumps in permeability; (b) that both discrete analogues produce equivalent results in comparable execution times; and (c) the significant reductions in computing resource, memory, and CPU, to accrue from employing automatic adaptive mesh refinement.

The implementation of an aeronautical CFD flow code onto distributed memory parallel systems

The parallelization of an industrially important in-house computational fluid dynamics (CFD) code for calculating the airflow over complex aircraft configurations using the Euler or Navier–Stokes equations is presented. The code discussed is the flow solver module of the SAUNA CFD suite. This suite uses a novel grid system that may include block-structured hexahedral or pyramidal grids, unstructured tetrahedral grids or a hybrid combination of both. To assist in the rapid convergence to a solution, a number of convergence acceleration techniques are employed including implicit residual smoothing and a multigrid full approximation storage scheme (FAS). Key features of the parallelization approach are the use of domain decomposition and encapsulated message passing to enable the execution in parallel using a single programme multiple data (SPMD) paradigm. In the case where a hybrid grid is used, a unified grid partitioning scheme is employed to define the decomposition of the mesh. The parallel code has been tested using both structured and hybrid grids on a number of different distributed memory parallel systems and is now routinely used to perform industrial scale aeronautical simulations. Copyright © 2000 John Wiley & Sons, Ltd.

The implementation of an aeronautical CFD flow code onto distributed memory parallel systems

The parallelization of an industrially important in-house computational fluid dynamics (CFD) code for calculating the airflow over complex aircraft configurations using the Euler or Navier–Stokes equations is presented. The code discussed is the flow solver module of the SAUNA CFD suite. This suite uses a novel grid system that may include block-structured hexahedral or pyramidal grids, unstructured tetrahedral grids or a hybrid combination of both. To assist in the rapid convergence to a solution, a number of convergence acceleration techniques are employed including implicit residual smoothing and a multigrid full approximation storage scheme (FAS). Key features of the parallelization approach are the use of domain decomposition and encapsulated message passing to enable the execution in parallel using a single programme multiple data (SPMD) paradigm. In the case where a hybrid grid is used, a unified grid partitioning scheme is employed to define the decomposition of the mesh. The parallel code has been tested using both structured and hybrid grids on a number of different distributed memory parallel systems and is now routinely used to perform industrial scale aeronautical simulations. Copyright © 2000 John Wiley & Sons, Ltd.

Multigrid applications to three-dimensional elliptic coordinate generation

The multigrid algorithm was applied to solve the coupled set of elliptic quasilinear partial differential equations associated with three-dimensional coordinate generation. The results indicate that the multigrid scheme is more than twice as fast as conventional relaxation schemes on moderate-size grids. Convergence factors of order 0.90 per work unit were achieved on 36,000-point grids. The paper covers the form of transformation, develops the set of generation equations, and gives details on the multigrid approach used. Included are a development of the full-approximation storage scheme, details of the smoothing-rate analysis, and a section devoted to rational programming techniques applicable to the multigrid algorithm.