Author: Christian Jacobs, University of Southampton


Explicit finite difference (FD) algorithms lie at the core of many CFD models in order to solve the governing equations of fluid motion. Over the past decades huge efforts have been made by CFD model developers throughout the world to rewrite the implementation of these algorithms, in order to exploit new and improved computer hardware (for example, GPUs). Numerical modellers must therefore be proficient not only in their domain of expertise, but also in numerical analysis and parallel computing techniques.

As a result of this largely unsustainable burden on the numerical modeller, recent research has focussed on code generation as a way of automatically deriving code that implements numerical algorithms from a high-level problem specification. Modellers need only be concerned about writing the equations to be solved and choosing the appropriate numerical algorithm, and not about the specifics of the parallel implementation of the algorithm on a particular hardware architecture; this latter task is handled by computer scientists. A separation of concerns is therefore created, which is an important step towards the sustainability of CFD models as newer hardware arrives in the run-up to exascale computing.

As part of the ExaFLOW project, researchers at the University of Southampton have developed the OpenSBLI framework [1] ( ) which features such automated code generation techniques for finite difference algorithms. The flexibility that code generation provides has enabled them to investigate the performance of several FD algorithms that are characterised by different amounts of computational and memory intensity.

Author: Martin Vymazal, Imperial College London


High-order methods on unstructured grids are now increasingly being used to improve the accuracy of flow simulations since they simultaneously provide geometric flexibility and high fidelity. We are particularly interested in efficient algorithms for incompressible Navier-Stokes equations that employ high-order space discretization and a time splitting scheme. The cost of one step in time is largely determined by the amount of work needed to obtain the pressure field, which is defined as a solution to a scalar elliptic problem. Several Galerkin-type methods are available for this task, each of them have specific advantages and drawbacks.

High-order continuous Galerkin (CG) method is the oldest. Compared to its discontinuous counterparts, it involves a smaller number of unknowns (figure 1), especially in a low-order setting. The CG solution can be accelerated by means of static condensation, which produces a globally coupled system involving only those degrees of freedom on the mesh skeleton. The element interior unknowns are subsequently obtained from the mesh skeleton data by solving independent local problems that do not require any parallel communication. 

Author: Adam Peplinski, KTH


Computational Fluid Dynamics (CFD) relies on the numerical solution of partial differential equations and is one of the most computationally intensive parts of a wide range of scientific and engineering applications. Its accuracy is strongly dependent on the quality of the adopted grid and approximation space on which the solution is computed. Unfortunately for most interesting cases, finding the optimal grid in advance is not possible and some self-adapting algorithms have to be used during simulation. One of them is Adaptive Mesh Refinement (AMR), which allows to dynamically modify both grid structure and approximation space and provides the possibility to control the computational error during the simulation and to increase the accuracy of the numerical simulations at minimal computational cost.

Figure 1: The error of the stream-wise velocity component for the conforming mesh. Black lines show element boundaries.

Author: Carlos Falconi, ASCS


The 8th regular general meeting of asc(s took place in Leinfelden-Echterdingen on 12th May 2016. The Managing Director Alexander F. Walser reported a positive premium increase of 22% and briefed network members and invited guests on project activities of asc(s during 2015. The Scientific Project Manager Carlos J. Falconi D. presented ExaFLOW to the audience. He gave an overview of all technical objectives to be accomplished during the project period and informed of intermediate results. A discussion with members followed aiming at collecting feedback in regards exploitability of ExaFLOW results. The recently-elected board members of asc(s including Prof. Dr.-Ing. Dr. h.c. Dr. h.c. Prof. e.h. Michael M. Resch from the High Performance Computing Center at the University of Stuttgart, Dr. Steffen Frik from Adam Opel AG, Jürgen Kohler from Daimler AG, Dr. Detlef Schneider from Altair Engineering GmbH and Nurcan Rasig, Sales Manager at Cray Computer Deutschland underlined the importance of transferring know-how and applying achieved project results to more industrial cases.

Author: Christian Jacobs, University of Southampton


ExaFLOW-funded researchers at the University of Southampton have developed and released a new software framework called OpenSBLI, which can automatically generate CFD model code from high-level problem specifications. This generated code is then targetted towards a variety of hardware backends (e.g. MPI, OpenMP, CUDA, OpenCL and OpenACC) through source-to-source translation using the OPS library.

A key feature of OpenSBLI is the separation of concerns that is introduced between model developers, numerical analysts, and parallel computing experts. The numerical analysts can focus on the numerical methods and their variants, while the writing of architecture-dependant code for HPC systems is the task of the parallel computing experts who can support and introduce optimisations for the exascale hardware architectures and the associated backends, once available in the future. As a result of this abstraction, the end-user model developer need not change or re-write their high-level problem specification in order to run their simulations on new HPC hardware.

More details about OpenSBLI can be found in the paper: 

C. T. Jacobs, S. P. Jammy, N. D. Sandham (In Press). OpenSBLI: A framework for the automated derivation and parallel execution of finite difference solvers on a range of computer architectures. Journal of Computational Science. DOI: 10.1016/j.jocs.2016.11.001. Pre-print: and on the project's website: