High-order numerical methods for unstructured grids combine the superior accuracy of high-order spectral or finite difference methods with the geometrical flexibility of low-order finite volume or finite element schemes. The Flux Reconstruction (FR) approach [1] unifies various high-order schemes for unstructured grids within a single framework. Additionally, the FR approach exhibits a significant degree of element locality, and is thus able to run efficiently on modern many-core hardware platforms, such as Graphical Processing Units (GPUs).

 

The aforementioned properties of FR mean it offers a promising route to performing affordable, and hence industrially relevant, scale-resolving simulations of hitherto intractable unsteady flows within the vicinity of real-world engineering geometries. In this talk I will present PyFR (www.pyfr.org) [2], an open-source Python based framework for solving advection-diffusion type problems using the FR approach. The framework is designed to solve a range of governing systems on mixed unstructured grids containing various element types. It is also designed to target a range of hardware platforms via use of a custom Mako-derived domain specific language. The latest release of PyFR is able to solve the compressible Euler and Navier-Stokes equations on grids of quadrilateral and triangular elements in two dimensions, and hexahedral, tetrahedral, prismatic, and pyramidal elements in three dimensions, targeting clusters of multi-core CPUs, NVIDIA GPUs (K20, K40 etc.), AMD GPUs (S10000, W9100 etc.), and heterogeneous mixtures thereof. Results will be presented for various benchmark and ‘real-world’ flow problems, and scalability of PyFR will be demonstrated on clusters with 100s of NVIDIA GPUs. Throughout the talk the importance of algorithm-software-hardware co-design, in the context of next-generation computational fluid dynamics, will be highlighted.

 

References

 

[1] Huynh, H. T., A Flux Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin Methods, AIAA Paper 2007–4079, 2007.

 

[2] Witherden, F. D., Farrington A. M., Vincent P. E., PyFR: An Open Source Framework for Solving Advection-Diffusion Type Problems on Streaming Architectures using the Flux Reconstruction Approach, Computer Physics Communications, 185(11) pp. 3028–3040, 2014.