3,278 research outputs found
A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows
Both compressible and incompressible Navier-Stokes solvers can be used and
are used to solve incompressible turbulent flow problems. In the compressible
case, the Mach number is then considered as a solver parameter that is set to a
small value, , in order to mimic incompressible flows.
This strategy is widely used for high-order discontinuous Galerkin
discretizations of the compressible Navier-Stokes equations. The present work
raises the question regarding the computational efficiency of compressible DG
solvers as compared to a genuinely incompressible formulation. Our
contributions to the state-of-the-art are twofold: Firstly, we present a
high-performance discontinuous Galerkin solver for the compressible
Navier-Stokes equations based on a highly efficient matrix-free implementation
that targets modern cache-based multicore architectures. The performance
results presented in this work focus on the node-level performance and our
results suggest that there is great potential for further performance
improvements for current state-of-the-art discontinuous Galerkin
implementations of the compressible Navier-Stokes equations. Secondly, this
compressible Navier-Stokes solver is put into perspective by comparing it to an
incompressible DG solver that uses the same matrix-free implementation. We
discuss algorithmic differences between both solution strategies and present an
in-depth numerical investigation of the performance. The considered benchmark
test cases are the three-dimensional Taylor-Green vortex problem as a
representative of transitional flows and the turbulent channel flow problem as
a representative of wall-bounded turbulent flows
PyFR: An Open Source Framework for Solving Advection-Diffusion Type Problems on Streaming Architectures using the Flux Reconstruction Approach
High-order numerical methods for unstructured grids combine the superior
accuracy of high-order spectral or finite difference methods with the geometric
flexibility of low-order finite volume or finite element schemes. The Flux
Reconstruction (FR) approach 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 streaming architectures, 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 paper we present PyFR,
an open-source Python based framework for solving advection-diffusion type
problems on streaming architectures 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 an in-built domain specific language based on the
Mako templating engine. The current 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 elements in three
dimensions, targeting clusters of CPUs, and NVIDIA GPUs. Results are presented
for various benchmark flow problems, single-node performance is discussed, and
scalability of the code is demonstrated on up to 104 NVIDIA M2090 GPUs. The
software is freely available under a 3-Clause New Style BSD license (see
www.pyfr.org)
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