2,727 research outputs found
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)
A Compact Third-order Gas-kinetic Scheme for Compressible Euler and Navier-Stokes Equations
In this paper, a compact third-order gas-kinetic scheme is proposed for the
compressible Euler and Navier-Stokes equations. The main reason for the
feasibility to develop such a high-order scheme with compact stencil, which
involves only neighboring cells, is due to the use of a high-order gas
evolution model. Besides the evaluation of the time-dependent flux function
across a cell interface, the high-order gas evolution model also provides an
accurate time-dependent solution of the flow variables at a cell interface.
Therefore, the current scheme not only updates the cell averaged conservative
flow variables inside each control volume, but also tracks the flow variables
at the cell interface at the next time level. As a result, with both cell
averaged and cell interface values the high-order reconstruction in the current
scheme can be done compactly. Different from using a weak formulation for
high-order accuracy in the Discontinuous Galerkin (DG) method, the current
scheme is based on the strong solution, where the flow evolution starting from
a piecewise discontinuous high-order initial data is precisely followed. The
cell interface time-dependent flow variables can be used for the initial data
reconstruction at the beginning of next time step. Even with compact stencil,
the current scheme has third-order accuracy in the smooth flow regions, and has
favorable shock capturing property in the discontinuous regions. Many test
cases are used to validate the current scheme. In comparison with many other
high-order schemes, the current method avoids the use of Gaussian points for
the flux evaluation along the cell interface and the multi-stage Runge-Kutta
time stepping technique.Comment: 27 pages, 38 figure
Unsteady adjoint of pressure loss for a fundamental transonic turbine vane
High fidelity simulations, e.g., large eddy simulation are often needed for
accurately predicting pressure losses due to wake mixing in turbomachinery
applications. An unsteady adjoint of such high fidelity simulations is useful
for design optimization in these aerodynamic applications. In this paper we
present unsteady adjoint solutions using a large eddy simulation model for a
vane from VKI using aerothermal objectives. The unsteady adjoint method is
effective in capturing the gradient for a short time interval aerothermal
objective, whereas the method provides diverging gradients for long
time-averaged thermal objectives. As the boundary layer on the suction side
near the trailing edge of the vane is turbulent, it poses a challenge for the
adjoint solver. The chaotic dynamics cause the adjoint solution to diverge
exponentially from the trailing edge region when solved backwards in time. This
results in the corruption of the sensitivities obtained from the adjoint
solutions. An energy analysis of the unsteady compressible Navier-Stokes
adjoint equations indicates that adding artificial viscosity to the adjoint
equations can potentially dissipate the adjoint energy while potentially
maintain the accuracy of the adjoint sensitivities. Analyzing the growth term
of the adjoint energy provides a metric for identifying the regions in the flow
where the adjoint term is diverging. Results for the vane from simulations
performed on the Titan supercomputer are demonstrated.Comment: ASME Turbo Expo 201
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