Numerical Properties and GPU Implementation of a High Order Finite Volume Scheme

Speaker: Jean-Marie Le Gouez, The French Aerospace Lab ONERA
April 5, 2016

Presentation

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Abstract

We present the main features of a spatially high order Finite Volume scheme for compressible ﬂuid ﬂows. This scheme is based on a polynomial reconstruction by Weighted Least Squares of conservative variable or flux densities fields only known from their cell averages. The subsequent projection of these polynomials on the interfaces to compute the integral of exchanged normal ﬂux densities is extremely CPU efﬁcient and does not make use of limiters. However it requires a very high memory throughput on very wide stencils to reach the objective 4th order on irregular unstructured grid systems. The spatial resolution of the scheme and its extension to high order chimera interpolation are verified for linear convection and diffusion on unit squares meshed with a variety of triangles, and for the convection of an isentropic vortex across moving interfaces and coarse grids of arbitrary quadrangles. The solver is then tested on the case of the viscous Taylor-Green vortex in the conditions of the High order CFD Workshop. The optimized multi-GPU version of the code is used and systematic tests of strong and weak scalability are performed on a full hybrid cluster using up to 128 NVIDIA Tesla K20Xm. By approaching the main memory peak bandwidth through coalesced data access, the solution covering 20 time units for 512**3 dofs per equation is obtained in only 5 hours of wall-clock on 16 NVIDIA TESLA K20Xm boards. A derived version is being developed to deploy advanced features such as dynamic zonal refinement on octree type embedded grid systems, making an extensive use of hardware accelerators.

Biography

Jean-Marie Le Gouez is a senior research scientist at ONERA CFD department in Chatillon, in the Paris suburbs. He graduated from Ecole Polytechnique in Paris and holds a Masters Degree in Mechanical engineering from Stanford University. After over 20 years in developing CFD methods for incompressible, free surface flows and FSI, he joined Onera in 2006 as head of the CFD Department. He is now doing research on spatial schemes, high performance computing and modular software architecture in the research unit on novel software deployment in the same department.

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