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Analysis and implementation of the spectral difference method on triangles


Required Education : master or engineering school
Start date : 1 March 2017
Mission duration : 6 months
Salary : 650,00 euros/month


The CFD team develops and maintains advanced codes for fluid mechanics dedicated to industrial problems. We currently work with ONERA, Airbus, SAFRAN (Snecma / Turbomeca) and EDF.

Maintaining our expertise on CFD needs to propose new solutions or to adapt solutions published in the literature to industrial meshes / configurations. It is clear that turbulence-averaged simulations (RANS and URANS approaches) with second-order schemes are dedicated to design but they are not well adapted to compute off-design configurations. Off-design configurations need unsteady computations and high order (spatial and temporal) schemes to propagate flow physics inside the computational domain. Aeroacoustic, vortex-dominated flow and some turbulence-driven phenomena are examples of application of high order schemes.



The spectral difference approach is a recent high order way to discretize partial differential equations on unstructured grids. They are based on a polynomial reconstruction of data inside each mesh cell (Spectral Approach). Conservative fields are not assumed to be continuous at the mesh interface and one or several Riemann problems need to be computed on an interface. More information on the spectral difference approach and our solver called JAGUAR are available on http://www.cerfacs.fr/~puigt/jaguar.html .

At the present time, the spectral difference method is well defined for segments, quadrangles and hexahedra: a 1D treatment is performed direction per direction.  Balan et al. (http://www.sciencedirect.com/science/article/pii/S0021999111006978) proposed a 2D  extension of the spectral difference method on triangles for an order of accuracy of 2 and 3. The goal is to reproduce the current status of the SD method on triangles during the training period. After implementation in a 2D prototype, several computations will be performed to assess the capability of the current SD implementation. Finally, the last aspect to analyse will concern the extension to higher degree of accuracy: is the extension straightforward? Which are the key points? Which are the current limitations?

For this trainee period, we look for a student who

  • Desires to work in a team
  • Has a good knowledge in Fortran and in programming
  • Has a good knowledge in applied mathematics for CFD
  • Has a basic knowledge in numerical schemes for convection, especially in classical 1D schemes
  • Takes initiative.

Contacts :

Name: Puigt Guillaume
Phone: +33 5 61 19 30 94
Email: puigt[at]cerfacs.fr

Name: Boussuge Jean-François
Phone: +33 5 61 19 30 62
Email: boussuge[at]cerfacs.fr


This training position can continue by a PhD thesis on the same subject. Interactions with colleagues from ONERA are also planned.