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Home > Teams > MOST team: Turbulence Modelling and Simulation > Research activity

Axe 1 - Axis 1 - Development of a High Order Framework for finite volume methods on unstructured grids

Postdoctoral works of Manuel Bernard

Financial support : PSPC INNOV’HYDRO

Collaboration : G. Lartigue and V. Moureau (CORIA, Rouen)

The aim of this work is to improve the accuracy of numerical schemes on unstructured meshes in finite volume method context. Indeed, discretization errors generally increase while grid quality get worse, i.e. while shape of control volumes disgress from regular body. Thus, use of high order methods permits either to lower the error level for a given mesh, or to use coarser mesh for a given level of error. This method is based on three ingredients :

  • First, as the data available in finite volume method is constant over each control volume, it is necessary to deconvolute it in order to obtain its corresponding nodal value.
  • Once the accurate nodal values of the data and its successive derivatives are known, it is possible to perform Tayor series expansions anywhere in the domain.
  • Finally, flux are integrated accurately over each control volumes surface.

The main advantage of this method compared to other high order methods lies is the fact that, up to 3rd order implementation, the stencil remains compact (only direct neighbours are used). This is particularly interesting in a high performance computing context as it ensures the good behaviour of parallel simulation based on domain decomposition technique.

This method can be used in various applications, for exemple : mesh-to-mesh interpolation, curvature computation for level-set methods, convective and diffusive flux integration. Figure 1 represents the spatial distribution of a scalar bump after one convection period (one turnover through periodic domain) using a constant and uniform flow field. We observe that, by using the high order framework developed during this study, the accuracy of the signal transported is improved : iso-contours are regular and scalar is bounded between 0 and 1.


Peer-reviewed Publications

Bernard, M., Lartigue, G., Balarac, G., Moureau, V., & Puigt, G. (2020). A framework to perform high-order deconvolution for finite-volume method on simplicial meshes. International Journal for Numerical Methods in Fluids, 92(11), 1551–1583.