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35Th CFD/ADIGMA course on very high order discretization methods article pay-per-view 25€/article

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Schemes with order of accuracy higher than two have become an important subject of research in CFD, and the perspective of applying them in industrial aeronautical context is realistic within the next decade. In these course notes the basics and state of the art of the following methods are discussed in detail: Discontinuous Galerkin Finite Element methods; Spectral Element and Spectral Finite Volume methods; Residual Distribution methods. An effort was made to introduce the methods on model problems before applying them to the compressible and incompressible Navier-Stokes equations. Basic ideas like convergence analysis, a priori and duality based error estimates or adjoint consistency and shock capturing are discussed in much detail. Implementation issues are treated, such as efficient quadrature, parallelization, memory consumption and treatment of curved walls. Applications targeted are mainly in the area of steady and unsteady compressible aerodynamics, including transonic and supersonic flow.


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Schemes with order of accuracy higher than two have become an important subject of research in CFD, and the perspective of applying them in industrial aeronautical context is realistic within the next decade. In these course notes the basics and state of the art of the following methods are discussed in detail: Discontinuous Galerkin Finite Element methods; Spectral Element and Spectral Finite Volume methods; Residual Distribution methods. An effort was made to introduce the methods on model problems before applying them to the compressible and incompressible Navier-Stokes equations. Basic ideas like convergence analysis, a priori and duality based error estimates or adjoint consistency and shock capturing are discussed in much detail. Implementation issues are treated, such as efficient quadrature, parallelization, memory consumption and treatment of curved walls. Applications targeted are mainly in the area of steady and unsteady compressible aerodynamics, including transonic and supersonic flow.

The course was organized in collaboration with the European Union FP6 targeted research project ADIGMA, for which it serves as a dissemination activity. The notes bring together a balanced mix of contributions from European and American top researchers in the field.

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