A priori reduction method for solving the two-dimensional Burgers' equations

Cyrille Allery (1) , Aziz Hamdouni (1) , David Ryckelynck (2) , N. Verdon

1 LEPTIAB - Laboratoire d'Étude des Phénomènes de Transfert et de l'Instantanéité : Agro-industrie et Bâtiment
2 CDM - Centre des Matériaux

The two-dimensional Burgers' equations are solved here using the A Priori Reduction method. This method is based on an iterative procedure which consists in building a basis for the solution where at each iteration the basis is improved. The method is called a priori because it does not need any prior knowledge of the solution, which is not the case if the standard Karhunen-Loéve decomposition is used. The accuracy of the APR method is compared with the standard Newton-Raphson scheme and with results from the literature. The APR basis is also compared with the Karhunen-Loéve basis.

Mots clés: Reduced-order model; Burgers' equations; Karhunen-Loéve decomposition; Proper orthogonal decomposition (POD)

Domaines: Matériaux

Cyrille Allery, Aziz Hamdouni, David Ryckelynck, N. Verdon. A priori reduction method for solving the two-dimensional Burgers' equations. Applied Mathematics and Computation, 2011, 217, pp.6671-6679. ⟨10.1016/j.amc.2011.01.065⟩. ⟨hal-00585095⟩