Reduced basis method applied to a convective stability problem

Journal of Mathematics in Industry

Francisco Pla¹  Henar Herrero¹  Yvon Maday² 

[1] Dpto. Matemáticas, Univ. Castilla-La Mancha;Laboratoire Jacques-Louis Lions, UMR 7598, Sorbone Universités, UPMC Univ. Paris 06;

关键词: Reduced basis;    Linear stability;    Eigenvalues and eigenfunctions;    Bifurcation;    Rayleigh Bénard instability;    Convective flow;   

DOI  :  10.1186/s13362-018-0043-6

来源: DOAJ

【 摘 要 】

Abstract Numerical reduced basis methods are instrumental to solve parameter dependent partial differential equations problems in case of many queries. Bifurcation and instability problems have these characteristics as different solutions emerge by varying a bifurcation parameter. Rayleigh–Bénard convection is an instability problem with multiple steady solutions and bifurcations by varying the Rayleigh number. In this paper the eigenvalue problem of the corresponding linear stability analysis has been solved with this method. The resulting matrices are small, the eigenvalues are easily calculated and the bifurcation points are correctly captured. Nine branches of stable and unstable solutions are obtained with this method in an interval of values of the Rayleigh number. Different basis sets are considered in each branch. The reduced basis method permits one to obtain the bifurcation diagrams with much lower computational cost.

【 授权许可】

Unknown