Finite difference Laguerre-Legendre spectral method for the two-dimensional generalized Oldroyd-B fluid on a semi-infinite domain

• Published in: Applied mathematics and computation Vol. 402; p. 126138
• Main Authors: Chi, Xiaoqing, Jiang, Xiaoyun
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.08.2021
• Subjects: Generalized Oldroyd-B fluid; Laguerre-Legendre spectral method; Second order [formula omitted] scheme; Semi-infinite domain; Stability and convergence; Semi-infinite domain; Second order θ scheme; Laguerre-Legendre spectral method; Stability and convergence; Generalized Oldroyd-B fluid
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2021.126138

•A two-dimensional generalized Oldroyd-B fluid model on a semiinfinite domain is considered.•The time direction is approximated by the second order θ scheme combined with the weighted and shifted Gruünwald difference operator.•For the case of unbounded space, the mixed Laguerre-Legendre spectral method is proposed.•The theoretical analysis and numerical implementation of the scheme are discussed in detail.•The numerical method can improve the convergence accuracy with low computational cost. In this paper, we study the numerical solution for a two-dimensional generalized Oldroyd-B fluid flowing on a semi-infinite domain. The second order θ scheme with the weighted and shifted Grünwald difference operator is derived to approximate the time derivatives with orders in (0,2). For the case of unbounded space, the Laguerre-Legendre spectral method is proposed. The fully discrete scheme is obtained and proved to be stable, convergent with accuracy O(τ2+N(1−s)/2+M1−r), where τ is the time step size, N,M are the polynomial degrees. We also implement some numerical examples to further support the theoretical analysis.