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

Abstract

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.