A mixed spectral method for incompressible viscous fluid flow in an infinite strip

Abstract

Abstract. This paper considers the numerical simulation of incompressible viscous fluid flow in an infinite strip. A mixed spectral method is proposed using the Legendre approximation in one direction and the Legendre rational approximation in another direction. Numerical results demonstrate the efficiency of this approach. Some results on the mixed Legendre-Legendre rational approximation are established, from which the stability and convergence of proposed method follow.Mathematical subject classification: 65M70, 35Q30, 41A10, 41A20.

Curvilinearity and Orthogonality

“…General properties of orthogonal rational functions were studied in [2,13]. Specific examples of orthogonal rational functions on the semi-axis were given in [1,9,14]. Alternative orthogonal rational functions on a half-line which provide term-byterm increasing rate of decay at infinity were introduced in [7].…”