A third-order accurate in time method for boundary layer flow problems

Abstract

The boundary layer flow problem arises in numerous industrial applications. As a result, it has received considerable attention over the last five decades which has involved developing numerical procedures to approximate the solution of time-dependent parabolic and first-order hyperbolic partial differential equations (PDEs). In this paper, we develop a method that guarantees third-order temporal accuracy. Stability conditions are derived using Von Neumann stability analysis that guarantee convergence of the proposed algorithm. In addition, we present a consistency analysis. The performance of the proposed algorithm is demonstrated for linear and nonlinear parabolic PDEs that extend the models for the Stokes first and second problems by incorporating the effect of heat transfer using viscous dissipation and thermal radiation. A comparison of performance in terms of convergence rate and estimation accuracy is shown.