An Efficient Moving Mesh Method for a Model of Turbulent Flow in Circular Tubes (Journal of Computational Mathematics, 2018)
This paper presents an efficient moving mesh method to solve a nonlinear singularproblem with an optimal control constrained condition. The physical problem is governedby a new model of turbulent flow in circular tubes proposed by Luo et al. using Prandtl'smixing-length theory. Our algorithm is formed by an outer iterative algorithm for handlingthe optimal control condition and an inner adaptive mesh redistribution algorithm forsolving the singular governing equations. We discretize the nonlinear problem by using an upwinding approach, and the resulting nonlinear equations are solved by using the Newton-Raphson method. The mesh is generated and the grid points are moved by using thearc-length equidistribution principle. The numerical results demonstrate that proposedalgorithm is effective in capturing the boundary layers associated with the turbulent model.