A combined method for solving 2D incompressible flow and heat transfer by spectral collocation method and artificial compressibility method. (September 2017) - Zhang, Jing-Kui; Dong, Hua; Zhou, En-Ze; Li, Ben-Wen; Tian, Xi-Yan
Highlights: A combined method SCM-ACM is developed firstly for incompressible flow. The discretized equations in matrix form are presented using the SCM-ACM. The SCM-ACM is used for exact solution, lid-driven flow and natural convection. The accuracy and characteristic of convergence are tested. Abstract: A combined method is developed for solving 2D steady incompressible flow and heat transfer by spectral collocation method (SCM) and artificial compressibility method (ACM). Instead of the steady governing equations, the unsteady artificial compressibility equations are introduced and solved. The steady results can be obtained by solving the unsteady equations when the pressure, velocity and temperature time derivatives approach to zero. The partial differential equations are discretized by SCM with Chebyshev polynomial and the spatial domain is discretized by the Chebyshev-Gauss-Lobbatto (CGL) collocation points. The artificial compressibility parameter c is investigated and determined firstly. Then, the accuracy of the SCM-ACM is tested by solving an exact solution with three time schemes (explicit scheme, implicit scheme and fourth order explicit Runge-Kutta scheme). Lastly, two classical cases (the lid-driven cavity flow and natural convection in a square cavity) are solved by the SCM-ACM with explicit scheme. The results show that the SCM-ACM can be used for the solving of incompressible flow and heat transfer, and high accuracy can be achieved after some calculation steps by the SCM-ACM especially with the fourth order explicit Runge-Kutta scheme. The SCM-ACM inherits the characteristics of exponential convergence and high accuracy from spectral method, and it is simplified, efficient and easy to implement which derives from the ACM. The SCM-ACM provides a new selection for the solution of incompressible flow and heat transfer.