Discontinuous Galerkin Method for Solving Steady and Unsteady Incompressible Navier Stokes Equations

Purpose: To develop high order discontinuous galerkin method for solving steady and unsteady incompressible flow based on artificial compressibility method. Design/methodology/approach: This paper uses discontinuous galerkin finite element procedure which is based on the artificial compressibility technique in connection with a dual time stepping approach. A second order implicit discretization is applied to achieve the required accuracy in real time while an explicit low storage fourth order Runge Kutta scheme is used to march in the pseudo-time domain. A nodal high order discontinuous galerkin finite element is used for the spatial discretization. Findings: Provides stable and accurate methods for solving incompressible viscous flows compared with previous numerical results and experimental results. Research limitations: It is limited to two-dimensional steady and unsteady laminar viscous flow.Practical implications – A very useful source of information and favorable advice for people is applied to piping system and low speed aerodynamics. Originality: This works presents an extension of the previous work of [1] and [2] to time and space accurate method for solving unsteady incompressible flows