Comparison of Pressure-Based Runge-Kutta Schemes for Unsteady Incompressible Flows

摘要

A new line of pressure-based algorithms using implicit Runge-Kutta schemes are developed and compared with an explicit Runge-Kutta based SIMPLER algorithm and the traditional Crank-Nicolson based SIMPLER algorithm for unsteady incompressible flows. This paper establishes that once the pressure field is obtained, the velocity field can be solved by using various versions of the Runge-Kutta time integration method. The new algorithms are shown to accurately simulate both steady and unsteady flow problems. Metrics such as maximum possible time step and unsteady characteristics of the candidate problems are compared. For an unsteady simulation of normal flow on a flat plate, the explicit Runge-Kutta based algorithm is nine times faster than the conventional SIMPLER algorithm, while the implicit Runge-Kutta methods are up to 24 times faster.