Runge–Kutta–Chebyshev projection method

• Published in: Journal of computational physics Vol. 219; no. 2; pp. 976 - 991
• Main Authors: Zheng, Zheming, Petzold, Linda
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 10.12.2006; Elsevier
• Subjects: Approximation; Computation; Computational techniques; Derivatives; Exact sciences and technology; Extended stability regions; Incompressible flow; Incompressible Navier–Stokes equations; Mathematical analysis; Mathematical methods in physics; Mathematical models; Navier-Stokes equations; Physics; Projection; Projection methods; Runge-Kutta method; Runge–Kutta–Chebyshev method; Incompressible flow; Extended stability regions; Incompressible Navier–Stokes equations; Runge–Kutta–Chebyshev method; Projection methods; Second order; Runge-Kutta- Chebyshev method; Digital simulation; Stability region; Calculation methods; Incompressible Navier-Stokes equations; Differential equations; Calculation; Runge-Kutta methods; Diffusion; Navier-Stokes equations
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2006.07.005

In this paper a fully explicit, stabilized projection method called the Runge–Kutta–Chebyshev (RKC) projection method is presented for the solution of incompressible Navier–Stokes systems. This method preserves the extended stability property of the RKC method for solving ODEs, and it requires only one projection per step. An additional projection on the time derivative of the velocity is performed whenever a second-order approximation for the pressure is desired. We demonstrate both by numerical experiments and by order analysis that the method is second order accurate in time for both the velocity and the pressure. Being explicit, the RKC projection method is easy to implement and to parallelize. Hence it is an attractive candidate for the solution of large-scale, moderately stiff, diffusion-like problems.