A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific Computing
A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates
Journal of Computational Physics
Explicit Runge-Kutta methods for parabolic partial differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Approximate Projection Methods: Part I. Inviscid Analysis
SIAM Journal on Scientific Computing
An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
RKC time-stepping for advection-diffusion-reaction problems
Journal of Computational Physics
Stability of approximate projection methods on cell-centered grids
Journal of Computational Physics
On stabilized integration for time-dependent PDEs
Journal of Computational Physics
A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems
Journal of Computational Physics
Performance of stabilized explicit time integration methods for parallel air quality models
SpringSim '07 Proceedings of the 2007 spring simulation multiconference - Volume 2
Journal of Computational Physics
Semi-Lagrangian Runge-Kutta Exponential Integrators for Convection Dominated Problems
Journal of Scientific Computing
Mathematics and Computers in Simulation
Stabilized explicit Runge-Kutta methods for multi-asset American options
Computers & Mathematics with Applications
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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.