A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
An improvement of fractional step methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions
Journal of Computational Physics
Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2
SIAM Journal on Numerical Analysis
An analysis of the fractional step method
Journal of Computational Physics
Comments on the fractional step method
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows
Journal of Computational Physics
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
ACM Transactions on Mathematical Software (TOMS)
A staggered grid, high-order accurate method for the incompressible Navier-Stokes equations
Journal of Computational Physics
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
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This paper investigates the temporal accuracy of the velocity and pressure when explicit Runge-Kutta methods are applied to the incompressible Navier-Stokes equations. It is shown that, at least up to and including fourth order, the velocity attains the classical order of accuracy without further constraints. However, in case of a time-dependent gradient operator, which can appear in case of time-varying meshes, additional order conditions need to be satisfied to ensure the correct order of accuracy. Furthermore, the pressure is only first-order accurate unless additional order conditions are satisfied. Two new methods that lead to a second-order accurate pressure are proposed, which are applicable to a certain class of three- and four-stage methods. A special case appears when the boundary conditions for the continuity equation are independent of time, since in that case the pressure can be computed to the same accuracy as the velocity field, without additional cost. Relevant computations of decaying vortices and of an actuator disk in a time-dependent inflow support the analysis and the proposed methods.