A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Journal of Scientific Computing
On error estimates of projection methods for Navier-Stokes equations: first-order schemes
SIAM Journal on Numerical Analysis
An analysis of the fractional step method
Journal of Computational Physics
Projection method I: convergence and numerical boundary layers
SIAM Journal on Numerical Analysis
On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes
Mathematics of Computation
The Accuracy of the Fractional Step Method
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
A semi-Lagrangian high-order method for Navier-Stokes equations
Journal of Computational Physics
A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations
Journal of Scientific Computing
Velocity-Correction Projection Methods for Incompressible Flows
SIAM Journal on Numerical Analysis
A new class of truly consistent splitting schemes for incompressible flows
Journal of Computational Physics
Journal of Computational Physics
Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows
Journal of Scientific Computing
Open and traction boundary conditions for the incompressible Navier-Stokes equations
Journal of Computational Physics
An eigen-based high-order expansion basis for structured spectral elements
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
We present an unconditionally stable splitting scheme for incompressible Navier-Stokes equations based on the rotational velocity-correction formulation. The main advantages of the scheme are: (i) it allows the use of time step sizes considerably larger than the widely-used semi-implicit type schemes: the time step size is only constrained by accuracy; (ii) it does not require the velocity and pressure approximation spaces to satisfy the usual inf-sup condition: in particular, the equal-order finite element/spectral element approximation spaces can be used; (iii) it only requires solving a pressure Poisson equation and a linear convection-diffusion equation at each time step. Numerical tests indicate that the computational cost of the new scheme for each time step, under identical time step sizes, is even less expensive than the semi-implicit scheme with low element orders. Therefore, the total computational cost of the new scheme can be significantly less than the usual semi-implicit scheme.