A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Boundary conditions for incompressible flows
Journal of Scientific Computing
On error estimates of projection methods for Navier-Stokes equations: first-order schemes
SIAM Journal on Numerical Analysis
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
SIAM Journal on Scientific Computing
A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates
Journal of Computational Physics
Projection Method II: Godunov--Ryabenki Analysis
SIAM Journal on Numerical Analysis
On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes
Mathematics of Computation
Performance of under-resolved two-dimensional incompressible flow simulations, II
Journal of Computational Physics
The Accuracy of the Fractional Step Method
SIAM Journal on Numerical Analysis
Convergence of gauge method for incompressible flow
Mathematics of Computation
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
Algebraic splitting for incompressible Navier-Stokes equations
Journal of Computational Physics
Error Analysis of Pressure Increment Schemes
SIAM Journal on Numerical Analysis
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
A second-order boundary-fitted projection method for free-surface flow computations
Journal of Computational Physics
Runge-Kutta-Chebyshev projection method
Journal of Computational Physics
A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics
Journal of Computational Physics
Hi-index | 31.46 |
In this paper, a continuous projection method is designed and analyzed. The continuous projection method consists of a set of partial differential equations which can be regarded as an approximation of the Navier-Stokes (N-S) equations in each time interval of a given time discretization. The local truncation error (LTE) analysis is applied to the continuous projection methods, which yields a sufficient condition for the continuous projection methods to be temporally second order accurate. Based on this sufficient condition, a fully second order accurate discrete projection method is proposed. A heuristic stability analysis is performed to this projection method showing that the present projection method can be stable. The stability of the present scheme is further verified through numerical experiments. The second order accuracy of the present projection method is confirmed by several numerical test cases.