Boundary conditions for incompressible flows
Journal of Scientific Computing
Stability of pressure boundary conditions for Stokes and Navier-Stokes equations
Journal of Computational Physics
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
SIAM Journal on Numerical Analysis
Stabilization of Low-order Mixed Finite Elements for the Stokes Equations
SIAM Journal on Numerical Analysis
Understanding And Implementing the Finite Element Method
Understanding And Implementing the Finite Element Method
Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces
Journal of Computational Physics
A lagged implicit segregated data reconstruction procedure to treat open boundaries
Journal of Computational Physics
An unconditionally stable rotational velocity-correction scheme for incompressible flows
Journal of Computational Physics
Improvements on open and traction boundary conditions for Navier-Stokes time-splitting methods
Journal of Computational Physics
Stable and Spectrally Accurate Schemes for the Navier-Stokes Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
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We present numerical schemes for the incompressible Navier-Stokes equations (NSE) with open and traction boundary conditions. We use pressure Poisson equation (PPE) formulation and propose new boundary conditions for the pressure on the open or traction boundaries. After replacing the divergence free constraint by this pressure Poisson equation, we obtain an unconstrained NSE. For Stokes equation with open boundary condition on a simple domain, we prove unconditional stability of a first order semi-implicit scheme where the pressure is treated explicitly and hence is decoupled from the computation of velocity. Using either boundary condition, the schemes for the full NSE that treat both convection and pressure terms explicitly work well with various spatial discretizations including spectral collocation and C^0 finite elements. Moreover, when Reynolds number is of O(1) and when the first order semi-implicit time stepping is used, time step size of O(1) is allowed in benchmark computations for the full NSE. Besides standard stability and accuracy check, various numerical results including flow over a backward facing step, flow past a cylinder and flow in a bifurcated tube are reported. Numerically we have observed that using PPE formulation enables us to use the velocity/pressure pairs that do not satisfy the standard inf-sup compatibility condition. Our results extend that of Johnston and Liu [H. Johnston, J.-G. Liu, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term. J. Comp. Phys. 199 (1) (2004) 221-259] which deals with no-slip boundary conditions only.