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
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids
Journal of Computational Physics
SIAM Journal on Scientific Computing
Vorticity boundary condition and related issues for finite difference schemes
Journal of Computational Physics
Essentially compact schemes for unsteady viscous incompressible flows
Journal of Computational Physics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
Spectral methods in MatLab
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
Finite difference schemes for incompressible flow based on local pressure boundary conditions
Journal of Computational Physics
Efficient computation of viscous incompressible flow
Efficient computation of viscous incompressible flow
A new class of truly consistent splitting schemes for incompressible flows
Journal of Computational Physics
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
An hybrid finite volume-finite element method for variable density incompressible flows
Journal of Computational Physics
Journal of Computational Physics
An implicit technique for solving 3D low Reynolds number moving free surface flows
Journal of Computational Physics
Open and traction boundary conditions for the incompressible Navier-Stokes equations
Journal of Computational Physics
Stable and accurate pressure approximation for unsteady incompressible viscous flow
Journal of Computational Physics
An unconditionally stable rotational velocity-correction scheme for incompressible flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Stable and Spectrally Accurate Schemes for the Navier-Stokes Equations
SIAM Journal on Scientific Computing
A gradient stable scheme for a phase field model for the moving contact line problem
Journal of Computational Physics
Hi-index | 31.50 |
We present numerical schemes for the incompressible Navier-Stokes equations based on a primitive variable formulation in which the incompressibility constraint has been replaced by a pressure Poisson equation. The pressure is treated explicitly in time, completely decoupling the computation of the momentum and kinematic equations. The result is a class of extremely efficient Navier-Stokes solvers. Full time accuracy is achieved for all flow variables. The key to the schemes is a Neumann boundary condition for the pressure Poisson equation which enforces the incompressibility condition for the velocity field. Irrespective of explicit or implicit time discretization of the viscous term in the momentum equation the explicit time discretization of the pressure term does not affect the time step constraint. Indeed, we prove unconditional stability of the new formulation for the Stokes equation with explicit treatment of the pressure term and first or second order implicit treatment of the viscous term. Systematic numerical experiments for the full Navier-Stokes equations indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition. Additionally, various numerical examples are presented, including both implicit and explicit time discretizations, using spectral and finite difference spatial discretizations, demonstrating the accuracy, flexibility and efficiency of this class of schemes. In particular, a Galerkin formulation is presented requiring only C0 elements to implement.