Integral conditions for the pressure in the computation of incompressible viscous flows
Journal of Computational Physics
A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Journal of Computational Physics
Comparison of finite-volume numerical methods with staggered and colocated grids
Computers and Fluids
The numerical solution of parabolic free boundary problems arising from thin film flows
Journal of Computational Physics
Implicit solution of the incompressible Navier-Stokes equations on a non-staggered grid
Journal of Computational Physics
On the rotation and skew-symmetric forms for incompressible flow simulations
Applied Numerical Mathematics - Special issue: Transition to turbulence
An analysis of the fractional step method
Journal of Computational Physics
Journal of Computational Physics
Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows
Journal of Computational Physics
A unified method for computing incompressible and compressible flows in boundary-fitted coordinates
Journal of Computational Physics
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
An accurate compact treatment of pressure for colocated variables
Journal of Computational Physics
The Accuracy of the Fractional Step Method
SIAM Journal on Numerical Analysis
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
Stability of pressure boundary conditions for Stokes and Navier-Stokes equations
Journal of Computational Physics
A semi-implicit method for resolution of acoustic waves in low Mach number flows
Journal of Computational Physics
Finite difference schemes for incompressible flow based on local pressure boundary conditions
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
Semi-implicit projection methods for incompressible flow based on spectral deferred corrections
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Pressure Correction Algebraic Splitting Methods for the Incompressible Navier-Stokes Equations
SIAM Journal on Numerical Analysis
High order accurate solution of the incompressible Navier-Stokes equations
Journal of Computational Physics
A 2D compact fourth-order projection decomposition method
Journal of Computational Physics
Journal of Computational Physics
The Shifted Box Scheme for Scalar Transport Problems
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Higher-order mimetic methods for unstructured meshes
Journal of Computational Physics
On the influence of different stabilisation methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
Journal of Computational Physics
A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics
Journal of Computational Physics
A Higher-Order Formulation of the Mimetic Finite Difference Method
SIAM Journal on Scientific Computing
Mimetic finite difference method for the Stokes problem on polygonal meshes
Journal of Computational Physics
A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
We present a new finite-difference numerical method to solve the incompressible Navier-Stokes equations using a collocated discretization in space on a logically Cartesian grid. The method shares some common aspects with, and it was inspired by, the Box scheme. It uses centered second-order-accurate finite-difference approximations for the spatial derivatives combined with semi-implicit time integration. The proposed method is constructed to ensure discrete conservation of mass and momentum by discretizing the primitive velocity-pressure form of the equations. The continuity equation is enforced exactly (to machine accuracy) at the collocated locations, whereas the momentum equations are evaluated in a staggered manner. This formulation preempts the appearance of spurious pressure modes in the embedded elliptic problem associated with the pressure. The method shows uniform order of accuracy, both in space and time, for velocity and pressure. In addition, the skew-symmetric form of the non-linear advection term of the Navier-Stokes equations improves discrete conservation of kinetic energy in the inviscid limit, to within the order of the truncation error of the time integrator. The method has been formulated to accommodate different types of boundary conditions; fully periodic, periodic channel, inflow-outflow and lid-driven cavity; always ensuring global mass conservation. A novel aspect of this finite-difference formulation is the derivation of the discretization near boundaries using the weak form of the equations, as in the finite element method. The method of manufactured solutions is utilized to perform accuracy analysis and verification of the solver. To assess the applicability of the new method presented in this paper, four realistic flow problems have been simulated and results are compared with those in the literature. These cases include a lid-driven cavity, backward-facing step, Kovasznay flow, and fully developed turbulent channel.