Unsteady solution of incompressible Navier-Stokes equations
Journal of Computational Physics
An upwind differencing scheme for the incompressible Navier-Stokes equations
Applied Numerical Mathematics
Effects of the computational time step on numerical solutions of turbulent flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A numerical method for solving incompressible viscous flow problems
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Comparison of second- and fourth-order discretizations for multigrid Poisson solvers
Journal of Computational Physics
Performance of under-resolved two-dimensional incompressible flow simulations, II
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Fast and high accuracy multigrid solution of the three dimensional Poisson equation
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
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow
Journal of Computational Physics
Journal of Computational Physics
Computational Engineering - Introduction to Numerical Methods
Computational Engineering - Introduction to Numerical Methods
An immersed boundary method for complex incompressible flows
Journal of Computational Physics
A novel algorithm for incompressible flow using only a coarse grid projection
ACM SIGGRAPH 2010 papers
Hi-index | 31.45 |
We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. After solving the Poisson equation on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. A particular version of the method is applied here to the vorticity-stream function, primitive variable, and vorticity-velocity formulations of incompressible Navier-Stokes equations. We compute several benchmark flow problems on two-dimensional Cartesian and non-Cartesian grids, as well as a three-dimensional flow problem. The method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field, which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid. A linear acceleration rate is obtained for all the cases we consider due to the linear-cost elliptic Poisson solver used, with reduction factors in computational time between 2 and 42. The computational savings are larger when a suboptimal Poisson solver is used. We also find that the computational savings increase with increasing distortion ratio on non-Cartesian grids, making the CGP method a useful tool for accelerating generalized curvilinear incompressible flow solvers.