Difference schemes for the Navier-Stokes equations on a net consisting of Dirichlet cells
USSR Computational Mathematics and Mathematical Physics
Direct numerical simulation of turbulence on the Connection Machine
CFD '92 Proceedings of the conference on Parallel computational fluid dynamics '92 : implementations and results using parallel computers: implementations and results using parallel computers
Local reconstruction of a vector field from its normal components on the faces of grid cells
Journal of Computational Physics
Conservation properties of unstructured staggered mesh schemes
Journal of Computational Physics
The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods
SIAM Journal on Numerical Analysis
COVOLUME SOLUTIONS OF THREE DIMENSIONAL DIV-CURL EQUATIONS
COVOLUME SOLUTIONS OF THREE DIMENSIONAL DIV-CURL EQUATIONS
Analysis of an exact fractional step method
Journal of Computational Physics
A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows
Journal of Computational Physics
A numerical method for large-eddy simulation in complex geometries
Journal of Computational Physics
Higher-order mimetic methods for unstructured meshes
Journal of Computational Physics
Discrete calculus methods for diffusion
Journal of Computational Physics
Symmetry-preserving upwind discretization of convection on non-uniform grids
Applied Numerical Mathematics
Energy-preserving integrators for fluid animation
ACM SIGGRAPH 2009 papers
Multiplicable discrete operators in PDE solvers
FANDB'09 Proceedings of the 2nd WSEAS international conference on Finite differences, finite elements, finite volumes, boundary elements
Journal of Computational Physics
Computers & Mathematics with Applications
Energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
Differential forms for scientists and engineers
Journal of Computational Physics
Symmetry-preserving discretization of Navier-Stokes equations on collocated unstructured grids
Journal of Computational Physics
Hi-index | 31.50 |
A three-dimensional unstructured mesh discretization of the rotational from of the incompressible Navier-Stokes is presented. The method uses novel and highly efficient algorithms for interpolating the velocity vector and constructing the convention term. The resulting discretization is shown to conserve mass, kinetic energy, and vorticity to machine precision both locally and globally. The spatial accuracy of the method is analyzed and found to be second order on regular meshes and first order on irregular meshes. The numerical efficiency, accuracy, and conservation properties of the method are tested on three-dimensional meshes and found to be in agreement with theory.