Solving diffusion equations with rough coefficients in rough grids
Journal of Computational Physics
Journal of Computational Physics
Covolume Solutions of Three-Dimensional Div-Curl Equations
SIAM Journal on Numerical Analysis
A unified method for computing incompressible and compressible flows in boundary-fitted coordinates
Journal of Computational Physics
Conservation properties of unstructured staggered mesh schemes
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods
SIAM Journal on Numerical Analysis
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
Journal of Computational Physics
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Higher-order mimetic methods for unstructured meshes
Journal of Computational Physics
Discrete Laplacians on general polygonal meshes
ACM SIGGRAPH 2011 papers
HOT: Hodge-optimized triangulations
ACM SIGGRAPH 2011 papers
Journal of Computational Physics
Direct numerical simulation of turbulence using GPU accelerated supercomputers
Journal of Computational Physics
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
Journal of Computational Physics
Differential forms for scientists and engineers
Journal of Computational Physics
Journal of Computational Physics
Mimetic finite difference method
Journal of Computational Physics
Mimetic scalar products of discrete differential forms
Journal of Computational Physics
Symmetry-preserving discretization of Navier-Stokes equations on collocated unstructured grids
Journal of Computational Physics
Hi-index | 31.49 |
A general methodology for the solution of partial differential equations is described in which the discretization of the calculus is exact and all approximation occurs as an interpolation problem on the material constitutive equations. The fact that the calculus is exact gives these methods the ability to capture the physics of PDE systems well. The construction of both node and cell based methods of first and second-order are described for the problem of unsteady heat conduction - though the method is applicable to any PDE system. The performance of these new methods are compared to classic solution methods on unstructured 2D and 3D meshes for a variety of simple and complex test cases.