Voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids

Voronoi cell nite di erence method for the di usion operator on arbitrary unstructured grids

Voronoi cells and the notion of natural neighbours are used to develop a nite di erence method for the di usion operator on arbitrary unstructured grids. Natural neighbours are based on the Voronoi diagram, which partitions space into closest-point regions. The Sibson and the Laplace (non-Sibsonian) interpolants which are based on natural neighbours have shown promise within a Galerkin framewor...

Voronoi-cell finite difference method for accurate electronic structure calculation of polyatomic molecules on unstructured grids

We introduce a new numerical grid-based method on unstructured grids in the three-dimensional real-space to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a discrete Laplacian operator based on Voronoi cells and their natural neighbors, featuring high adaptivity and simplicity. To resolve multicenter Coulomb singularity in ...

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

SPE 163649: The Multiscale Finite Volume Method on Unstructured Grids

Finding a pressure solution for large-scale reservoirs that takes into account fine-scale heterogeneities can be very computationally intensive. One way of reducing the workload is to employ multiscale methods that capture local geological variations using a set of reusable basis functions. One of these methods, the multiscale finite-volume (MsFV) method is well studied for 2D Cartesian grids, ...

A high-order spectral difference method for unstructured dynamic grids

A high-order spectral difference (SD) method has been further extended to solve the three dimensional compressible Navier–Stokes (N–S) equations on deformable dynamic meshes. In the SD method, the solution is approximated with piece-wise continuous polynomials. The elements are coupled with common Riemann fluxes at element interfaces. The extension to deformable elements necessitates a time-dep...