Marcel Vinokur

TL;DR: A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed, which is much simpler than the discontinuous Galerkin and spectral volume methods for un Structured grids.

TL;DR: In this article, the time-dependent, three-dimensional incompressible Navier-Stokes equations are solved in generalized coordinate systems by means of a fractional-step method whose primitive variable formulation uses as dependent variables, in place of the Cartesian components of the velocity: pressure (defined at the center of the computational cell), and volume fluxes across the faces of the cells.

TL;DR: It is shown that if all grid cells are partitioned into structured sub-cells in a similar manner, the discretizations become universal, and are reduced to the same weighted sum of unknowns involving just a few simple adds and multiplies.

TL;DR: Yee et al. as mentioned in this paper proposed a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties for the compressible Euler equations.

TL;DR: A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed, based on the differential form to attain a simpler formulation and higher efficiency.