Compact high-order upwind schemes using reconstruction from cell-averages are derived for application with the compressible three-dimensional Navier-Stokes equations. An adaptive-octree mesh, combined with the Adams-BashforthMoulton family of predictor-corrector schemes, provides a conservative highorder time-integration platform supporting localized h-refinement and timestep sub-cycling. Numer...

Dissipative numerical approximations to the linear advection equation are considered with respect to their behaviour in the limit of weak dissipation. The context is wave propagation under typical far-field conditions where grids are highly stretched and waves are underresolved. Three classes of schemes are analysed: explicit two-level (i) symmetric and (ii) upwind schemes of optimal accuracy a...

This study proposes one-dimensional advection–diffusion equation (ADE) with finite differences method (FDM) using implicit spreadsheet simulation (ADEISS). By changing only the values of temporal and spatial weighted parameters with ADEISS implementation, solutions are implicitly obtained for the BTCS, Upwind and Crank–Nicolson schemes. The ADEISS uses iterative spreadsheet solution technique. ...

Second-order accurate upwind and centered schemes are presented in a framework that facilitates their analysis and comparison. The upwind scheme employed consists of a reconstruction step (Van Leer 1977) followed by an upwind step (Roe 1981). The two centered schemes are of Lax-Friedrichs (L-F) type. They are the nonstaggered versions of the N-T scheme (called ORD in Nessyahu-Tadmor 1990) and t...

We study the relationship between finite volume and mixed finite element methods for the the hyperbolic conservation laws, and the closely related convection-diffusion equations.A general framework is proposed for the derivation and a functional framework is developed which could allow the analysis of relating finite volume (FV) schemes. We show via two nonstandard formulations, that numerous F...

The computations reported in this paper demonstrate the remarkable versatility of central schemes as black-box, Jacobian-free solvers for ideal magnetohydrodynamics (MHD) equations. Here we utilize a family of high-resolution, non-oscillatory central schemes for the approximate solution of the oneand two-dimensional MHD equations. We present simulations based on staggered grids of several MHD p...

A central-upwind finite-volume (CUFV) scheme for shallow-water model on a nonorthogonal equiangular cubed-sphere grid is developed, consequently extending the 1D reconstruction CUFV transport scheme developed by us. High-order spatial discretization based on weighted essentially non-oscillatory (WENO) is considered for this effort. The CUFV method combines the alluring features of classical upw...