We present in this paper a stability study concerning nite volume schemes applied to the Maxwell system. A stability condition is proved for the rst-order upwind scheme using a rectangular mesh. Stability comparisons between the Yee scheme and the nite volume formulation are proposed. We also compare the stability domains obtained when considering the Maxwell system and the convection equation.

Finite Volume upwind schemes for the Euler equations in the low Mach number regime face a problem of lack of convergence toward the solutions of the incompressible system. However, if applied to cell centered triangular grid, this problem disappears and convergence toward the incompressible solution is recovered. Extending the work of [3] that prove this result for regular triangular grid, we g...

Direct numerical simulation (DNS) has become a powerful tool in studying fundamental phenomena of laminar-turbulent transition of high-speed boundary layers. Previous DNS studies of supersonic and hypersonic boundary layer transition have been limited to perfect-gas flow over flat-plate boundary layers without shock waves. For hypersonic boundary layers over realistic blunt bodies, DNS studies ...

This paper covers the construction and research of a scheme to solve problem with nonlinear dispersion wave equations, described by model Korteweg–de Vries equation. The article proposes approximating equation based on improved “Upwind Leapfrog” schemes. Its difference operator is linear combination operators “Standard schemes, while modified obtained from schemes optimal weight coefficients. C...

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwin...

A new version of the residual-based scheme has been developping for computing compressible ow on unstructured grids. The third-order and forth-order of this scheme will be tested by the pure advection case and several cases governing by the Euler equations. Then this new version is compared with the classical upwind schemes such as Roe scheme.

Numerical solutions are never exact due to errors emanating from the scheme used in discretizing governing equations and flow domain. For convection-diffusion flow, magnitude of these varies depending on interpolate nodal values quantities interfaces. An interpolation that minimizes would give results consistent experimental results. This paper documents performance three linear schemes; upwind...

A nonlinear first-order boundary value problem with discontinuous solutions is considered. It arises in the study of gasflow through a duct and allows, in general, for multiple solutions. New convergence results for three difference schemes are presented and the sharpness of numerical layers is established. For the EO-scheme, stability of a physically correct solution with respect to time evolu...