A main issue in nonstationary, compressible magnetohydrodynamic (MHD) simulations is controlling the divergence of the magnetic flux. This paper presents a general procedure showing how to modify the intercell fluxes in a conservative MHD finite volume code such that the scheme becomes locally divergence preserving. That is, a certain discrete divergence operator vanishes exactly during the ent...

in this paper high order multidimensional positive definite advection transport algorithm (mpdata) and compact finite difference methods are applied to one (1-d) and two-dimensional (2-d) advection equation. mpdata methods are designed based on upwind scheme using anti-diffusive velocity that compensates diffusivity of upwind method. in high order compact method one implicit relation between a ...

This paper deals with the numerical solution of the two-dimensional transport equation on a sphere. Two diierent mass-conservative advection schemes are considered The rst is the standard rst-order scheme using forward Euler in time and rst-order upwind in space. The second scheme uses for time stepping a second-order explicit two-step method and for the space discretization a ux-limited, third...

In this paper, we present total variation diminishing (TVD) multigrid methods for computing the steady state solutions for systems of hyperbolic conservation laws. An efficient multigrid method should avoid spurious numerical oscillations. This can be achieved by designing methods which preserve monotonicity and TVD properties through the use of upwind interpolation and restriction techniques. ...

This paper presents an analysis of Godunov scheme in the low Mach number regime. We study the Riemann problem and show that the interface pressure contains acoustic waves of order OðM Þ where M is the reference Mach number even if the initial data are well-prepared and contain only pressure fluctuations of order OðM2 Þ. We then propose to modify the fluxes computed by Godunov type schemes by so...

The diiusive characteristics of two upwind schemes, multi-dimensional uctuation splitting and dimensionally-split nite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear...

Some new nonlinear analytical solutions are found for axisymmetric horizontal flows dominated by strong heat sources. These flows are common in multiscale atmospheric and oceanic flows such as hurricane embryos and ocean gyres. The analytical solutions are illustrated with several examples. The proposed exact solutions provide analytical support for previous numerical observations and can be al...

A numerical technique, composed of the Van Leer-Tai-Powell optimization and a modified procedure, is applied to design multistage schemes that give optimal damping of high frequencies for given upwind-biased spatial differencing with implicit and explicit residual smoothing. The analysis is done for a scalar convection equation in one space dimension. The object of this technique is to make the...

Based on the well-posedness of the stationary Wigner equation with inflow boundary conditions given in [1], we prove without any additional prerequisite conditions that the solution of the Wigner equation with symmetric potential and inflow boundary conditions will be symmetric. This improve the result in [6] which depends on the convergence of solution formulated in the Neumann series. By nume...