In this talk we consider the numerical difficulties that arise when horizontal advection is coupled with chemistry on a sphere, using operator splitting. From a numerical point of view, these two processes are the most difficult parts of an atmospheric model for global studies. The advection process is solved on a uniform grid and on a so-called reduced grid, where less cells are used near the ...

the starting behavior of a supersonic axisymmetric mixed compression air intake was numerically investigated. the code solves reynolds-averaged navier–stokes equations using an explicit finite volume method in a structured grid by the roe flux difference splitting scheme. further, it uses the baldwin–lomax algebraic model to compute the turbulent viscosity coefficient. the correct method of sur...

This paper describes the development of the stream-tube based dispersion model for modeling contaminant transport in open channels. The operator-splitting technique is employed to separate the 2D contaminant transport equation into the pure advection and pure dispersion equations. Then the total variation diminishing (TVD) schemes are combined with the second-order Lax-Wendroff and third–order ...

This paper presents a high-resolution numerical method for solving mass transport problems involving advection and anisotropic diffusion in shallow water based on unstructured mesh. An alternating operator-splitting technique is adopted to advance the numerical solution with advection and diffusion terms solved separately in two steps. By introducing a new r-factor into the Total Variation Dimi...

Abstract This paper is concerned with the rigorous error analysis of a fully discrete scheme obtained by using central fluxes discontinuous Galerkin (dG) method in space and Peaceman–Rachford splitting time. We apply to general class wave-type problems show that resulting approximations as well derivatives thereof satisfy bounds order polynomial degree used dG discretization two In particular, ...

The aim of this paper is to construct semi-implicit numerical schemes for a two-phase (two-fluid) flow model, allowing for violation of the CFL criterion for sonic waves while maintaining a high level of accuracy and stability on volume fraction waves. By using an appropriate hybridization of a robust implicit flux and an upwind explicit flux, we obtain a class of first-order schemes, which we ...

Spectral deferred correction is a flexible technique for constructing high-order, stiffly-stable time integrators using a low order method as a base scheme. Here we examine their use in conjunction with splitting methods to solve initial-boundary value problems for partial differential equations. We exploit their close connection with implicit Runge–Kutta methods to prove that up to the full ac...