Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

A case study of the direct radiative effect of biomass burning aerosols on precipitation in the Eastern Amazon

Numerical experiments with the Brazilian additions to the Regional Atmospheric Modeling System were performed with two nested grids (50 and 10 km horizontal resolution, respectively) with and without the effect of biomass burning for 8 different situations for 96 h integrations. Only the direct radiative effect of aerosols is considered. The results were analyzed in large areas encompassing the BR163 road (one of the main areas of deforestation in the Amazon). mainly where most of the burning takes place. The precipitation change due to the direct radiative impact of biomass burning is generally negative (i.e., there is a decrease of precipitation). However, there are a few cases with a positive impact. Two opposite forcing mechanisms were explored: (a) the thermodynamic forcing that is generally negative in the sense that the aerosol tends to stabilize the lower atmosphere and (b) the dynamic impact associated with the low level horizontal pressure gradients produced by the aerosol plumes. In order to understand the non-linear relationship between the two effects, experiments were performed with 4-fold emissions. In these cases, the dynamic effect overcomes the stabilization produced by the radiative forcing and precipitation increase is observed in comparison with the control experiment. This study suggests that. in general, the biomass burning radiative forcing decreases the precipitation. However, very large concentrations of aerosols may lead to an increase of precipitation due to the dynamical forcing associated with the horizontal pressure gradients. (C) 2009 Elsevier B.V. All rights reserved.

Impact of biomass burning aerosols on precipitation in the Amazon: A modeling case study

A study of the potential role of aerosols in modifying clouds and precipitation is presented using a numerical atmospheric model. Measurements of cloud condensation nuclei (CCN) and cloud size distribution properties taken in the southwestern Amazon region during the transition from dry to wet seasons were used as guidelines to define the microphysical parameters for the simulations. Numerical simulations were carried out using the Brazilian Development on Regional Atmospheric Modeling System, and the results presented considerable sensitivity to changes in these parameters. High CCN concentrations, typical of polluted days, were found to result in increases or decreases in total precipitation, depending on the level of pollution used as a reference, showing a complexity that parallels the aerosol-precipitation interaction. Our results show that on the grids evaluated, higher CCN concentrations reduced low-to-moderate rainfall rates and increased high rainfall rates. The principal consequence of the increased pollution was a change from a warm to a cold rain process, which affected the maximum and overall mean accumulated precipitation. Under polluted conditions, cloud cover diminished, allowing greater amounts of solar radiation to reach the surface. Aerosol absorption of radiation in the lower layers of the atmosphere delayed convective evolution but produced higher maximum rainfall rates due to increased instability. In addition, the intensity of the surface sensible heat flux, as well as that of the latent heat flux, was reduced by the lower temperature difference between surface and air, producing greater energy stores at the surface.

A geometric mass-preserving redistancing scheme for the level set function

In this paper we describe and evaluate a geometric mass-preserving redistancing procedure for the level set function on general structured grids. The proposed algorithm is adapted from a recent finite element-based method and preserves the mass by means of a localized mass correction. A salient feature of the scheme is the absence of adjustable parameters. The algorithm is tested in two and three spatial dimensions and compared with the widely used partial differential equation (PDE)-based redistancing method using structured Cartesian grids. Through the use of quantitative error measures of interest in level set methods, we show that the overall performance of the proposed geometric procedure is better than PDE-based reinitialization schemes, since it is more robust with comparable accuracy. We also show that the algorithm is well-suited for the highly stretched curvilinear grids used in CFD simulations. Copyright (C) 2010 John Wiley & Sons, Ltd.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.