Effect Of Grid Spacing Research Articles

Grid dependence of k–ε model for oscillatory boundary layers

The low Reynolds number k–ε model is used in some commercial hydrodynamic models to determine boundary layer properties. Such models have been found to produce grid-dependent solutions. A reliable engineering estimate of fundamental boundary layer properties is of utmost importance for practicing engineers. Here, the effect of grid spacing in four different versions of the low Reynolds number k–ε model is studied using direct numerical simulation data of a one-dimensional sinusoidal oscillatory boundary layer. A detailed comparison is made for cross-stream velocities, turbulent kinetic energy, bottom shear stress, friction factor and phase difference. For the present data, the limiting value of the distance to the first grid point from the wall is expressed in terms of Stokes layer thickness. It is observed that, in order to predict the boundary layer properties with reasonable accuracy, the first grid point should be placed at a distance of about 0·02 times the Stokes layer thickness from the wall. The results of the present study may be useful for practicing engineers and researchers in their choice of appropriate grid spacing for low Reynolds number k–ε models.

Simulation of the New England Sea Breeze: The Effect of Grid Spacing

Abstract The fifth-generation Pennsylvania State University–National Center for Atmospheric Research (Penn State– NCAR) Mesoscale Model (MM5) was run for seven cases from 2001 in which a sea breeze develops along the eastern New England coast. The results from model runs with 36-, 12-, and 4-km grid spacing are compared with observations as well as output from the National Centers for Environmental Prediction (NCEP) Eta Model on a 40-km grid. As expected, analysis of the individual cases shows that the higher-resolution grids are able to resolve realistic details in the flow, details that the 36-km grids and the 40-km NCEP Eta Model miss entirely. Contrary to expectations, the error statistics show that the ability to forecast specific variables at specific locations does not improve very much when using higher resolution. Even more surprisingly, the 4-km grids produced the biggest errors in forecasting surface dewpoint.

Numerical solution of the linearized Euler equations with high-order centered schemes

The unsteady, linearized Euler equations governing propagation of acoustic disturbances in the presence of a uniform free stream or sound scattering from solid surfaces are solved numerically. The governing equations are discretized in space using the standard fourth- and sixth-order central-difference schemes, and compact finite-difference schemes with spectrallike resolution are also used. The semidiscrete system of equations obtained after space discretization is marched in time using high-order, Runge–Kutta schemes. Numerical boundary conditions are applied at the far field in order to limit the extent of the computational domain. Solutions are computed first on Cartesian, equally spaced grids. Computed results for propagation of a pulse in a uniform medium are compared with existing analytic solutions. Next, sound scattering from a cylinder surface is computed using a nonuniform body-fitted numerical mesh. The effects of grid spacing, time accuracy, the method used for space discretization, and the boundary conditions on the computed solutions are investigated.

COMPUTATIONAL HEAT AND MASS TRANSPORT IN CONCRETE WALLS EXPOSED TO FIRE

A numerical method has been developed for the prediction of coupled heat and mass transfer and related processes in porous media exposed to elevated temperatures. The computer model predictions have been validated against experimental results of carbonate aggregate concrete slabs subjected to the ASTM E119 standard fire exposure. Output from the model depicts the coupled relationships between the temperature, moisture content, and pore pressure histories and distributions. This article investigates the numerical effect of grid spacing on the pore pressure fluctuations and the influence of the pore pressure on the spalling potential of concrete exposed to elevated temperatures.

Electrostatic potentials and electrostatic interaction energies of rat cytochrome b5 and a simulated anion-exchange adsorbent surface

Electrostatic potentials were determined for the soluble tryptic core of rat cytochrome b5 (using a structure derived from homology modeling) and a simulated anion-exchange surface through application of the linearized finite-difference Poisson-Boltzmann equation with the simulation code UHBD. Objectives of this work included determination of the contributions of the various charged groups on the protein surface to electrostatic interactions with a simulated anion-exchange surface as a function of orientation, separation distance, and ionic strength, as well as examining the potential existence of a preferred contact orientation. Electrostatic interaction free energies for the complex of the model protein and the simulated surface were computed using the electrostatics section of UHBD employing a 110(3) grid. An initial coarse grid spacing of 2.0 A was required to obtain correct boundary conditions. The boundary conditions of the coarse grid were used in subsequent focusing steps until the electrostatic interaction free energies were relatively independent of grid spacing (at approximately 0.5 A). Explicit error analyses were performed to determine the effects of grid spacing and other model assumptions on the electrostatic interaction free energies. The computational results reveal the presence of a preferred interaction orientation; the interaction energy between these two entities, of opposite net charge, is repulsive over a range of orientations. The electrostatic interaction free energies appear to be the summation of multiple fractional interactions between the protein and the anion-exchange surface. The simulation results are compared with those of ion-exchange adsorption experiments with site-directed mutants of the recombinant protein. Comparisons of the results from the computational and experimental studies should lead to a better understanding of electrostatic interactions of proteins and charged surfaces.

ITERATIVE TOMOGRAPHIC METHODS TO LOCATE SEISMIC LOW‐VELOCITY ANOMALIES: A MODEL STUDY1

ABSTRACTThe possibilities for reconstructing seismic velocity distributions containing low‐velocity anomalies by iterative tomographic methods are examined studying numerical and analogue 2D model data. The geometrical conditions of the model series were designed to generalize the geometrical characteristics of a typical cross‐hole tomographic field case. Models with high (30%) and low (8%) velocity contrasts were realized. Traveltimes of 2D ultrasonic P‐waves, determined for a dense net of raypaths across each model, form the analogue data set. The numerical data consists of traveltimes calculated along straight raypaths. Additionally, a set of curved‐ray traveltimes was calculated for a smoothed version of the high‐contrast model.The Simultaneous Iterative Reconstruction Technique (SIRT) was chosen from the various tomographic inversion methods. The abilities of this standard procedure are studied using the low‐contrast model data. The investigations concentrate on the resolving power concerning geometry and velocity, and on the effects caused by erroneous data due to noise or a finite time precision. The grid spacing and the source and receiver patterns are modified. Smoothing and slowness constraints were tested. The inversion of high‐contrast analogue model data shows that curved raypaths have to be considered. Hence, a ray‐tracing algorithm using velocity gradients was developed, based on the grid structure of the tomographic inversion. This algorithm is included in the SIRT‐process and the improvements concerning anomaly localization, resolution and velocity reconstruction are demonstrated. Since curved‐ray tomography is time‐consuming compared with straight‐ray SIRT, it is necessary to consider the effects of grid spacing, ray density, slowness constraints and the