Numerical Methods for Engineers and Scientists

Hoffman, Joe D.; Frankel, Steven

doi:10.1201/9781315274508

Cited by 234 publications

(284 citation statements)

References 0 publications

Supporting

Mentioning

245

Contrasting

Unclassified

Order By: Relevance

“…Since there are n lines, and each line has four constants, 4n boundary conditions are needed. The boundary conditions are as follows (Hoffman and Frankel, 2001):…”

Section: Interpolation Methodsmentioning

confidence: 99%

Filling missing meteorological data in heating and cooling seasons separately

Anjomshoaa

Salmanzadeh

2018

Intl Journal of Climatology

View full text Add to dashboard Cite

Hourly weather data are needed for building energy calculations; however, many available data from previous years are 3-hr-based. Therefore, appropriate interpolation methods should be employed in order to fill the gaps of the data. In this paper, linear and cubic spline functions are used to interpolate the weather data of Kerman, Iran. Weather data have different behaviours in heating and cooling seasons. Therefore, this paper analyses the interpolation methods in heating and cooling seasons separately. In order to specify all the weather psychrometric characteristics, three independent parameters are required. First, temperature and pressure were taken as two of the parameters. Then, humidity ratio and relative humidity were tested and analysed as the third parameter. Furthermore, the methods of filling weather data gaps were examined in particular to their effects on calculating accurate energy consumption. The results showed that the best interpolation method for each variable depends on the criterion of accuracy. Each method gives the best accuracy for a specific case. However, for temperature and pressure data, cubic splines were more accurate than the linear ones in all cases. For other weather data, it is important to consider the purpose of filling the gaps. The appropriate criterion of accuracy is different according to whether the average or the extreme values of the data are required. For calculation of the energy consumption variables, one interpolation technique should be used for all weather elements; linear interpolation by using relative humidity as the third psychrometric variable yielded better results for this aim. K E Y W O R D Scooling season, heating season, hourly weather data, linear interpolation, missing data, spline functions, temporal gaps

show abstract

“…Since there are n lines, and each line has four constants, 4n boundary conditions are needed. The boundary conditions are as follows (Hoffman and Frankel, 2001):…”

Section: Interpolation Methodsmentioning

confidence: 99%

Filling missing meteorological data in heating and cooling seasons separately

Anjomshoaa

Salmanzadeh

2018

Intl Journal of Climatology

View full text Add to dashboard Cite

show abstract

“…Equation (10) is solved numerically using an implicit backwardtime centered-space approximation, [26] making a balance of the number of colloids N on a uniform grid of positions and orientations. Boundary grid points are a half or quarter of the grid size in the main domain.…”

Section: Nonspherical Colloidal Dynamics With Diffusion and Interactionsmentioning

confidence: 99%

Shape Dependent Colloidal Deposition and Detachment

Torres‐Díaz

Jerri

Benczédi

et al. 2019

Advcd Theory and Sims

View full text Add to dashboard Cite

Models of deposition and detachment dynamics of different shaped anisotropic colloids are reported to understand how equilibrium deposited amounts compare to spherical colloids. For different shaped colloids including spheres, ellipsoids, toroids, and buckled particles with varying aspect ratios, interaction potentials with substrates are computed using the Derjaguin approximation. Using these potentials, the Smoluchowski equation is used to model the dynamics of deposition and detachment versus particle-substrate attraction and aspect ratio for each particle shape. Average times for deposition and detachment and their ratio show steady-state deposited amounts can be enhanced by several orders of magnitude for different particle shapes compared to spherical colloids of the same volume. From a mechanistic standpoint, the present findings indicate how local Gaussian curvature of different particle shapes can lead to stronger adhesive interactions, longer detachment times, and higher deposited amounts compared to spherical colloids, which provides general design rules for controlling and optimizing colloidal deposition.

show abstract

“…Pressure transducer p 1 malfunctioned and is not considered in further analysis. Third-order accurate finite differencing formulas (similar to that used by Suzuki et al [2010]) were used to estimate the pressure gradients, defined as the first derivative located at the center transducer, p 3 , [Hoffman and Frankel, 2001]. The horizontal pore pressure gradient is approximated as:…”

Section: Data Processingmentioning

confidence: 99%

Observations of wave‐induced pore pressure gradients and bed level response on a surf zone sandbar

et al. 2017

View full text Add to dashboard Cite

Horizontal and vertical pressure gradients may be important physical mechanisms contributing to onshore sediment transport beneath steep, near‐breaking waves in the surf zone. A barred beach was constructed in a large‐scale laboratory wave flume with a fixed profile containing a mobile sediment layer on the crest of the sandbar. Horizontal and vertical pore pressure gradients were obtained by finite differences of measurements from an array of pressure transducers buried within the upper several centimeters of the bed. Colocated observations of erosion depth were made during asymmetric wave trials with wave heights between 0.10 and 0.98 m, consistently resulting in onshore sheet flow sediment transport. The pore pressure gradient vector within the bed exhibited temporal rotations during each wave cycle, directed predominantly upward under the trough and then rapidly rotating onshore and downward as the wavefront passed. The magnitude of the pore pressure gradient during each phase of rotation was correlated with local wave steepness and relative depth. Momentary bed failures as deep as 20 grain diameters were coincident with sharp increases in the onshore‐directed pore pressure gradients, but occurred at horizontal pressure gradients less than theoretical critical values for initiation of the motion for compact beds. An expression combining the effects of both horizontal and vertical pore pressure gradients with bed shear stress and soil stability is used to determine that failure of the bed is initiated at nonnegligible values of both forces.

show abstract

Numerical Methods for Engineers and Scientists

Cited by 234 publications

References 0 publications

Filling missing meteorological data in heating and cooling seasons separately

Filling missing meteorological data in heating and cooling seasons separately

Shape Dependent Colloidal Deposition and Detachment

Observations of wave‐induced pore pressure gradients and bed level response on a surf zone sandbar

Contact Info

Product

Resources

About