A Method to Accelerate Convergence and to Preserve Radiative Energy Balance in Solving the P1 Equation by Iterative Methods

2002 ◽  
Vol 124 (3) ◽  
pp. 580-582 ◽  
Author(s):  
Genong Li and ◽  
Michael F. Modest
Keyword(s):  
Energy Balance ◽  
Boundary Conditions ◽  
Iterative Methods ◽  
Radiative Energy ◽  
The Third ◽  
Iterative Solutions ◽  
Accelerate Convergence ◽  
Acceleration Method

An acceleration method is proposed particularly for the P1 equation. The radiative energy balance is used as a constraint to correct iterative solutions. The method not only accelerates convergence but also preserves the radiative energy balance, the latter being of great importance when radiation calculations are coupled with flow calculations. This acceleration method can be applied to other elliptical problems with boundary conditions of the second and/or the third kind.

A TEST OF THE RADIATIVE ENERGY BALANCE OF THE SHAW MODEL FOR SNOWCOVER

1996 ◽  
Vol 10 (10) ◽  
pp. 1359-1367 ◽  
Author(s):  
G. N. FLERCHINGER ◽  
J. M. BAKER ◽  
E. J. A. SPAANS
Keyword(s):  
Energy Balance ◽  
Radiative Energy

scholarly journals Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110609
Author(s):  
Hossein Talebi Rostami ◽  
Maryam Fallah Najafabadi ◽  
Davood Domiri Ganji
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Variable Properties ◽  
The Third ◽  
Koch Snowflake

This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it.

scholarly journals Evaporation suppression and energy balance of water reservoirs covered with self-assembling floating elements

2018 ◽  
Vol 22 (7) ◽  
pp. 4015-4032 ◽  
Author(s):  
Milad Aminzadeh ◽  
Peter Lehmann ◽  
Dani Or
Keyword(s):  
Energy Balance ◽  
Water Storage ◽  
Climatic Conditions ◽  
Heat Fluxes ◽  
Conservation Strategy ◽  
Radiative Energy ◽  
Water Reservoirs ◽  
Local Climate ◽  
Self Assembling ◽  
Evaporation Suppression

Abstract. The growing pressure on natural freshwater resources and the projected climate variability are expected to increase the need for water storage during rainy periods. Evaporative losses present a challenge for the efficiency of water storage in reservoirs, especially in arid regions with chronic water shortages. Among the available methods for suppressing evaporative losses, self-assembling floating elements offer a simple and scalable solution, especially for small reservoirs. The use of floating elements has often been empirically based; we thus seek a framework for systematic consideration of floating element properties, local climate and reservoir conditions to better predict evaporative loss, energy balance and heat fluxes from covered water reservoirs. We linked the energy balance of the water column with energy considerations of the floating elements. Results suggest significant suppression of evaporative losses from covered reservoirs in which incoming radiative energy is partitioned to sensible and long wave fluxes that reduce latent heat flux and thus increase the Bowen ratio over covered water reservoirs. Model findings were consistent with laboratory-scale observations using an uncovered and covered small basin. The study offers a physically based framework for testing design scenarios in terms of evaporation suppression efficiency for various climatic conditions; it hence strengthens the science in the basis of this important water resource conservation strategy.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

Evaluating and Improving Parameterizations of the Variance of Temperature Fluctuations Over Heterogeneous Landscapes for Surface Boundary Conditions in Atmospheric Models

2021 ◽  
Author(s):  
Tyler Waterman ◽  
Gabriel Katul ◽  
Andy Bragg ◽  
Nathaniel Chaney
Keyword(s):  
Energy Balance ◽  
Boundary Conditions ◽  
Weather Prediction ◽  
Potential Temperature ◽  
Temperature Fluctuations ◽  
Higher Order ◽  
Parameterization Scheme ◽  
Surface Boundary ◽  
Local Energy ◽  
Temperature Variance

<p>The implementation of higher-order turbulence closure schemes in Earth system models (e.g., the Cloud Layers Unified by Binormals; CLUBB) aims to improve the modeling of convection and radiative transfer in numerical weather prediction and climate models. However, the added value of these schemes is constrained by the specification of boundary conditions on higher-order statistics. At the land surface, many of the higher order turbulence statistics that are required as boundary conditions are parameterized using formulations more appropriate for stationary and planar-homogeneous flow in the absence of subsidence. A case in point is the variance of the potential temperature fluctuations.  Because of the additive nature of variances arising from non-uniformity in surface heating, current parameterizations are not readily generalizable. The current scheme used in CLUBB, as well as other models, relies on limited studies over uniform terrain, with the variance entirely determined by local sensible heat flux, friction velocity, and the Obukhov stability parameter without regard to local site characteristics. This presentation aims to address this weakness by leveraging the National Ecological Observation Network (NEON) network of eddy covariance towers to validate the current parameterization scheme for potential temperature variance, as well as propose improvements for more heterogeneous terrain.</p><p>The turbulence fluctuations of temperature at 39 NEON sites are processed and quality controlled, removing points occurring at night, while precipitation is falling, and with sub-zero temperatures. Results overall indicate the current scheme performs well, especially over flat homogeneous terrain where local flux relationships dominate. When there is sufficiently heterogeneous, rough terrain or non-closure of the local energy balance, however, existing schemes fail to accurately estimate the variances in temperature. In these cases, the parameterization needs to be modified, and initial results suggest simple adjustments can yield improvements and reduce error close to that of the uniform sites with local energy balance closure. The successful improvement of the temperature variance parameterization scheme implies high potential for similar, new, empirically derived parameterizations for the surface boundaries for other higher order turbulent statistics (e.g. temperature skewness) in atmospheric turbulence models.</p>

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