scholarly journals Implementation of a synthetic inflow turbulence generator in idealised WRF v3.6.1 large eddy simulations under neutral atmospheric conditions

2021 ◽  
Vol 14 (1) ◽  
pp. 323-336
Author(s):  
Jian Zhong ◽  
Xiaoming Cai ◽  
Zheng-Tong Xie
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Periodic Case ◽  
Atmospheric Conditions ◽  
Mean Velocity ◽  
Large Eddy ◽  
Inflow Turbulence ◽  
Turbulence Generation ◽  
Turbulence Generator

Abstract. A synthetic inflow turbulence generator was implemented in the idealised Weather Research and Forecasting large eddy simulation (WRF-LES v3.6.1) model under neutral atmospheric conditions. This method is based on an exponential correlation function and generates a series of two-dimensional slices of data which are correlated both in space and in time. These data satisfy a spectrum with a near “-5/3” inertial subrange, suggesting its excellent capability for high Reynolds number atmospheric flows. It is more computationally efficient than other synthetic turbulence generation approaches, such as three-dimensional digital filter methods. A WRF-LES simulation with periodic boundary conditions was conducted to provide prior mean profiles of first and second moments of turbulence for the synthetic turbulence generation method, and the results of the periodic case were also used to evaluate the inflow case. The inflow case generated similar turbulence structures to those of the periodic case after a short adjustment distance. The inflow case yielded a mean velocity profile and second-moment profiles that agreed well with those generated using periodic boundary conditions, after a short adjustment distance. For the range of the integral length scales of the inflow turbulence (±40 %), its effect on the mean velocity profiles is negligible, whereas its influence on the second-moment profiles is more visible, in particular for the smallest integral length scales, e.g. those with the friction velocity of less than 4 % error of the reference data at x/H=7. This implementation enables a WRF-LES simulation of a horizontally inhomogeneous case with non-repeated surface land-use patterns and can be extended so as to conduct a multi-scale seamless nesting simulation from a meso-scale domain with a kilometre-scale resolution down to LES domains with metre-scale resolutions.

scholarly journals Implementation of a synthetic inflow turbulence generator in idealised WRF v3.6.1 large eddy simulations under neutral atmospheric conditions

2019 ◽  
Author(s):  
Jian Zhong ◽  
Xiaoming Cai ◽  
Zheng-Tong Xie
Keyword(s):  
Three Dimensional ◽  
Inertial Subrange ◽  
Order Moment ◽  
Periodic Case ◽  
Atmospheric Conditions ◽  
Mean Velocity ◽  
Large Eddy ◽  
Inflow Turbulence ◽  
Turbulence Generation ◽  
Turbulence Generator

Abstract. A synthetic inflow turbulence generator was implemented in the idealised Weather Research and Forecasting large eddy simulation (WRF-LES v3.6.1) model under neutral atmospheric conditions. This method is based on an exponential correlation function, and generates a series of two-dimensional slices of data which are correlated both in space and in time. These data satisfy a spectrum with a near −5/3 inertial subrange, suggesting its excellent capability for high Reynolds number atmospheric flows. It is more computationally efficient than other synthetic turbulence generation approaches, such as three-dimensional digital filter methods. A WRF-LES model with periodic boundary conditions was configured to provide a priori turbulent information for the synthetic turbulence generation method and used as an evaluation for the inflow case. The comparison shows that the inflow case generated similar turbulence structures as these in the periodic case after a short adjustment distance. The inflow case yielded a mean velocity profile in a good agreement with the desired one, and 2nd order moment statistics profiles close to the desired ones after a short distance. For the range of the integral length scale which we tested, its influence on the profiles of the mean velocities is not significant, whereas its influence on the second moment statistics profiles is evident, in particular for very small integral length scales. This implementation can be extended to the WRF-LES simulation of a horizontally inhomogeneous case with non-repeated surface landuse pattern and a multi-scale seamless nesting case from a meso-scale domain with a km-resolution down to LES domains with metre resolutions.

Large eddy simulation of forest canopy flow for wildland fire modeling

2014 ◽  
Vol 44 (12) ◽  
pp. 1534-1544 ◽  
Author(s):  
Eric Mueller ◽  
William Mell ◽  
Albert Simeoni
Keyword(s):  
Large Eddy Simulation ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Forest Canopy ◽  
Wildland Fire ◽  
Periodic Boundary Conditions ◽  
Static Case ◽  
Eddy Simulation ◽  
Turbulent Statistics ◽  
Large Eddy

Large eddy simulation (LES) based computational fluid dynamics (CFD) simulators have obtained increasing attention in the wildland fire research community, as these tools allow the inclusion of important driving physics. However, due to the complexity of the models, individual aspects must be isolated and tested rigorously to ensure meaningful results. As wind is a driving force that can significantly dictate the behavior of a wildfire, the simulation of wind is studied in the context of a particular LES CFD model, the Wildland–urban interface Fire Dynamics Simulator (WFDS). As WFDS has yet to be tested extensively with regard to wind flow within and above forest canopies, a study of its ability to do so is carried out. First, three simulations are conducted using periodic boundary conditions. Two of these assume a spatially heterogeneous forest and one models wind downstream of a canopy edge. Second, two simulations are conducted with specified “inflow” conditions using two inflow profiles: one static and one dynamic (driven by a precursor simulation). Using periodic boundary conditions, the model is found to generate profiles of mean velocity and turbulent statistics that are representative of experimental measurements. The dynamic inflow scenario is found to perform better than the static case.

scholarly journals Correlation functions by separation of variables: the XXX spin chain

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Giuliano Niccoli ◽  
Hao Pei ◽  
Véronique Terras
Keyword(s):  
Integral Representation ◽  
Boundary Conditions ◽  
Thermodynamic Limit ◽  
Correlation Functions ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Periodic Boundary Conditions ◽  
Multiple Integral ◽  
Periodic Case ◽  
Zero Temperature

We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted (quasi-periodic) boundary conditions. We first detail all steps of our method in the case of anti-periodic boundary conditions. The model can be solved in the SoV framework by introducing inhomogeneity parameters. The action of local operators on the eigenstates are then naturally expressed in terms of multiple sums over these inhomogeneity parameters. We explain how to transform these sums over inhomogeneity parameters into multiple contour integrals. Evaluating these multiple integrals by the residues of the poles outside the integration contours, we rewrite this action as a sum involving the roots of the Baxter polynomial plus a contribution of the poles at infinity. We show that the contribution of the poles at infinity vanishes in the thermodynamic limit, and that we recover in this limit for the zero-temperature correlation functions the multiple integral representation that had been previously obtained through the study of the periodic case by Bethe Ansatz or through the study of the infinite volume model by the q-vertex operator approach. We finally show that the method can easily be generalized to the case of a more general non-diagonal twist: the corresponding weights of the different terms for the correlation functions in finite volume are then modified, but we recover in the thermodynamic limit the same multiple integral representation than in the periodic or anti-periodic case, hence proving the independence of the thermodynamic limit of the correlation functions with respect to the particular form of the boundary twist.

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

2019 ◽  
Author(s):  
Pier Paolo Poier ◽  
Louis Lagardere ◽  
Jean-Philip Piquemal ◽  
Frank Jensen
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Force Fields ◽  
Periodic Boundary Conditions ◽  
Computational Effort ◽  
Polarizable Force Fields ◽  
Energy Models ◽  
Capacity Model ◽  
Energy Gradient ◽  
Polarization Models

<div> <div> <div> <p>We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. </p><div> <div> <div> <p>By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p><div><div><div> </div> </div> </div> <p> </p><div> <div> <div> <p>variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p> </div> </div> </div> </div> </div> </div> </div> </div> </div>

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

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