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Title: Implementation of the Immersed Boundary Method in the Weather Research and Forecasting model

Abstract

Accurate simulations of atmospheric boundary layer flow are vital for predicting dispersion of contaminant releases, particularly in densely populated urban regions where first responders must react within minutes and the consequences of forecast errors are potentially disastrous. Current mesoscale models do not account for urban effects, and conversely urban scale models do not account for mesoscale weather features or atmospheric physics. The ultimate goal of this research is to develop and implement an immersed boundary method (IBM) along with a surface roughness parameterization into the mesoscale Weather Research and Forecasting (WRF) model. IBM will be used in WRF to represent the complex boundary conditions imposed by urban landscapes, while still including forcing from regional weather patterns and atmospheric physics. This document details preliminary results of this research, including the details of three distinct implementations of the immersed boundary method. Results for the three methods are presented for the case of a rotation influenced neutral atmospheric boundary layer over flat terrain.

Authors:
 [1]
  1. Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
900883
Report Number(s):
UCRL-TH-226657
TRN: US200711%%628
DOE Contract Number:
W-7405-ENG-48
Resource Type:
Thesis/Dissertation
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; BOUNDARY CONDITIONS; BOUNDARY LAYERS; FORECASTING; IMPLEMENTATION; PHYSICS; ROTATION; ROUGHNESS; SCALE MODELS; WEATHER

Citation Formats

Lundquist, Katherine Ann. Implementation of the Immersed Boundary Method in the Weather Research and Forecasting model. United States: N. p., 2006. Web. doi:10.2172/900883.
Lundquist, Katherine Ann. Implementation of the Immersed Boundary Method in the Weather Research and Forecasting model. United States. doi:10.2172/900883.
Lundquist, Katherine Ann. Sun . "Implementation of the Immersed Boundary Method in the Weather Research and Forecasting model". United States. doi:10.2172/900883. https://www.osti.gov/servlets/purl/900883.
@article{osti_900883,
title = {Implementation of the Immersed Boundary Method in the Weather Research and Forecasting model},
author = {Lundquist, Katherine Ann},
abstractNote = {Accurate simulations of atmospheric boundary layer flow are vital for predicting dispersion of contaminant releases, particularly in densely populated urban regions where first responders must react within minutes and the consequences of forecast errors are potentially disastrous. Current mesoscale models do not account for urban effects, and conversely urban scale models do not account for mesoscale weather features or atmospheric physics. The ultimate goal of this research is to develop and implement an immersed boundary method (IBM) along with a surface roughness parameterization into the mesoscale Weather Research and Forecasting (WRF) model. IBM will be used in WRF to represent the complex boundary conditions imposed by urban landscapes, while still including forcing from regional weather patterns and atmospheric physics. This document details preliminary results of this research, including the details of three distinct implementations of the immersed boundary method. Results for the three methods are presented for the case of a rotation influenced neutral atmospheric boundary layer over flat terrain.},
doi = {10.2172/900883},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 2006},
month = {Sun Jan 01 00:00:00 EST 2006}
}

Thesis/Dissertation:
Other availability
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  • Flow and dispersion processes in urban areas are profoundly influenced by the presence of buildings which divert mean flow, affect surface heating and cooling, and alter the structure of turbulence in the lower atmosphere. Accurate prediction of velocity, temperature, and turbulent kinetic energy fields are necessary for determining the transport and dispersion of scalars. Correct predictions of scalar concentrations are vital in densely populated urban areas where they are used to aid in emergency response planning for accidental or intentional releases of hazardous substances. Traditionally, urban flow simulations have been performed by computational fluid dynamics (CFD) codes which can accommodatemore » the geometric complexity inherent to urban landscapes. In these types of models the grid is aligned with the solid boundaries, and the boundary conditions are applied to the computational nodes coincident with the surface. If the CFD code uses a structured curvilinear mesh, then time-consuming manual manipulation is needed to ensure that the mesh conforms to the solid boundaries while minimizing skewness. If the CFD code uses an unstructured grid, then the solver cannot be optimized for the underlying data structure which takes an irregular form. Unstructured solvers are therefore often slower and more memory intensive than their structured counterparts. Additionally, urban-scale CFD models are often forced at lateral boundaries with idealized flow, neglecting dynamic forcing due to synoptic scale weather patterns. These CFD codes solve the incompressible Navier-Stokes equations and include limited options for representing atmospheric processes such as surface fluxes and moisture. Traditional CFD codes therefore posses several drawbacks, due to the expense of either creating the grid or solving the resulting algebraic system of equations, and due to the idealized boundary conditions and the lack of full atmospheric physics. Meso-scale atmospheric boundary layer simulations, on the other hand, are performed by numerical weather prediction (NWP) codes, which cannot handle the geometry of the urban landscape, but do provide a more complete representation of atmospheric physics. NWP codes typically use structured grids with terrain-following vertical coordinates, include a full suite of atmospheric physics parameterizations, and allow for dynamic synoptic scale lateral forcing through grid nesting. Terrain following grids are unsuitable for urban terrain, as steep terrain gradients cause extreme distortion of the computational cells. In this work, we introduce and develop an immersed boundary method (IBM) to allow the favorable properties of a numerical weather prediction code to be combined with the ability to handle complex terrain. IBM uses a non-conforming structured grid, and allows solid boundaries to pass through the computational cells. As the terrain passes through the mesh in an arbitrary manner, the main goal of the IBM is to apply the boundary condition on the interior of the domain as accurately as possible. With the implementation of the IBM, numerical weather prediction codes can be used to explicitly resolve urban terrain. Heterogeneous urban domains using the IBM can be nested into larger mesoscale domains using a terrain-following coordinate. The larger mesoscale domain provides lateral boundary conditions to the urban domain with the correct forcing, allowing seamless integration between mesoscale and urban scale models. Further discussion of the scope of this project is given by Lundquist et al. [2007]. The current paper describes the implementation of an IBM into the Weather Research and Forecasting (WRF) model, which is an open source numerical weather prediction code. The WRF model solves the non-hydrostatic compressible Navier-Stokes equations, and employs an isobaric terrain-following vertical coordinate. Many types of IB methods have been developed by researchers; a comprehensive review can be found in Mittal and Iaccarino [2005]. To the authors knowledge, this is the first IBM approach that is able to use a pressure-based coordinate. The immersed boundary method presented here uses direct forcing, first suggested by Mohd-Yusof [1997], to impose a no-slip boundary condition. Additionally, the WRF model has been modified to include a no-slip bottom boundary condition enabling direct comparisons with the IBM solution for problems with gently sloping terrain. The accuracy and efficiency of the immersed boundary solver is examined within the context of a two-dimensional Witch of Agnesi hill. Results are also presented for two-dimensional flow over several blocks of New York City, which demonstrate the IB method's ability to handle extremely complex terrain with sharp corners and steep terrain gradients.« less
  • The Weather Research and Forecasting (WRF) Model with the immersed boundary method is an extension of the open-source WRF Model available for wwww.wrf-model.org. The new code modifies the gridding procedure and boundary conditions in the WRF model to improve WRF's ability to simutate the atmosphere in environments with steep terrain and additionally at high-resolutions.
  • Mesoscale models, such as the Weather Research and Forecasting (WRF) model, are increasingly used for high resolution simulations, particularly in complex terrain, but errors associated with terrain-following coordinates degrade the accuracy of the solution. Use of an alternative Cartesian gridding technique, known as an immersed boundary method (IBM), alleviates coordinate transformation errors and eliminates restrictions on terrain slope which currently limit mesoscale models to slowly varying terrain. In this dissertation, an immersed boundary method is developed for use in numerical weather prediction. Use of the method facilitates explicit resolution of complex terrain, even urban terrain, in the WRF mesoscale model.more » First, the errors that arise in the WRF model when complex terrain is present are presented. This is accomplished using a scalar advection test case, and comparing the numerical solution to the analytical solution. Results are presented for different orders of advection schemes, grid resolutions and aspect ratios, as well as various degrees of terrain slope. For comparison, results from the same simulation are presented using the IBM. Both two-dimensional and three-dimensional immersed boundary methods are then described, along with details that are specific to the implementation of IBM in the WRF code. Our IBM is capable of imposing both Dirichlet and Neumann boundary conditions. Additionally, a method for coupling atmospheric physics parameterizations at the immersed boundary is presented, making IB methods much more functional in the context of numerical weather prediction models. The two-dimensional IB method is verified through comparisons of solutions for gentle terrain slopes when using IBM and terrain-following grids. The canonical case of flow over a Witch of Agnesi hill provides validation of the basic no-slip and zero gradient boundary conditions. Specified diurnal heating in a valley, producing anabatic winds, is used to validate the use of flux (non-zero) boundary conditions. This anabatic flow set-up is further coupled to atmospheric physics parameterizations, which calculate surface fluxes, demonstrating that the IBM can be coupled to various land-surface parameterizations in atmospheric models. Additionally, the IB method is extended to three dimensions, using both trilinear and inverse distance weighted interpolations. Results are presented for geostrophic flow over a three-dimensional hill. It is found that while the IB method using trilinear interpolation works well for simple three-dimensional geometries, a more flexible and robust method is needed for extremely complex geometries, as found in three-dimensional urban environments. A second, more flexible, immersed boundary method is devised using inverse distance weighting, and results are compared to the first IBM approach. Additionally, the functionality to nest a domain with resolved complex geometry inside of a parent domain without resolved complex geometry is described. The new IBM approach is used to model urban terrain from Oklahoma City in a one-way nested configuration, where lateral boundary conditions are provided by the parent domain. Finally, the IB method is extended to include wall model parameterizations for rough surfaces. Two possible implementations are presented, one which uses the log law to reconstruct velocities exterior to the solid domain, and one which reconstructs shear stress at the immersed boundary, rather than velocity. These methods are tested on the three-dimensional canonical case of neutral atmospheric boundary layer flow over flat terrain.« less
  • The intensity of use of a mineral is traditionally defined as the consumption (production plus net imports) of the mineral divided by gross national product. It has been proposed that this ratio of raw material input to gross economic output is a predictable function of per capita income and that the relationship is based on economic theory. Through the theory has never been clearly defined, the intensity of use method has been used to make long-term forecasts. This dissertation formulates a theoretical model of the consumption of minerals and the resulting intensity of use, which is used to test themore » validity of the traditional intensity of use measure and its forecasting ability. Previous justifications of the intensity of use hypothesis state that changes in technical efficiency substitution rates among inputs, and demands are explained by per capita income, which, as it grows, produces a regular intensity of use pattern. The model developed in this research shows that the life of the goods in use, foreign trade of raw and final goods, prices, consumer preferences, and technical innovations, as well as the above factors fully explain economic use, which is not simply a function of per capita income.« less
  • This dissertation is concerned with the study and extension of the Integrating Model of the Mid Range Energy Forecasting System (MEFS). The MEFS consists of a family of models which have been utilized since 1974 by the federal government to predict the supply of and demand for a variety of energy products in the United States for up to fifteen years into the future. The Integrating Model combines energy-supply possibilities developed from the system's satellite supply models and energy-demand information developed from an econometric demand model, and solves for a system equilibrium using a sequence of linear programs. This researchmore » is concerned with two important criticisms of the Integrating Model: (1) The market structure employed is questionable. (2) The equilibrating procedure used is not well understood. The original developers of the Integrating Model argue that the system finds a competitive-market solution. However, a study of the mathematical structure of the system indicates that marginal costs are improperly specified for this type of solution. It is demonstrated that marginal costs in excess of those expected for a competitive solution are employed. A study of a two product model using mathematical and graphical analysis reveals that the equilibrating mechanism employed is a variation of the Gauss-Seidel numerical procedure. The rapid convergence commonly experienced in past applications is due to the utilization of large-scale linear programming for the numerical procedure.« less