Comparison of DHM Results for One- and Two-Dimensional Flows with Experimental and Numerical Data

In this chapter, the performance of DHM for one- and two-dimensional flows is compared with the results of HEC-RAS, HEC-RAS 2D, WSPG, TUFLOW, Mike 21, and OpenFOAM models. The latter four models are currently widely used in industry, and benchmarking their data with DHM can shed more light on the reliability of DHM. As the results indicate, for applications which do not violate the assumptions made in DHM, the results are in agreement

Examination of Hydrologic Computer Programs DHM and EDHM

The Diffusion Hydrodynamic Model or DHM is a coupled one- and two-dimensional (2-D) surface flow model based upon a diffusion formulation of the well-known Navier–Stokes equations, developed by research hydrologists of the USGS (United States Geological Survey) for use in modeling floodplains and dam-break situations. The Fortran 77 source code and various applications were published in 1987 by the USGS as a Technical Report authored by Hromadka and Yen. The DHM program led to the development of several subsequent computational programs such as the FLO-2D computational model and other similar programs. The original DHM program had a limit of applications to problems with no more than 250 nodes and modeling grids. That limitation was recently removed by a program version named EDHM (Extended DHM), which provides for 9999 nodes and grids. However, the computational code is preserved in order that the baseline code algorithmic procedures are untouched. In this paper, the DHM and EDHM are rigorously compared and examined to identify any variations between the two Fortran codes. It is concluded from this investigation that the two sets of algorithm codes are identical, and outcomes from either program are similar for appropriately sized applications

Computational Vector Mechanics in Atmospheric and Climate Modeling

The mathematical underpinnings of vector analysis are reviewed as they are applied in the development of the ensemble of numeric statements for subsequent matrix solution. With the continued advances in computational power, there is increased interest in the field of atmospheric modelling to decrease the computational scale to a micro‐scale. This interest is partially motivated by the ability to solve large scale matrix systems in the number of occasions to enable a small‐scale time advancement to be approximated in a finite‐difference scheme. Solving entire large scale matrix systems several times a modelling second is now computationally feasible. Hence the motivation to increase computational detail by reducing modelling scale

Reduction of the Diffusion Hydrodynamic Model to Kinematic Routing

In this chapter, the kinematic routing option of the diffusion hydrodynamic model for one-dimensional flows is presented along with the underlying pinning of kinematic flow. The kinematic model results are compared with the full model and K-634 model output data for the mild and steep channel

Diffusion Hydrodynamic Model Theoretical Development

In this chapter, the governing flow equations for one- and two-dimensional unsteady flows that are solved in the diffusion hydrodynamic model (DHM) are presented along with the relevant assumptions. A step-by-step derivation of the simplified equations which are based on continuity and momentum principles are detailed. Characteristic features of the explicit DHM numerical algorithm are discussed

Verification of Diffusion Hydrodynamic Model

The efficacy of the one- and two-dimensional diffusion hydrodynamic model (DHM) for predicting flow characteristics resulting from a dam-break scenario is tested. The model results, for different inflow scenarios, are compared with the standard United States Geological Survey (USGS) K-634 model. The sensitivity of the model results to grid spacing and the chosen time step are presented. The model results are in close agreement

Program Description of the Diffusion Hydrodynamic Model

The numerical algorithm, with a focus on the interface element that is used in the diffusion hydrodynamic model, is presented in this chapter. The source program was written in FORTRAN language, and it can be downloaded from this book companion website. The channel, flood plain, and the interface flow details are discussed

Applications of Diffusion Hydrodynamic Model

The diffusion hydrodynamic model is applied for seven engineering applications that are commonly encountered in real-world applications. Of the seven applications, six relate to two-dimensional flows. The results are compared to other model results, where available. The results underscore the reliability of the DHM along with its limitation for modeling rapidly varying flows

Mathematical Model of Cryospheric Response to Climate Changes

Abstract: This paper focuses on the development of simplified mathematical models of the cryosphere which may be useful in further understanding possible global climate change impacts and in further assessing future impacts captured by global circulation models (GCMs). The mathematical models developed by leveraging the dominating effects of freezing and thawing within the cryosphere to simplify the relevant heat transport equations are tractable to direct solution or numerical modeling. In this paper, the heat forcing function is assumed to be a linear transformation of temperature (assumed to be represented by proxy realizations). The output from the governing mathematical model is total ice volume of the cryosphere. The basic mathematical model provides information as a systems modeling approach that includes sufficient detail to explain ice volume given the estimation of the heat forcing function. A comparison between modeling results in the estimation of ice volume versus ice volume estimates developed from use of proxy data are shown in the demonstration problems presented