Prasada Rao

On numerical modeling of overland flow

The reliability of several finite difference numerical formulations for solving one-dimensional kinematic and diffusion wave equations that describe overland flow is investigated. Particular emphasis is placed on two numerical schemes which are second order accurate in space and time, one each from the explicit and implicit families, respectively: the MacCormack and the 4-point implicit schemes. The end numerical solutions are compared to analytical solutions used as benchmark data, and to implicit and explicit schemes widely used to solve the overland flow governing equations. The magnitude of the time step was selected from the CFL stability condition. The algorithms are used to solve two examples, and the results are compared in terms of accuracy and required computational time. In both cases, the results indicate that the MacCormack and 4-point implicit methods are superior in terms of accuracy to the other widely used schemes. The MacCormack and 4-point implicit methods are comparable in accuracy, but the MacCormack algorithm is computationally more efficient.

A parallel RMA2 model for simulating large-scale free surface flows

Abstract In this work, a popular two-dimensional finite element hydrodynamic serial model (RMA2) is ported over to parallel platform using evolving programming paradigms, and its performance tested over both a traditional supercomputer and over a cluster. The parallel code is based on domain decomposition principles and uses MPI protocols for all inter-processor communication. Focus is equally distributed among the performance data and on the accuracy of the end parallel solution. The data structures and kernels available in the portable extensible toolkit for scientific computation (PETSc) libraries have been used in the parallel code formulation. With focus shifting on modeling real life flows, which are characterized by large size domains, the current serial codes are limited by the required computational time. Developing parallel versions of these serial codes, will address this primary limitation without loosing any of the serial modeling audience. The strategy used in this work can aid modelers in developing parallel versions of their serial codes. As the results indicate, one can arrive at the parallel version by using the parallel software libraries, and the serial code need not be rewritten from scratch. Additionally, the format of the input/output data files can be left unchanged. The end parallel code can accelerate the solution to the desired state without loosing any accuracy in the end solution.

Numerical modeling of open channel flows using a multiple grid ENO scheme

In this work, the performance details of a multiple grid ENO scheme for modeling transient one dimensional open channel flows is investigated. The formulation in a multiple grid formulation differs from the conventional algorithm in that, at a constant time period, the equations are solved across different grid levels, so as to facilitate faster propagation of the boundary condition. This results in a faster convergence of the solution to the desired time level. Focus in this paper is split across both testing the accuracy of the end solution and in quantifying the resultant computational savings. Tests conducted for flows with shocks indicate that the solution from current formulation is inline with the theoretical predictions.

A parallel hydrodynamic model for shallow water equations

A parallel implementation of a finite difference model for solving two-dimensional, time-dependent, open channel flows is presented. The algebraic equations resulting from the finite difference discretization of the two dimensional shallow water flow equations are solved by using explicit MacCormack scheme. The parallel code has been implemented on distributed-shared memory system, by using domain decomposition techniques. The message passing interface (MPI) protocols are incorporated for inter processor data communication. The effect of using two different geometry partitions is investigated. A comparison of the wallclock time of the code between these two partitions is made, and code performances with respect to different number of processors are presented.

A multiple domain algorithm for modeling one-dimensional transient contaminant transport flows

Solving numerically the transient one-dimensional advection dispersion equation by using an explicit scheme is limited by the choice of time step size according to the Courant-Friedrich-Levy (CFL) stability condition. For transient simulations over large domains, a small time step would require a very large computational time. To address this issue, we investigate the performance of coupling an explicit solution with a multiple domain methodology for modeling transient phenomena. In this approach, at a constant time period the numerical solution is computed over a series of spatial domains that are characterized by varying grid spacing. This facilitates spreading the effect of the boundary condition across a wider interior domain with reduced computational effort. Emphasis has been equally distributed in testing the effect of this coupling on both the accuracy of the end solution and on the associated computational savings. Two improvements that reflect on the accuracy of the solution are discussed and their performance analyzed. A two-dimensional application is presented in the following paper.

Enhanced TABS-MDS model for simulating large-scale free surface flows

Modeling flows, be it from surface water or ground water, often require using (legacy) serial application codes that have been formulated, strengthened and tested by various audiences over a span of a few years. A limitation in using these serial codes for modeling large-scale transient flows lies in the order of required computational time for completing the simulation. Strategies aimed at addressing this limitation without extensive modifications to the code can further enhance their application without losing any of their current users. In this study, we take an existing popular three-dimensional finite-element hydrodynamic code (TABS-MDS), a product of the U.S. Army Corps of Engineers, and integrate it under the umbrella of an advanced software library: PETSc. The advantage of using the powerful solvers and preconditioners from the software library for solving the end system of equations is illustrated. The results indicate that the choice of the solver combination can have a significant effect on the end computational time. The target audience of this paper are the numerical modelers from a multitude of disciplines who are interested in enhancing the performance of their serial codes.

A multiple domain algorithm for modeling two dimensional contaminant transport flows

To efficiently simulate large scale contaminant transport flows on serial computing platforms, the authors believe that explicit finite difference formulations need to be integrated with performance-enhancing tools. Such integration will not only increase the scope of modeling across various applications but is also aimed at achieving better physical modeling of the transport. In this paper we introduce the application of a multiple domain algorithm (integrated with a finite difference formulation) to solve the two dimensional advection dispersion equation. The efficiency of the abstractions and mechanisms provided by this integration, aimed at accelerating the solution to the desired transient state, is tested. The focus is first in discussing the formulation and then testing its reliability, with and without the integration. To check the latter, we have used an analytical solution as the benchmark solution. The results indicate that the primary purpose of using a multiple domain approach is met without any loss in the accuracy of the solution.

Numerical modeling of open channel flows with moving fronts using a variable boundary formulation

Modeling flows in open channels with explicit family of schemes is constrained by the choice of time step, which is limited by the Courant Friedrichs Lewy stability condition. For simulations over large spatial domains or long time durations, this limitation reflects in increased computational time. To address this limitation, in this work the affect of using varying boundary locations at both the upstream and downstream ends in the numerical code is investigated. The location of the two boundaries in this approach is an evolving function with time and not fixed as in the standard implementations. Such a formulation will aid in solving the flow equations over reduced number of nodes at every time, thus accelerating the solution to the desired state. The performance of this approach for modeling transient and stationary waves for mixed flow conditions is investigated. The results indicate that this approach can significantly accelerate the solution with out affecting its accuracy.

A moving domain formulation for modeling two dimensional open channel transient flows

Numerically solving the two dimensional open channel flow equations over large spatial domains coupled with long time periods using an explicit finite difference scheme is constrained by the required computational time. To overcome this limitation, in this paper the effect of using a moving boundary algorithm on both the accuracy of the transient solution and on the associated computational savings is investigated. While all the reported studies that relate to solving the two dimensional shallow water open channel flows have used fixed domain boundaries, this work differs from them in that the location of the domain boundaries is a function of the time period. The theory underlying the Eulerian school of thought is used for identifying the coordinates of the domain boundaries. The results indicate that for simulations in which the transient solution is required, the present approach can accelerate the solution with out affecting its accuracy.

Evaluation of V and W multiple grid cycles for modeling one and two-dimensional transient free surface flows

This paper presents a new approach for numerically solving a hyperbolic set of equations. This approach addressed to as multiple grid, when integrated with any finite difference formulation aims at accelerating the solution to the desired transient state. It differs from the standard approach in that the solution procedure is iterated across a series of spatial domains. By solving the flow equations on nodes spanned across these domains and then relating the solution methodology to the physics of the flow propagation the focus is to show that this methodology can accelerate the solution to the desired transient state. The manner in which these domains are visited and revisited gives rise to V and W cycles, whose algorithm framework and efficiency for modeling one and two-dimensional transient open channel flows had been investigated herein.