Numerical Treatment of a Modified MacCormack Scheme in a Nondimensional Form of the Water Quality Models in a Nonuniform Flow Stream

Two mathematical models are used to simulate water quality in a nonuniform flow stream. The first model is the hydrodynamic model that provides the velocity field and the elevation of water. The second model is the dispersion model that provides the pollutant concentration field. Both models are formulated in one-dimensional equations. The traditional Crank-Nicolson method is also used in the hydrodynamic model. At each step, the flow velocity fields calculated from the first model are the input into the second model as the field data. A modified MacCormack method is subsequently employed in the second model. This paper proposes a simply remarkable alteration to the MacCormack method so as to make it more accurate without any significant loss of computational efficiency. The results obtained indicate that the proposed modified MacCormack scheme does improve the prediction accuracy compared to that of the traditional MacCormack method

THE SIMULATION OF ONE-DIMENSIONAL SHALLOW WATER WAVE EQUATION WITH MACCORMACK SCHEMES

Many practical problems can be modeled using the one-dimensional shallow water wave equation. Therefore, the solution to the one-dimensional shallow water wave equation will be discussed to solve this problem. The research method used was the study of literature related to the shallow water wave equation and its solution method. The one-dimensional shallow water wave equation can be derived from the law of conservation of mass and the law of conservation of momentum. In this study, one of the finite difference methods will be discussed, namely the MacCormack method. The MacCormack method consists of two steps, namely the predictor and corrector steps. The MacCormack method was used to perform numerical simulations of the pond and tsunami models for one-dimensional (1D) shallow water wave equations with flat and non-flat topography. The simulation results showed that the channel's topography could affect the water surface's height and velocity. At the same time, a channel with a non-flat topography had a slower water velocity than the water velocity of a channel with a flat topography

Investigation of radiative interactions in supersonic internal flows

Analyses and numerical procedures are presented to study the radiative interactions of absorbing emitting species in chemically reacting supersonic flow in various ducts. The 2-D time dependent Navier-Stokes equations in conjunction with radiative flux equation are used to study supersonic flows undergoing finite rate chemical reaction in a hydrogen air system. The specific problem considered is the flow of premixed radiating gas between parallel plates. Specific attention was directed toward studying the radiative contribution of H2O, OH, and NO under realistic physical and flow conditions. Results are presented for the radiative flux obtained for different gases and for various combination of these gases. The problem of chemically reacting and radiating flows was solved for the flow of premixed hydrogen-air through a 10 deg compression ramp. Results demonstrate that the radiative interaction increases with an increase in pressure, temperature, amount of participating species, plate spacing, and Mach number. Most of the energy, however, is transferred by convection in the flow direction. In general the results indicate that radiation can have a significant effect on the entire flow field

The Fifth Annual Thermal and Fluids Analysis Workshop

The Fifth Annual Thermal and Fluids Analysis Workshop was held at the Ohio Aerospace Institute, Brook Park, Ohio, cosponsored by NASA Lewis Research Center and the Ohio Aerospace Institute, 16-20 Aug. 1993. The workshop consisted of classes, vendor demonstrations, and paper sessions. The classes and vendor demonstrations provided participants with the information on widely used tools for thermal and fluid analysis. The paper sessions provided a forum for the exchange of information and ideas among thermal and fluids analysts. Paper topics included advances and uses of established thermal and fluids computer codes (such as SINDA and TRASYS) as well as unique modeling techniques and applications

Trans-scale modelling of river morphodynamics

In a river, the local hydraulics, channel form and in-stream vegetation are interdependent. Although water, sediment and vegetation processes interact, they respond individually to flow characteristics at different spatial and temporal scales. This study employs a modelling approach that is based on the tendency of river systems to self-organise and produce emergence (emergent structures) in scale hierarchies. A hierarchical modelling strategy is proposed that arranges separate models describing vegetation and sediment dynamics at their appropriate scales, with their interaction described through feedback between the models. Prediction of the river state at time scales of decades, over a range of spatial scales, is required for ecological river management to be more effective. However, river systems are complex, with complexity rooted deep in the river processes of water, sediment and vegetation holding implications for their modelling. Dealing with complexity in river geomorphological modelling is vital for achieving reliable predictions over decades, especially when considering that small-scale processes must be described to achieve this. Description of small-scale river form is not only required for river habitat management, but also affects the rates at which river form at larger scales changes. Hierarchy and non-linear theory provide a way to deal with the complexity of rivers by separating the river system into parts, and enabling these parts to interact. Appropriate models and modelling methodologies were chosen or developed to represent the effect of interacting river processes of water, sediment and reeds at the progressively nested (largest) reach scale, the channel-type scale and (smallest) geomorphological-unit scale. Existing water flow models at the reach scale and the next largest channel-type scale are used. The reach scale water flow model solves one-dimensional (1-D) Saint-Venant equations whereas the channel-type scale water flow model is governed by twodimensional (2-D) Saint-Venant equations. The water flow model at the smallest organisational level chosen for modelling is the geomorphological-unit scale. Water flow at the geomorphological-unit scale is not based on the actual physics of water flow, but it does account for the smaller scale variability of the water distribution. ix The sediment model at the reach scale employs the Exner equation of sediment continuity in combination with gravel-bed-load transport equations to determine changes in bed elevation. At the channel-type scale, a Cellular Automaton (CA) model describes sediment transport through a river. The CA represents the river as a lattice of cells and predicts the volume of sediment stored in the cells. The sediment distribution obtained from the CA model describes the habitat for reeds. At the geomorphologicalunit scale, a combination of existing formulations is used to predict the dimensions and growth of bed-forms representing sediment dynamics. The vegetation models at the reach scale and the channel-type scale were developed specifically to describe dynamics of common reeds or Phragmites Australis. Reeds were chosen for modelling because of the large role they play as geomorphological modifiers. The reach scale model predicts the distribution of reed populations along the lateral river bank gradient whereas the channel-type scale reed model is a CA model that predicts the expansion of reed patches. The vegetation model at the geomorphological-unit scale is an existing model describing the growth of reeds by integrating finite differential equations of reed biomass growth. River process interactions affect river geomorphology across these organisational levels. The models are integrated to provide feedback within a hierarchical modelling structure. Process models simulating sediment, water and vegetation dynamics within a specific organisational level are coupled through sharing the same spatial scale. Models of the same process producing patterns at various organisational levels are linked to share model information across organisational levels. Trans-organisational modelling linkage allows models to share outputs which provide boundary conditions and values for model parameters at specific locations within the modelling domain. A hierarchical framework allows prediction of small-scale geomorphology and accounts for its variability at the large scale. The modelling strategy is demonstrated by simulations based on hypothetical scenarios of a gravel-bed river. The effect of sediment size and frequency of the flood event moving sediment, together with typical channel geometry, is shown for these. The modelling was computationally very intensive. x Results show that models focusing on only one organisational level can have very different outputs form those produced by trans-organisational modelling. the difference is due to emergence produced by dynamic small-scale processes that manifest at large scales.Emergence was found in changing flow resistance coefficients obtained from smaller scale modelling. The flow resistance affected the river bed elevation at the reach scale. Emergence was indicated by the channel aggrading more for modelling with the inclusion of the effect of smaller scale river process interactions than without it. Thes snall-scale process interactions include water flow affected by bed-forms and reeds. bed-forms and reed affected energy loss significantly and provided a strong coupling between the flow and the river bed elevation. Hierarchical modelling therefore allows for reliable river geomorphology modelling over a decadal time scale by describing river complexity more realisticall

NAS (Numerical Aerodynamic Simulation Program) technical summaries, March 1989 - February 1990

Given here are selected scientific results from the Numerical Aerodynamic Simulation (NAS) Program's third year of operation. During this year, the scientific community was given access to a Cray-2 and a Cray Y-MP supercomputer. Topics covered include flow field analysis of fighter wing configurations, large-scale ocean modeling, the Space Shuttle flow field, advanced computational fluid dynamics (CFD) codes for rotary-wing airloads and performance prediction, turbulence modeling of separated flows, airloads and acoustics of rotorcraft, vortex-induced nonlinearities on submarines, and standing oblique detonation waves

Transonic flow studies

Major emphasis was on the design of shock free airfoils with applications to general aviation. Unsteady flow, transonic flow, and shock wave formation were examined

Aerodynamic Analyses Requiring Advanced Computers, part 2

Papers given at the conference present the results of theoretical research on aerodynamic flow problems requiring the use of advanced computers. Topics discussed include two-dimensional configurations, three-dimensional configurations, transonic aircraft, and the space shuttle

Computation of viscous incompressible flows

Incompressible Navier-Stokes solution methods and their applications to three-dimensional flows are discussed. A brief review of existing methods is given followed by a detailed description of recent progress on development of three-dimensional generalized flow solvers. Emphasis is placed on primitive variable formulations which are most promising and flexible for general three-dimensional computations of viscous incompressible flows. Both steady- and unsteady-solution algorithms and their salient features are discussed. Finally, examples of real world applications of these flow solvers are given

Development of an upwind, finite-volume code with finite-rate chemistry

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques, and a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical, and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data