Modified method of characteristics for the shallow water equations

Flow in open channels is frequently modelled using the shallow water equations (SWEs) with an up-winded scheme often used for the nonlinear terms in the numerical scheme (Delis et al., 2000; Erduran et al., 2002). This paper presents a mathematical model based on the SWEs to compute one dimensional (1-D) open channel flow. Two techniques have been used for the simulation of the flood wave along streams which are initially dry. The first one uses up-winding applied to the convective acceleration term in the SWEs to overcome the problem of numerical instabilities. This is applied to the integration of the shallow water equations within the domain, so the scheme does not require any special treatment, such as artificial viscosity or front tracking technique, to capture steep gradients in the solution. As in all initial value problems, the main difficulty is the boundaries, the conventional method of characteristics (MOC) can be applied in a straight forward way for a lot of cases, but when dealing with a very shallow initial depths followed by a flood wave, it is not possible to overcome the problem of reflections. So a modified method of characteristics (MMOC) is the second technique that has been developed by the authors to obtain a fully transparent downstream boundary and is the main subject of this paper. The mathematical model which integrates the SWEs using a staggered finite difference scheme within the domain and the MMOC near the boundary has been tested not only by comparing its results with some analytical solutions for both steady and unsteady flow but also by comparing the results obtained with the results of other models such as Abiola et al. (1988)

Method for measuring the characteristics of a gas Patent

Device for simultaneously determining density, velocity, and temperature of streaming ga

A Method for Dynamic Characterization and Response Prediction Using Ground Vibration Test(GVT)Data for Unknown Structures.

The Objective Of This Proposed Work Is To Develop A Reliable Method For Dynamic Characterization And Prediction Of Dynamic Response Of Structures Of Known/Unknown Configurations, By Processing The Free Vibration Data Generated Experimentally From The Ground Vibration Tests (GVT)Of The Prototype Vehicles. The Methodology Would Make Use Of The Measured Dynamic Data In Terms Of Mode Shapes, Natural Frequencies, Modal Damping, Point Impedances Etc.And Generate Modal (Scaled) Stiffness And Inertia Information That Will Be Used For Prediction Of Response Characteristics Of The Prototype Structure . With These Objectives, The Present Work Develops The Mathematical Formulation Of The Method, And Demonstrates Its Reliability By Performing The Experiment On A Simple Cantilever Beam To Determine Its Dynamic Characteristics. Results On Scaled Modal Stiffness And Inertia, Generated Through The Method Using Experimental (GVT) Data Show Excellent Agreement With Those Generated By FE And Analytical Models .It Must Be Noted That A Valid Benchmarking Is Performed With The Condition That The Experimental Procedure Is 'Blind' To The Actual Stiffness And Inertia Distributions As Used In FEM Or Analytical Models . Agreement Of The Predicted Response Of The Structure With That From Direct Experiment And Those From The FE And Analytical Models Indicates That This Method Will Be A Promising Tool To Predict The Dynamic And Aeroelastic Characteristics Of Any Prototype Vehicle In The Future. Once The Reliability Of The Method Is Established,It Can Be Extended To Determine The Dynamic And Aeroelastic Characteristics Of All Aircraft For Which Dynamic Characteristics Are Available From A Ground -; Vibration Test (GVT)

Determination Of Dynamic Characteristics Of Heat Fire Detectors

The proposed methods for determining the dynamic characteristics of heat fire detectors in the time and frequency domains, focused on the use of existing thermal chambers. The proposed method for determining the transition function of the detector is implemented as follows. Heat fire detector creates a thermal effect in the form of a linearly increasing function. The response of the output signal to the influence of this type is measured and approximated using the Heaviside function at regular intervals.It is shown that information on the transition function of a heat fire detector can be used to determine its frequency characteristics by approximating it with Heaviside functions at the same time intervals. This method of determining the frequency characteristics will significantly reduce the time to determine them compared to the classical method, and also eliminate the need for additional equipment.As a result of the studies, the choice of the sampling interval was justified on the example of a class A1 heatfire detector and certain sampling intervals for determining their transition function (τ0≤1.05 s), amplitude-frequency characteristic (τ0≤0.27 s) and phase-frequency characteristic (τ0≤2.0 s).The proposed methods for determining the dynamic characteristics of heat fire detectors open up new opportunities for developing methods for monitoring their technical condition. This is because the information about the transition function of the detector can be used in two ways. The first method involves comparing a certain transition function of the detector with an exemplary one. The second method consists in determining other characteristics of the detector based on information about its transient function and comparing them with standard values

Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation

We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and nonlinear matrix PDE integrable by the method of characteristics as particular reductions. Some other reductions are suggested.Comment: 12 page