A new composite scheme for two-layer shallow water flows with shocks

This paper is devoted to solve the system of partial differential equations governing the flow of two superposed immiscible layers of shallow water flows. The system contains source terms due to bottom topography, wind stresses, and nonconservative products describing momentum exchange between the layers. The presence of these terms in the flow model forms a nonconservative system which is only conditionally hyperbolic. In addition, two-layer shallow water flows are often accompanied with moving discontinuities and shocks. Developing stable numerical methods for this class of problems presents a challenge in the field of computational hydraulics. To overcome these difficulties, a new composite scheme is proposed. The scheme consists of a time-splitting operator where in the first step the homogeneous system of the governing equations is solved using an approximate Riemann solver. In the second step a finite volume method is used to update the solution. To remove the non-physical oscillations in the vicinity of shocks a nonlinear filter is applied. The method is well-balanced, non-oscillatory and it is suitable for both low and high values of the density ratio between the two layers. Several standard test examples for two-layer shallow water flows are used to verify high accuracy and good resolution properties for smooth and discontinuous solutions.     

Mathematical Development and Verification of a Finite Volume Model for Morphodynamic Flow Applications

The accuracy and efficiency of a class of finite volume methods are investigated for numerical solution of morphodynamic problems in one space dimension. The governing equations consist of two components, namely a hydraulic part described by the shallow water equations and a sediment part described by the Exner equation. Based on different formulations of the morphodynamic equations, we propose a family of three finite volume methods. The numerical fluxes are reconstructed using a modified Roe's scheme that incorporates, in its reconstruction, the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of the source terms. The method is well-balanced, non-oscillatory and suitable for both slow and rapid interactions between hydraulic flow and sediment transport. The obtained results for several morphodynamic problems are considered to be representative, and might be helpful for a fair rating of finite volume solution schemes, particularly in long time computations.     

Baseline subtraction technique in the frequency–wavenumber domain for high sensitivity damage detection

This paper suggests a method for high-sensitivity damage detection. The method is based on pitch-catch measurements of Lamb waves combined with a baseline subtraction technique in the frequency–wavenumber domain. Small amplitude converted modes, generated during the interaction of propagating waves with damage, can thus be detected with minimal a priori information regarding their expected location in the frequency–wavenumber plane. This method is applied in the present paper to a case of notches with varied depth. Finite element simulations are carried out in the temporal domain to mimic results obtainable in real-world experiments. Two cases are studied, namely when each of the two pure fundamental modes are incident on a notch. The advantages of the method are detailed. The procedure to implement this method is described in the context of Structural Health Monitoring (SHM) or Non-Destructive Testing (NDT).     

A two‐dimensional finite volume morphodynamic model on unstructured triangular grids

We discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi‐steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well‐balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed–load in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump‐shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi‐steady approach only when the bed–load rapidly interacts with the hydrodynamics. Copyright © 2009 John Wiley & Sons, Ltd.     

The coupling in transient regime between the modelings of thermal and mass transfers inside a heated room and its radiator

In the present study, a simultaneous modelling, in transient regime and 3D, of the thermal and mass transfers inside a room of habitat (including its internal walls), heated by a hot water radiator, and the thermal and mass transfers inside the heating equipment is carried out. The adopted CFD code, at numerical simulations, is on a macroscopic scale. Comparing numerical values to the experimental quantities showed that the results of the used numerical code are satisfactory.