The classical Exner model coupled with a bed-load sediment flux formula is widely used to describe the morphodynamics of coastal environments. However, the main drawbacks of this model are (i) Lack of robustness, (ii) Lack of differentiation between sediment and fluid velocities, and (iii) Generation of instabilities when the interactions between sediment and fluid flow become more important. Moreover, Exner's model does not allow us to know with which characteristic velocity the bottom is moving. This set of drawbacks weakens the effectiveness of most sediment transport models proposed in the literature, particularly the Exner model. In this work, we reformulate the bed-load equation and we propose a new averaged sediment transport model for application in coastal or estuarine environments. The proposed model incorporates phase shift effects into the bed-load equation. The bedform's characteristic velocity, sediment, and fluid velocity are differentiated. We developed a new first-order, well-balanced, positivity-preserving, path-preserving, and central wind (WBPP-PCCU) scheme to solve the proposed hyperbolic sediment transport model (HSTM). We used the Averaging Essentially Non-Oscillatory (AENO) reconstruction coupled with the third-order Runge-Kutta Semi-Implicit (SI-RK3) method to achieve second-order accuracy. The balance and positivity of the water depth properties were proven. In this work, a resonance condition is proposed. The model facilitates the application of several other schemes such as Roe, HLLC, HLLEM, PVM (polynomial viscosity matrix), RVM (rational viscosity matrix), which require the diagonalization of the Jacobian matrix. The accuracy, robustness, positivity preservation, and equilibrium properties of the resulting model are evaluated using a series of carefully selected test cases. The proposed model provides an excellent ability to simulate sediment transport in a wide range of coastal environments.
Accurate modeling and prediction of materials properties is of utmost importance to design engineers. In this study, newly developed two-dimensional laminate constitutive equations (LCE) were derived directly from an existing shell model without using a classical correction factor. The resulted LCEs were subsequently used for the first time to analyze a laminated composite tube (LCT) subjected to in plane-loading. This led to additional composite-shell stiffness coefficients which are not currently available in some LCEs. The strains and stresses distribution fields were computed via Matlab. The accuracy and robustness of our analytical method were proven by opposing the as-obtained results of thick and thin LCTs with that of existing theories which use a correction factor. An excellent convergence was observed. Whereas a lower convergence was observed in the case of a laminated shell plate. Results also showed that the thickness ratio χ (2χ=h/R ) considerably influences the mechanical behavior of the LCT. In fact when χ<0.1, the distribution of stresses and strains of the tube were the same for the two opposed theories. When χ>0.1, the distribution of stresses and strains were not the same, hence the contribution of our ABCDE matrix. The new mechanical couplings in our LCE could be well illustrated in a finite element package with visualization tools to observe some intricate deformations which are yet to be seen. Thus the outcome of this work will be of particularly interest to promote advanced scientific and structural engineering applications.
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