Dynamic Wave Equations Research Articles

Potential Dam Breach Flood Assessment with the 2D Diffusion and Full Dynamic Wave Equations Using a Hydrologic Engineering Center-River Analysis System

Dam breaches have catastrophic consequences, causing severe property damage, life loss, and environmental impact. The potential dam breach downstream flooding of the Kulekhani reservoir, Nepal, was studied using a 2D Diffusion Wave Equation (DWE) and Full Dynamic Wave Equation (FDWE) through an open-source solver, Hydrologic Engineering Center-River Analysis System (HEC-RAS). The suitable dam breach model was identified based on the dam geometry and sixteen historical dam failure cases. The simulated downstream peak was tested with an empirical relation, considering reservoir volume and duration of failure. Model comparisons through the flood plain mapping of water depth, flow velocity, flood intensity as per guidelines of the American Society of Civil Engineers (ASCE), and arrival time were carried out for flood hazard assessment. FDWE was able to capture the physical flow phenomena in the river bend resulting in higher flow velocity at the outer bend, lower velocity at the inner bend, and formation of eddies due to the application of the turbulence model, considering possible momentum losses, whereas DWE was unable to capture these effects due to a simplified momentum equation. The total area of flood extension was found to be increased by 30% using FDWE than the DWE due to higher water surface elevation. Most of the towns along the Kulekhani River were classified as “Very High” intensity flood regions according to ASCE, due to the V-shape valley. The peak time difference at the Bagmati River confluence was evaluated between the models. This plays an important role in decision-making for the selection of the flood model to make a safe evacuation plan. The application of FDWE was found to be suitable for the rapidly varying unsteady flow in the steep meandering river.

On the extraction of complex behavior of generalized higher-order nonlinear Boussinesq dynamical wave equation and (1+1)-dimensional Van der Waals gas system

<p>In this paper, we apply the powerful sine-Gordon expansion method (SGEM), along with a computational program, to construct some new traveling wave soliton solutions for two models, including the higher-order nonlinear Boussinesq dynamical wave equation, which is a well-known nonlinear evolution model in mathematical physics, and the (1+1)-dimensional framework of the Van der Waals gas system. This study presents some new complex traveling wave solutions, as well as logarithmic and complex function properties. The 3D and 2D graphical representations of all obtained solutions, unveiling new properties of the considered model are simulated. Additionally, several simulations, including contour surfaces of the results, are performed, and we discuss their physical implications. A comprehensive conclusion is provided at the end of this paper.</p>

A preliminary development of a coupled surface and subsurface flow model for swale system

This study presents the preliminary stage of the development of a conjunctive surface-subsurface model for simulating the flow in a swale. The surface flow is modelled by one-dimensional dynamic wave equation. To improve accuracy, a third-order numerical scheme is used to solve the advection terms in the dynamic wave model. Meanwhile, the subsurface flow is modelled as one-dimensional vertical flow through nondeformable porous media without air compression effect. At preliminary stage, the surface and subsurface model are verified separately. The surface model is verified against the experimental data of surface runoff from a simulated rainfall. The surface model showed promising performance in terms of the reproduction of surface hydrograph. The overall discrepancy between the experimental and numerical model result in the reproduction of the hydrograph discharge is around 14%. For the subsurface flow model, the vertical moisture profile of the soil is verified against Philip’s analytical solution. The moisture profile obtained from the numerical model shows 100% agreement with Philip’s solution.

Coupling dynamic wave equation with land surface model and application to Zhengzhou “720” rainstorm

Coupling dynamic wave equation with land surface model and application to Zhengzhou “720” rainstorm

On the optical soliton structures in the magneto electro-elastic circular rod modeled by nonlinear dynamical longitudinal wave equation

On the optical soliton structures in the magneto electro-elastic circular rod modeled by nonlinear dynamical longitudinal wave equation

Lump interaction phenomena to the nonlinear ill-posed Boussinesq dynamical wave equation

In this manuscript, we discuss the dynamical behavior of ill-posed Boussinesq (IPB) dynamical wave equation. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The different wave structures are extracted by the utilization of Hirota's bilinear method (HBM) and different test function approaches. The wave structures in the forms of novel breather waves, lump solutions, two-wave solutions, and rogue wave solutions are obtained. Furthermore, with assistance of appropriate parameters, the acquired solutions' physical behavior is drawn out in 3 dimensional, and contour profiles. As a consequence of the obtained results, we can claim that the used methodology is simple, dynamic, extremely effective, and will serve as a useful tool for solving more severely nonlinear problems in a variety of domains, most notably ocean and coastal engineering. Additionally, our findings provide an important first step in comprehending the structure and physical behavior of complex structures. We hope that our findings will contribute significantly to our understanding of ocean waves. This work, we believe, is timely and will be of interest to a broad range of professionals involved in ocean engineering models. The obtained results are useful in grasping the fundamental scenarios of nonlinear sciences. With the help of Mathematica, the obtained results are verified by inserting them into the governing equation.

Plenty of wave solutions to the ill-posed Boussinesq dynamic wave equation under shallow water beneath gravity

<abstract><p>This paper applies two computational techniques for constructing novel solitary wave solutions of the ill-posed Boussinesq dynamic wave (IPB) equation. Jacques Hadamard has formulated this model for studying the dynamic behavior of waves in shallow water under gravity. Extended simple equation (ESE) method and novel Riccati expansion (NRE) method have been applied to the investigated model's converted nonlinear ordinary differential equation through the wave transformation. As a result of this research, many solitary wave solutions have been obtained and represented in different figures in two-dimensional, three-dimensional, and density plots. The explanation of the methods used shows their dynamics and effectiveness in dealing with certain nonlinear evolution equations.</p></abstract>

The exponential tracking and disturbance rejection for the nonlinear wave equation via boundary control without any geometrical conditions on the domain

We consider the problem of exponential tracking and disturbance rejection for the nonlinear unstable gradient-dependent wave equation via boundary control without any geometrical conditions on the domain. By splitting the tracking problem into a linear exponentially stable wave equation and a nonlinear dynamical regulator wave equation, we construct an explicit feedback and feedforward boundary controller that involves the reference, the disturbance and the solutions of the two problems. If the controller is applied on the whole boundary and the nonlinearity is globally Lipschitz, then we prove that the wave average tracks a desired reference signal exponentially by using the wave Green's function and the Banach contraction fixed point theorem. If the controller is applied on only a part of the boundary, then the same result is proved for a linear unstable gradient-dependent wave equation, but it is open for the nonlinear wave equation. Furthermore, as a robust analysis, we prove that the change of tracking error continuously depends on the change of disturbance. As usual, the rate of convergence of tracking error is independent of the feedforward part of the controller. A numerical example is given to confirm our theoretical results.

Plenty of analytical and semi-analytical wave solutions of shallow water beneath gravity

This article studies novel soliton wave solutions of the nonlinear fractional ill-posed Boussinesq (NLFIPB) dynamic wave equation by applying the extended Riccati-expansion (ERE) method. Jacques Hadamard has formulated the investigated model to figure out the dynamic characterizations of waves in shallow water under gravity. The obtained solutions are explained through some sketches in 2D and 3D and contour plots. At the same time, the results’ accuracy is checked by comparing the obtained solutions with semi-analytical solutions through the well–known Adomian decomposition (AD) method. The superiority of the ERE method over the original method is explained. All constructed solutions are checked by submitting them back into the original model through Mathematica 12 software.

The linear dynamics of wave functions in causal fermion systems

The dynamics of spinorial wave functions in a causal fermion system is studied. A so-called dynamical wave equation is derived. Its solutions form a Hilbert space, whose scalar product is represented by a conserved surface layer integral. We prove under general assumptions that the initial value problem for the dynamical wave equation admits a unique global solution. Causal Green's operators are constructed and analyzed. Our findings are illustrated in the example of the regularized Minkowski vacuum.

Evaluation of the Sediment Trap Structure Performance in the Saddang Irrigation

Irrigation canals require desilting basin to reduce sediment deposits in the main irrigation canals. The capacity of the Saddang River Irrigation Canal will be increased by 30% to accommodate long-term irrigation discharge needs. To optimize the ability of the desilting basin to trap suspended sediments, an evaluation was carried out using the 2-D finite-volume numerical method for hydrodynamic and sediment transport models. It solves the 2-D dynamic wave equations (the standard depth-averaged St.Venant equations) that are mainly used for river simulation. In addition, the diffusive wave solver is used for watershed runoff simulation and river simulation. The Community Edition SRH-2D model uses a flexible mesh that may contain arbitrarily quadrilateral and triangular cells. A hybrid mesh may achieve the best compromise between solution accuracy and computing demand. The SRH-2D Model solved variables include water surface elevation, water depth, depth averaged velocity, Froude number, and bed shear stress. Sediment Transport Model solved variables include sediment concentration, erosion and deposition, bed elevation, sediment transport rates, bed material D50 size, and bed material gradations. The optimization of the model is useful for improving the lining channel, flushing time period and the performance of the sediment trap.

Optical solitons and closed form solutions to the (3+1)-dimensional resonant Schrödinger dynamical wave equation

This paper investigates the new solitons and closed form solutions to [Formula: see text] dimensional resonant nonlinear Schrödinger equation (RNLSE) that explains the behavior of waves with the effect of group velocity dispersion and resonant nonlinearities in the optical fiber. The soliton solutions in single and combined forms like dark, singular, and dark-singular in mixed form are extracted by means of two innovative integration norms namely extended sinh-Gordon equation expansion and [Formula: see text]-expansion function methods. Moreover, kink and closed form solutions are also observed under different constraint conditions. By choosing the suitable selection of the parameters, three dimensional, two dimensional, and contour plots are sketched. The obtained outcomes show that the applied computational strategies are direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations.

Computational solutions of conformable space-time derivatives dynamical wave equations: Analytical mathematical techniques

In this article, the instigator sets up the profuse traveling wave solutions four types of fractional nonlinear equations in the sense of conformable derivatives by using the novel form of modified mathematical technique. The constructed traveling wave solutions are articulated in terms of trigonometric, hyperbolic and exponential functions. The derived results are fruitful for the physical demonstrations of problems in mathematical physics and engineering.

Performances of the New HEC-RAS Version 5 for 2-D Hydrodynamic-Based Rainfall-Runoff Simulations at Basin Scale: Comparison with a State-of-the Art Model

The Hydrologic Engineering Centre-River Analysis System (HEC-RAS), developed by the US Army Corps of Engineers, is one of the most known, analyzed and used model for flood mapping both in the scientific literature and in practice. In the recently released version (release 5.0.7), the HEC-RAS model has been enriched with novel modules, performing fully 2-D computations based on the 2-D fully dynamic equations as well as the 2-D diffusion wave equations; moreover the application of rainfall to each cell of the two-dimensional domain is now possible. Contrarily to the common applications for flood propagation in river reach, this specific module has never been analyzed in the literature. Therefore, the main purpose of this work is to assess the potential and the capabilities of the 2-D HEC-RAS model in rainfall-runoff simulations at the basin scale, comparing the results obtained using both the options (fully dynamic equations and diffusion wave equations) to the simulations obtained by using a 2-D fully dynamic model developed by the authors for research purposes. Both models have been tested in a small basin in Northern Italy to analyze the differences in terms of discharge hydrographs and flooded areas. The application of a criterion for hazard class mapping has shown significant variations between the two models. These results provide practical indications for the water engineering community in the innovative research field related to the use of 2-D SWEs at the basin scale.

On the optical solitons and local conservation laws of Chen–Lee–Liu dynamical wave equation

In this study, we dealt with the Chen–Lee–Liu equation. This equation models the propagation of soliton flow through optical fibers and other wave-guide mediums. Using the association between Lie point symmetries and local conserved vectors, we extracted some different types of optical soliton solutions of this equation. In addition, we construct the new conservation laws employing the Lie point symmetries of the equation by the approach of Kara and Mahomed.

Refinement of the channel response system by considering time‐varying parameters for flood prediction

AbstractImpulse response functions derived from different types of flood wave equations (simplified shallow water equations) are continuously developed to conduct the linear channel routing (LCR), which is based on the linearized Saint Venant equation and has been widely applied to avoid any possibility of numerical instability. The impulse response function proposed by Dooge, Napiórkowski, and Strupczewski (1987) and derived from the dynamic wave equation with complete force terms has been acknowledged as a classic work to establish a good physical interpretation for the LCR model; however, the flexibility of altering the shape of impulse response still needs to be improved. Based on the concept of this work, this study intends to introduce the time‐varying parameters in the model, so the values of parameters can be adjusted according to the inflow condition, flood stage, and the cross‐sectional shape. Moreover, an integrated routing procedure is proposed to formulate the impulse response function for lateral‐flow inputs and then to connect multiple inputs from subwatersheds or alongside the main channel with the impulse response function of each channel segment to reflect the spatial variation of hydraulic characteristics among different segments. In the discussion of this article, the impulse response function is analysed to show its sensitivity to hydraulic variables with spatial and temporary variations. Flood‐event simulations of a studied watershed are also provided to verify the applicability of the proposed channel routing system.

Perturbed nonlinear Schrödinger dynamical wave equation with Kerr media in nonlinear optics via optical solitons

In this paper, we have presented the analytical analysis of integrable perturbed nonlinear Schrödinger (PNLSE) equation with third-order dispersion (TOD) in Kerr media using our newly proposed technique, extended modified auxiliary equation mapping method. By the implementation of this technique, we have obtained a variety of some new families and more general form of exact traveling wave solutions including triangular-type solutions, periodic and doubly periodic-like solutions, combined soliton-like solutions, kink and anti-kink type soliton-like solutions using three parameters which is the key difference of our newly proposed method. PNLSE is a well-known governing model to study the propagation of optical solitons in nonlinear optical fibers and other telecommunication networks with a type of Kerr law nonlinearity. This particular type of nonlinearity originates when a light wave in an optical fiber is subjected to nonlinear responses. For graphical representation of our newly found results, we have presented them with detailed dynamical physical representation using Mathematica 10.4 to explain in a more efficient manner the behavior of different physical structures of solutions. Also, the computational work and efficiency of the method demonstrate the reliability, straightforwardness, and simplicity of the technique for solving other nonlinear complicated partial differential equations.

Propagation of harmonic waves in a cylindrical rod via generalized Pochhammer-Chree dynamical wave equation

In this manuscript, three novel schemes (Generalized direct algebraic; Improved simple equation and Modified F-expansion methods) are successfully utilized to find the solitary solutions of generalized form of Pochhammer-Chree equation.The concerned wave model has been used in the scrutiny for the propagating of harmonic waves in a cylindrical rod and several problems in fluid mechanics and waves theory in physics. The obtained results have imperative role in the field of the nonlinear science.

Regional Flood Forecasting using SWMM for Urban Catchment

Urban flooding is the inundation of land or property in a designed atmosphere, significantly in additional densely inhabited areas, caused by precipitation overwhelming the capability of drain systems, like storm sewers. Due to expeditious increment and improper urban designing the probabilities of creek, localized or flash urban floods have drastically multiplied. This study explores the application of Storm Water Management Model (SWMM) to densely populated area of Vijayawada city, which is fragmented into 58 sub-catchments. The study area is delineated in SWMM by the assistance of blueprint AutoCAD maps showing drainage network and Reference Level details. From this elaborated elevation data of drain networks, the flow direction has been evaluated to create the descriptive view of the area in SWMM. In this study area 2016, 2017 and 2018 extreme rainfall events of 24 hrs interval is considered for runoff analysis. The focus of the current wok is to model runoff conditions by applying Dynamic wave equation for routing floods and Green-Ampt equation for infiltration in SWMM. The model outputs guided in visualizing the runoff from extreme precipitation events and to analyze the accuracy of the storm water network system.

Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations

In this paper, modified variational iteration algorithm-II is investigated for finding approximate solutions of nonlinear Parabolic equations. Comparisons of the MVIA-II with trigonometric B-spline collocation method, variational iteration method, homotopy perturbation transform method, Adomian decomposition method, and modified variational iteration method are carried out, which show that the proposed algorithm (MVIA-II) is robust one. Some nonlinear Parabolic equations are given to demonstrate the implementation and accuracy of the MVIA-II.